Entries from ParentsTeachingKids

But when you're talking about young kids, at least, all kids hate it, no matter what their skills. I myself find it quite uncomfortable, once I've understood and solved a problem, to go back and start all over again trying to solve the problem a whole different way--or to work through and understand a different solution offered by the book.

My neighbor and I spent some time trying to figure out why this should be so. Why is doing-it-a-different-way so unpleasant? I think this passage from W.W. Sawyer's Prelude to Mathematics explains it:



I think it's unnatural to throw out the pattern you've just discovered & go off to find a whole new one. It goes against the grain.

I think that's the source of the aversion children, 'weak students,' and adult students like me feel to doing it.

it's not the same thing for us

Around the blogosphere I see an awful lot of complaining about weak students and lazy students and recalcitrant students and students who think their learning style matters.

I'm sympathetic, to a point.

That point is here, asking myself why a 'weak student' would not enjoy having his teacher tell him to 'do it another way.'

I strongly suspect that the practice of doing a problem 'another way'--or simply perceiving that two or more different ways of doing a problem exist--is a different thing for the expert than it is for the novice.

I say this because of my own experience. Slowly, I'm turning myself into what is called, I believe, a talented novice. (I'll check the phrase.)

A talented novice is neither fish nor fowl, neither expert nor beginner.

For that very reason, a talented novice can be a terrific teacher.

As I move into talented novice territory, I find that 'doing a problem more than one way' is becoming a whole different thing. It's starting to be fun. It means making connections--extending the pattern--rather than throwing the pattern out and starting again.

back to school with Steven Pinker

Learning math is hard. Children do not spontaneously see a string of beads as elements in a set, or points on a line as numbers. If you give them a bunch of blocks and tell them to do something together, they will exercise their intuitive psychology for all they're worth, but not necessarily their intuitive sense of number. (The better curricula explicitly point out connections across ways of knowing. Children might be told to do every arithmetic problem three different ways: by counting, by drawing diagrams, and by moving segments along a number line.) And without practice that compiles a halting sequence of steps into a mental reflex, a learner will always be building mathematical structures out of the tiniest nuts and bolts, like the watchmaker who never made subassemblies and had to start from scratch every time he put down a watch to answer the phone.

Yes, he's going to have to do a problem he's already solved all over again, solving it a different way.

BUT I'm asking him to use the same methods he used yesterday & the day before. It's not chaos; there's a predictable pattern to the two or three different ways he's going to solve the problem.

I'm trying to give him a stable structure he can hold onto while he does (and I do) the hard work of learning math.

Multiple Approaches to a Computational Procedure: Flexibility Rooted in Conceptual Understanding

Although proofs and explanations should be rigorous, mathematics is not rigid.... Dowker (1992)asked 44 professional mathematicians to estimate mentally the results of products and quotients of 10 multiplication and division problems involving whole numbers and decimals. The most striking result of her investigation "was the number and variety of specific estimation strategies used by the mathematicians." "The mathematicians tended to use strategies involving the understanding of arithmetical properties and relationships" and "rarely the strategy of 'Proceeding algorithmically.'"

"To solve a problem in multiple ways" is also an attitude of Chinese teachers. For all four topics, they discussed alternative as well as standard approaches. For the topic of subtraction, they described at least three ways of regrouping, including the regrouping of subtrahends. [they also talked about which approach worked best in which situation] For the topic of multidigit multiplication, they mentioned at least two explanations of the algorithm. One teacher showed six ways of lining up the partial products. For the division with fractions topic the Chinese teachers demonstrated at least four ways to prove the standard algorithm and three alternative methods of computation.

For all the arithmetic topics, the Chinese teachers indicated that although a standard algorithm may be used in all cases, it may not be the best method for every case. Applying an algorithm flexibly allows one to get the best solution for a given case. For example, the Chinese teachers pointed out that there are several ways to compute 1 3/4 dividedby 1/2. Using decimals, the distributive law, or other mathematical ideas, all the alternatives were faster and easier than the standard algorithm. Being able to calculate in multiple ways means that one has transcended the formality of an algorithm and reached the essence of the numerical operations--the underlying mathematical ideas and principles. The reason that one problem can be solved in multiple ways is that mathematics does not consist of isolated rules, but connected ideas. Being able to and tending to solve a problem in more than one way, therefore, reveals the ability and the predilection to make connections between and among mathematical areas and topics.

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AnneDwyerOnSingaporeMath 27 Aug 2005 - 00:06 CatherineJohnson


You might want to check out the discussion on teaching things more than one way.

I started by saying that my principle has become 'teach things more than one way.'

Carolyn, Bernie, Chris & others objected.

I have to say that while 'teaching things more than one way' is a core principle for me at this point, whether rightly or wrongly, I don't really know what I mean by that.

In practice, what I've been doing so far is to teach bar models each and every day, along with, each and every day, the standard American 'symbolic' approach. I had Christopher start with the very first word problem in Primary Mathematics Book 3A, which is the first semester of 3rd grade in Singapore, & do one word problem a day, drawing a bar model to illustrate the problem set-up, and then doing the math using the standard algorithms.

And that's it. Each problem takes him a couple of minutes (a little more when he was starting out).

His 'real' math lesson obviously takes a lot longer.

Another example. A couple of days ago a Saxon 8/7 lesson taught two different ways of prime factoring a number. I threw out one of them, and substituted the RUSSIAN MATH approach, which I insisted he learn, almost entirely because when I learned it I found it incredibly fun to do. Christopher ended up liking it as much as I did.

Then yesterday, after Drew & Marc taught Christopher how to subtract-a-fraction-with-borrowing, I forced him to sit with me and watch while I subtracted the same fraction without borrowing, ending up with a whole number and a negative fraction. Then I subtracted the negative fraction from the positive whole number and voila. Fraction subtracted without borrowing.

I didn't make him do the subtraction-problem-without-borrowing himself, but only because he was in a MOOD. If he hadn't been in a MOOD, I would have insisted he do one or two such problems.

Now, I wouldn't insist he practice this approach to mastery, because it's Clunky, and forcing a child to practice Clunky Subtraction would be Wrong. IMHO. It's wrong because math isn't clunky, or shouldn't be.

The only reason I'd insist he work a couple of Clunky Subtraction problems is to make sure he really saw that the reason we borrow or regroup is that regrouping is an elegant, mathematically powerful way to do things--NOT because we can't subtract a bigger number from a smaller number! I know for a fact that a lot of kids think the reason you borrow-or-regroup is that you can't subtract a larger number from a smaller. Well, I don't want Christopher thinking that.

(I actually vividly remember the day, just this year, when my neighbor showed me that YES YOU CAN subtract 17 from 25 without borrowing. She's a statistician, and yet even she was puzzled for a moment when I asked her, 'Why do you have to borrow?')

The point is that I'm feeling my way, basing a lot of what I do on my own experience of relearning math, and on what I read in Liping Ma or see in the PRIMARY MATH series. I have no idea whether & when what I'm doing is a good idea, and whether or when it's a waste of time.

Here is Anne on PRIMARY MATHEMATICS:

I have been studying the Singapore math textbooks and workbooks. This is what Dr. Ma says the math teachers in China do.

When a new topic is introduced for the first time, there is an illustration which visually explains the topic. It is very simple and straight forward and ties into all the other illustrations that have been used in the book. There is usually a short English explanation and an equation if appropriate. For example, in 1B on the topic of comparing numbers: the illustration is comparing the number of stamps. The first illustration has 3 stamps. There is a cartoon of a child saying the number 3. The second illustration has 4 stamps, but 3 of them are exactly the same as in the first picture. The exact same cartoon child is saying the number 4.

Then, there are more illustrations but with all different types of things. For example, when learning about ten and ones, sometimes the illustration is bundles of sticks, sometimes blocks of ten etc.

Finally, there is a set of problems by themselves with no illustration.

Then, the workbook has all different exercises for the same type of problems. For example, Daniel is working on equivalent fractions in 3B. There are about 5 different exercises on this subject, some with illustrations to help and some without.

Since topics are always introduced in the same way with the same type of illustrations, you can tie back to what was learned before.

Additionally, word problems are very uniform also. For subtraction word problems for one, two and three digit numbers, there will always be one that uses the words more than, one that will use how many left, and one that will be how many of one type of thing.

Also, Singapore math introduces the first multistep problems in 2A, but only in the textbook.

So in Singapore math, the student is introduced to the concept first by visual illustration and then the procedure. And he has learned to do problems in several different ways right from the beginning. No one asks him to do the same problem in a different way but different exercises in the workbook show him how to do different problems in different ways for the same concept.

As for Everyday Math...well, I've been studying that too for comparison. I won't bore you with my rantings here. I have just one example that I think sums things up:

In the Everyday Math journal that students use in class, there are pages of Math Boxes that are review. In the first semester second grade, there are 120 Math Box pages with 6 problems on each page.

In one particular box, there was a problem to count back by 5s starting with 45. And there were spaces to put in the numbers. Then underneath is said, "Can you keep going?" And had this: 0, , .

Well, of course, my daughter had left this blank. Her teacher filled it in for her with -5 and -10.

What possible sense does it make to throw in negative numbers in a problem in second grade?

But that is Everyday Math.

fraction subtraction without borrowing

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SusanOnMadMinutes 13 Nov 2005 - 18:34 CatherineJohnson


Susan used Mad Minutes with both kids--

I agree about the "mad minute" approach for all levels of math ability. I used it with both kids and I'm glad I did. It just helps with the speed and proficiency.

Gifted kids are notorious for not wanting to memorize anything. It's too boring. I had to make mine do speed drills all through first and second grade. I'm still doing it with my LD 8th grader.

I remember when math kid was learning multiplication in the first grade. He informed me that it was stupid to memorize them because he could always just count the the groups. I said, "Quick, what's 7 X 8?" His eyes went up looking for those groups, and after a couple of seconds of his looking for them and then trying to skip count by 7, I said, "That's why you memorize them."

I think it helps in the confidence department, as well, to get that speed going earlier than if it just came through practice. And if practice is the key, like "exposure" to lots of words was to the whole language crowd, then what exactly happens to the kids who don't get enough of that practice? Where is the place where enough practice crystalizes into math fact proficiency, especially with these "spiraling" curriculums that keep pushing mastery on down the road?

Trailblazers, as well as other NCTM curriculums, never seem to have a plan for the ones left behind. And I guess you can't ever know who is accountable since mastery was never the goal to begin with.

Interestingly, both kids do love the minute drills where they try to beat their last best score, so I never have any trouble giving them to them.

Well, that's two.

I have to say....I simply can't see any reason on the planet why worksheets would be bad (though TRAILBLAZERS explicitly states that worksheets are destructive!)

Given that there's no (apparent) downside, and given that they've worked for other kids, I'm certainly going to be using them with any child whose math education I'm involved in. (I'm starting to pick up a few! It's incredibly fun. More on that later.)

modifying worksheets

That reminds me.

One of the kids who took my Singapore Math class just could not get through a Saxon work sheet--and he didn't improve any over time, either. All the other kids got fast fast. (It really was remarkable.)

This particular boy is BOUNCY; he is one high-energy kid. He just can't stand the thought of a 5-minute worksheet; he probably takes one look at those sheets and sees what I would see if I were contemplating singlehandedly painting a two-story house.

I told his mom: try having him do ONE LINE of the worksheet as fast as he can.

I don't know if she'll get to it, but when they get back from Italy in January, I think I'll experiment with him, and see how he does. Just click the stop watch and tell him to call 'TIME!' when he hits the end of one line.

I bet that will work.

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FromAroundTheEdusphere 06 Sep 2005 - 04:32 CarolynJohnston


Here and there in the "edusphere" I've seen mention of Professor Plum. He's a fellow educational radical (as I've grown to think of people who favor actual instruction in the classroom), and today I checked out his website.

I learned, among other things, that Direct Instruction actually refers to a very specific method of instruction, and to a commercially available set of curricula. It's not just what happens when I Directly Instruct Ben on how to do a math problem, as I had thought. Professor Plum has a lot of material on it here, if you're curious.

But on a quick perusal, I wasn't attracted to Direct Instruction. I couldn't find what I thought was a sufficiently clear description of what Direct Instruction is about. I learned that it is scripted interaction between teachers and children, and that a great deal of teacher training is needed to implement it properly -- all of which statements I've also seen recently in the Connected Math context. I'd like to see more beef, up front and center.

One of Professor Plum's links also took me here, to a site for parents on how to develop contracts for children that help them achieve academic success. I really like this guy's ideas, which are built around a principle I've been using to good effect around here since Ben was a little toddler, namely bribery. It's not really bribery, of course; it's merely setting up a system of targeted incentives intentionally, rather than accidentally setting up the wrong ones haphazardly. There are lots of good suggestions and examples on this website; a lot of detail of the sort that makes you braver about actually implementing his suggestions.

I also did very much like a recent post of Professor Plum's, entitled Basic Features of Effective Instruction. This post is a gem; it summarizes the features of effective teaching very well, I think (I'd love to know whether KTM teachers agree with me on that!). While reading it, it struck me that I hadn't seen teaching methods of any sort described with such clarity since Ben was very young, and I was working with Applied Behavioral Analysts to implement the Lovaas curriculum, which is designed to treat young autism-spectrum children. There is no tougher customer to teach than a very young autistic child; they are extremely disinclined to pay the teacher any attention at all, and they are often not motivated by the things that motivate typical children (like praise and attention). A teacher can't mess around; her message has to be crystal clear, and her incentives have to be right on. Many of the principles he outlines here are typical-kid versions of those one uses in Applied Behavioral Analysis, to decrease confusion and ineffectiveness (and no surprise either, since he has worked with autism spectrum kids in his career). A terrific post.

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WallStreetJournalSingaporeMath 12 Sep 2005 - 19:32 CatherineJohnson


I'm teaching my little Singapore Math class again this fall, in the Main Street School after-school program. Last year I had one blinding success, a boy who took to the Singapore bar models like a fish to water and decided, apparently as a direct result, that he liked math and wanted to do well in it. He was a Phase 3 kid, now boosted to Phase 4!

So I'm looking foward to it.

(The other kids all did great, too; I don't mean to draw negative comparisons. They just didn't experience major life epiphanies as a result of drawing bar models.)

I was revising my course writeup today, and had to go hunting for the WALL STREET JOURNAL article on Singapore math, which I apparently had neglected to post anywhere on the site. So here's the link.


Excerpts:

Singapore's curriculum was developed over the past few decades by math experts hired by the Ministry of Education, who continually interviewed math teachers to find out what works and where kids need help. The elementary textbooks cover only one-third of the topics typically found in U.S. textbooks, but the material is taught far more thoroughly. While rote learning plays a part, kids in Singapore also learn to use visual tools to understand abstract concepts.

Singapore math texts, for example, ask kids to draw bars and other diagrams to visualize problems -- a technique called "bar modeling." When this strategy is applied consistently over a number of years, children tend to be better able to break down complex problems and do rapid calculations in their head.

[snip]

The National Council of Teachers of Mathematics in the U.S. suggests that it might not be possible to copy what Singapore's done simply by importing its books. The success of its math program may have roots in Singapore's highly disciplined culture, where the entire community -- particularly parents -- expects kids to buckle down and work hard, argues the NCTM.

There's little doubt, though, that math teaching in America needs to be overhauled. Tuesday, Boston College will release a four-year global study that is expected to show the math gap with Asia remains. The college's last study, the 1999 Trends in International Mathematics and Science Study (TIMSS), ranked eighth-graders in Singapore the best in math, while U.S. kids came in 19th, just behind Latvia. American kids also fall further behind the longer they're in school; as fourth-graders, American kids ranked 7th on the 1995 study.

That decline has already had an impact on U.S. universities.

today's horror factoids:

• Among U.S. freshmen who plan to major in science or engineering, one in

five requires remedial math courses

• Enrollment by U.S. citizens or permanent residents in graduate science and engineering programs, meantime,

dropped 10 percent between 1994 and 2001. Enrollment of foreign students grew 35 percent.


another link to the WSJ article: As math skills slip, U.S. schools seek answers from Asia


key words: decline in U.S. engineering math and science enrollment

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InnumeracyPart2 13 Nov 2005 - 19:59 CatherineJohnson


A section of the innumeracy article Carolyn linked to caught my eye:

Wieman says getting students comfortable with math as a way of describing the natural world is a nut he has had trouble cracking. He said methods such as those developed by his Physics Education Technology program can give students without science backgrounds a deep understanding of scientific concepts, "yet when something involves a simple arithmetic calculation, their brains click into this totally different mode."

Steven Pollack, a CU physics professor whose research focus is improving the education of physicists, says the problem also happens in reverse. Physics students often can't conceptualize or explain the results of the equations they so breezily manipulate.

This is something I've been wondering about.

This may sound crazy, but, as a kid, I was reasonably good at math. I got straight A's, I had no trouble learning whatever I was supposed to learn (my one bad moment, in 2nd grade, WHICH I REMEMBER TO THIS DAY, involved--guess what?--fractions).

I took my SATs cold, with no practice, a year after I'd looked at my last math book and got a 620, which put me way up in the top percentile of the nation's 17 year olds at the time. (IIRC, I may have been in the top 95th percentile for girls.)

So....I was reasonably good at math.

That's why when Christopher came home with his 39 on Unit 6 it never crossed my mind I couldn't simply sit down and teach him what he'd missed.

no can do

You all know the end of that story. I discovered I knew practically NOTHING about math.....which is an exaggeration, but is sure the way I felt. I've been obsessively re-teaching myself elementary mathematics ever since, and intend to go on to trig & calculus & and a bit beyond.

So what does it mean to say that I was 'reasonably good' at math?

It means I could set up two-variable algebra problems and solve them in a jif. Thirty years later, I could still do it. Easily.

But I had no idea why setting up two equations (or 3 or 4) worked.

This is why I'm such a fan of the Singapore Math bar models (one of the reasons); it was a bar model that first explained to me what subtraction really meant.

the difference between two numbers

I had a Helen-Keller-at-the-water-pump moment the first time I drew this bar model. I had simply never noticed that the 'number' of boys and girls in Mrs. Johnston's class, up to the number 10, is the same number. The 'extra' five boys are the difference.

For my entire life I had heard the word 'difference' used to name the number you end up with when you subtract one number from another, but I had never, ever realized that 'difference' actually did mean difference. It wasn't just some random word that had gotten attached to the operation somewhere back in the mists of time.

I now point this out to any kids I teach--and they all seem to find it extremely cool, too. I say, and then I repeat frequently, Subtraction is finding the DIFFERENCE between two numbers.

Then I point out that, if you're subtracting 3 from 5, 3 and 5 are the same number until you get past the 3-that-is-inside-the-5.

quick question re: number partition theory

The article on Everyday Math that I linked to yesterday, Weighing the Factors says this is number partition theory.

Is it?

odd man out

Teaching the how-many-boys-and-girls problem to kids, I also point out what would happen in Mrs. Johnston's class if you paired each girl with a boy.

You would have five boys left over.

That seems to make enormous sense to grade school kids, perhaps because they spend their grade school years being assigned partners or buddies to walk in lines with, or go to the bathroom with, etc.

This is obviously the way to teach the concept of even and odd, too. If you have an odd number of kids, there's going to be one child left over when you assign them to teams.

AND this image works great for teaching the idea that you always get an even sum if you add two even numbers or two odd numbers, but you get an odd sum if you add an even & an odd. In my experience so far, kids can instantly see that, when you add two odd numbers, you get two 'odd men out'--and now those two finally have a partner!

why don't numbers & concepts connect more easily?

This brings me back to my original point: somehow, you can learn numerical manipulations, including more advanced numerical manipulations that require you to set up equations and solve them, and not have a clue what it all means.

I don't understand this.

I don't understand how I could have so much fun setting up equations & solving them, and never gain the slightest idea why what I was doing worked.


keywords: conceptual understanding & bar model difference between two numbers comparison of numbers subtraction as comparison subtraction has two meanings


partial product division in Everyday Math
fighting innumeracy at CO
subtraction as the difference between 2 numbers
study sheet: subtracting integers & absolute value
notes on integer, subtraction, & absolute value study sheet

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WilliamKSmithCalculus 16 Sep 2005 - 12:16 CatherineJohnson


Here's another recommendation from Barry Garelick:

Calculus with Analytic Geometry by William K. Smith (also available at Amazon)

I've already ordered my copy.

Have I mentioned I'm planning to take calculus?

Well, I am. I'm planning to take calculus.

But first I have to 're-take' algebra & geometry. Then trig, which I've never studied.

You folks here at ktm are helping me so much. Even though I'm a writer, I can't locate the words to describe what you've given me. The reason I can't 'locate the words,' of course, is that I don't actually know what I'm learning from ktm. I study & absorb what people say, but then forget the source of my new knowledge once it's been assimilated into my store of old knowledge. I'm left with the hazy feeling that 'I'm learning a huge amount from the Commenters at ktm.'

So I'm going to start taking notes. God is in the details.

thank you!

integers! integers!

So Christopher's math class started integers on Monday—a topic he knows virtually nothing about—and he's having a test tomorrow. He is way not prepared, so I'm busy today writing an Integer Lesson. Probably won't be posting much (though I may have a couple of things from Barry.)

I'm taking a moment to make one more plug for Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa, though.

I could probably add & subtract integers in my sleep. (Though I did have to do some review last year when I first re-encountered the topic, which I take as a sign that my knowledge was more procedural than conceptual.)

But last night, after working with Christopher for awhile, who was semi-lost (I don't think he could pass a test at this point) the Math Fog rolled in.

This is the good thing about working with people who know less math than you do. Concepts and procedures you thought you understood turn out to be not quite so clear. I assume that's what Bernie meant when he said the other day that he'd realized there were aspects of reciprocals he hadn't thought about (if I've got that wrong, Bernie, I'll change it!) Carolyn has said something similar at times. I'll be asking her about some elementary concept that, for her, is as simple as breathing in and out, and suddenly she'll see why Ben--or anyone else--might get confused.

lost in translation

This is another one of those constructivist insights that's been lost in translation.

For me, and I think for most teachers & writers, teaching or writing about a subject always forces you to understand it far better than you did.

Radical constructivists conclude from this that children should explain all of their answers in words.

I'm pretty sure that's wrong, because math is not language. Math is math. A child who can explain his answer by showing the mathematical steps he took to find it has produced a proper mathematical explanation as far as I'm concerned. (Russian Math & the Chinese teachers in Liping Ma all offer mathematical explanations & demonstrations.)

But what really bothers me about the 'explain your answer in words' business is that it puts the onus on the child to teach himself. The teacher doesn't have to work and fight and struggle to find the right words; the child does. I know that's wrong.

While I'm on the subject, why don't I just go ahead and take umbrage at the suggestion that a child is capable of explaining math in words?

Writing is hard. Writing well is extremely hard. Finding the words to explain any mathematical concept well is a vast and ambitious undertaking in itself, not a toss-off in the middle of a homework assignment or state assessment. (I'm seriously against the extended response (pdf file)requirement that's taken over IL state rubrics. At least, for the time being I am. [update 5-14-06 sorry, link no longer works])

back to Russian Math

I shouldn't be putting words in people's mouths, so if I've misunderstood Bernie or Carolyn I'll issue a CORRECTION.

In the meantime, why don't I just return to quoting myself.

It's true for me that when I work with a child for awhile, I realize I don't understand things as well as I thought (or hoped).

After Christopher went to bed, I got out Mathematics 6 and turned to the section on adding & subtracting integers.

The first thing that struck me was the fact that this topic appears at the very end of the book. Prentice Hall Pre -Algebra^* opens with integers, and I question that. I question it not based on any profound grasp of pre-algebra as a coherent whole. I question it on grounds that Nurk & Telgmaa are geniuses, and they put adding & subtracting integers last, not first.

I'm sure they have their reasons. (I intend to figure out what their reasons were.)

Reading through Nurk & Telgmaa's discussion, I realized why I was confused. I think I realized why Christopher was confused, too. I hope so.

We were both, I believe, stumbling over this type of problem:

5 - (-7) = ?

Both Saxon Math 8/7 & Russian Math teach addition & subtraction of integers using the number line. Saxon's lessons were particularly strong, I thought.

But when I tried to untangle myself by resorting to the number line, I got stuck.

Start at zero, move five to the right, then.......then what?

What was my next move? My very next move, without renaming or re-expressing - (- 7) as + 7 ?

I was stuck.

Reading through Mathematics 6 I realized that the problem is something Wayne Wickelgren & his daughter Ingrid have raised: the same letter or sign has been made to stand for two different things.

There are two 'minus signs' in 5 - (-7). One means 'opposite,' and the other means 'subtract.'

One means 'perform an operation' and the other doesn't (I don't think. Is 'taking the opposite of a number' considered an operation? I don't know.)

In any case, for both Christopher and me, 'subtract' and 'take the opposite of' are two different things.

Mathematics 6 has a formal demonstration of the fact that:

5 - 7 = 5 + ( -7 )

This is something I think I figured out on my own many, many years ago. I've been using it ever since to de-confuse myself when dealing with long lines of integers to add & subtract. At some point, if I'm getting confused about whether I can or can't use the commutative or associative properties, I just turn the whole thing into addition.

Reading Mathematics 6 I realized that's what needed to happen with 5 - ( -7):

5 - ( - 7) = 5 + [ - ( - 7) ]

Voila!

Christopher and I both understand that 'the opposite of the opposite' is the number you started with originally; the opposite of the opposite of 7 is 7. (This wasn't an especially hard idea for Christopher, but the number line really nails it down.)

Once you convert '5 minus negative 7' to '5 + the opposite of the opposite of 7' it's in a form Christopher understands, and can do.

AND it's in a form you can perform on the number line, if you like or just want to check.

5 - ( - 7) =

5 + [ - ( - 7) ] =

5 + [ 7 ] =

5 + 7

Once you've converted a 'double negative' subtraction problem into addition, you no longer have an anomaly, The One Subtraction Problem That Cannot Be Done On A Number Line.


We'll see how it goes. This morning I had Christopher quickly rewrite 12 subtraction problems as addition problems. (I haven't explained to him why a subtraction problem can be rewritten as an addition problem, and I don't know whether I'll get to that today. I haven't closely studied Mathematics 6's presentation to see whether I can introduce it 18 hours before the test.

Fortunately, Ed had already introduced the idea that 'subtraction is addition' last night, when he used the addition-of-debt-to-debt (a concept that is not foreign to our household) to show Christopher that:

- 7 - 7 = - 14

I think he had a lesson in Saxon on subtracting a positive from a negative being the same thing as adding a negative to a negative, so he probably had some knowledge to build on before Ed gave him the add-one-debt-to-another example.

It's the minus-minus issue that's throwing him.

I hope.

one last thing

Looking at this, it strikes me I'm also going to have to create some problems that I ask Christopher to 'simplify'—'simplify' defined broadly as 'write it in the simplest possible correct way that will allow you to recognize what the computation is and do it.'

For instance:

-7 + 5

He probably needs some practice rewriting this as 5 - 7.

I'll see.

I'm also going to try to put together an incredibly simple 2 - 1 type problem that he can always solve quickly when he gets jumbled up. Something like this:

1 - ( - 1) = 2

-1 -1 = -2

-1 - ( - 1 ) = 0

He hasn't learned the Polya line about how 'For each complicated problem you can't do, there is a simple problem you also can't do.' I realize it's not clear that you can explicitly teach problem solving, but I'm going to have to try. He's got to learn the strategy of creating a super-simple version of a hard problem in order to see how to deal with the hard problem SOON.






^*new title: Prentice Hall Mathematics: Explorations & Applications

keywords: subtraction negative minus absolute value subtraction is addition integers extended response

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TeachingSubtractionAndIntegers 18 Sep 2005 - 02:42 CatherineJohnson


click on Printable Version to print


What is subtraction?

Subtraction is the ______________ of addition.


When you subtract, you __________ ___________ ___________________ of the number you are subtracting.


An absolute value is always _________________.


1 - 2 = _________

1 - ( - 2 ) = _________

-1 - 2 = _________

-1 + -2 = _________

1 - | 2 | = _________

-1 - | 2 | = _________

-1 - | -2 | = _________


answers
study sheet for class quiz on pages 2 - 16, Prentice Hall Mathematics: Explorations & Applications & Prentice Hall Pre -Algebra

outloud sheets: integers & absolute value
answer key
notes on outloud sheets for integers & absolute values
Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

---

PracticeSheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:38 CatherineJohnson


I wrote up a study sheet for Christopher's test (it's in the next post) & dragged him through it kicking and screaming.

I think it worked, but we'll see.


If you hit 'Printable Version' it prints out great, exactly enough space for answers in big, round middle-school handwriting.

update

Christopher said last night he doesn't like it when I tell people he screams when we do math.

I told him, Stop screaming and I'll be happy to stop telling people.

We are at an impasse.

---

StudySheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:45 CatherineJohnson


(study sheet is here: subtracting integers & absolute value)


Here is how Christopher does this problem:

-1 - ( - 2 )


He pencils in a vertical line across both of the minus signs in the middle, turning them into plus signs:

- 1 + ( + 2 ) =


That works for him every time, no matter what the numbers, and he isn't thrown off by the same problem written with an absolute value:

-1 - | - 2 | =


This reminds me of Carolyn's belief that you need to get math into a child's hand.


For some reason a problem like:

-1 - 2

makes sense to him. He 'sees' that he's adding two negative numbers.

Here, too, however, he does a swoop and swoop thing: he squeezes in a plus sign between the 1 and the second minus sign, like this:

-1+-2 =

Ed's explanation to Christopher that you can think of -1 - 2 as adding two debts -- first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3 -- seems to have been the ticket.

I tried that explanation on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!


From one of Carolyn's first posts:

That's what the standard algorithms are: they are moves that you learn how to make. Those moves get into your fingers, just like learning the piano or the violin or typing, and eventually you can do them completely mindlessly.


swoop and swoop
the craft of math
subtraction as the difference between 2 numbers
outloud study sheet: subtracting integers & absolute value
answer key
notes on integer, subtraction, & absolute value study sheet
Carolyn on introducing absolute value

keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

---

ILikeMathPart3 17 Sep 2005 - 02:47 CatherineJohnson


I almost forgot!

Monday or Tuesday night, when Christopher was doing one of his first homework assignments from Prentice Hall Mathematics: Explorations & Applications, he saw an illustration on the side of the page with the caption:

The early Egypticans drew pairs of legs walking in different directions to stand for addition and subtraction.

He looked up at me and said happily, "I like math. I just don't like math when you make me do it."


BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
fun with Saxon Math in the summer
SundaySchool
I like math
I like math, part 2
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids
Christopher on his 39
I like math, part 3

---

PrenticeHallPreAlgebraQuestion 21 Sep 2005 - 10:24 CatherineJohnson


Well, Christopher managed an 85 on his first math quiz.....but we're gonna need to step up the pace around here.

Ed checked his homework tonight, which prompted vast quantities of screaming and yelling (maybe there's something to that brain periodization business after all), and now reports that Christopher has essentially zero comprehension of how to solve a story problem involving negative numbers. He's just looking at the problem and trying to figure out which operations to do. Ed says he's more or less guessing.

The good news is he got points off for mechanics, failing to put in the degree sign and the like. He would have had an 89 if he'd LABELED EVERYTHING CORRECTLY. So from now on he will label everything correctly.

The bad news is that the teacher is doing what she did last year, which is putting problems on the test they've never done before or even seen in class or on homework. He had two story problems like this one:

The boiling point of oxygen is -297 and the boiling point of nitrogen is -320. How much higher is the boiling point of oxygen?

Here's my question.

Distance, I know, is always expressed as an absolute value.

Is 'distance' on a thermometer the same thing?

Say the question had been written as, How much lower is the boiling point of nitrogen than the boiling point of oxygen?

Would the answer still be 23?

anyone know of a good source of story problems?

To get Christopher through this course, I'm going to need two things:

• LOTS of practice computation problems (integers, fractions, the works)
• LOTS of practice word problems

Does anyone know of good supplies of either?

I am also going to need vast supplies of Iron Will.

teach kids good handwriting in school

Christopher's handwriting was so bad in Kindergarten that his teacher told us he was considered 'at risk' for dyslexia. (Kids with learning disabilities often (usually?) have bad handwriting.)

That was one of those four-star fun-with-childbearing moments. Two autistic kids, and this one's gonna be dyslexic!

Ed pooh-poohed the whole thing (he is the pooh-pooher in the family), and in fact Christopher began reading on his own literally 2 weeks later (THANK YOU, GOD).....and that was the last any of his teachers had to say about handwriting until he had Ms. Duque in 5th grade last year.

So tonight he missed at least one problem on his homework because his handwriting is still so bad he can't read it himself. His test is a mess; I don't know how he managed to do as well as he did given what a visual morass it is.

Two summers ago I researched handwriting programs, and we spent one summer working on handwriting....and then Ms. Duque pushed him on it last year, though she didn't teach it. When my parents went to school, handwriting was taught in formal handwriting-practice programs that worked. (Ever noticed that ALL members of the greatest generation have beautiful handwriting?)

Today there are schools on Long Island that don't even teach cursive anymore, or maybe it's the other way around.

Anyway, handwriting is one of those ROTE NON-CONCEPTUAL NON-CRITICAL-THINKING SKILLS that have been drop-kicked right out of the curriculum. Replaced by character education. Last year the school spent 20 minutes each and every morning for six months doing their No Put Downs program. This year the program's even bigger as far as I can tell. The teachers are all being trained, and one of Christopher's teachers told us on back-to-school night that, thanks to all the character education she would be doing during class time, 'your children will be better people.' [update: This teacher was Mrs. R. 3-25-2006]

The point is, if Christopher is going to speed through these tests, he's going to have to develop fluency not just in math facts & computation, but in handwriting, too.

Well, at least he had those couple of months with me. I have a couple of cursive practice books sitting in his homework file, so maybe I'll pull those out and get started again. One more thing to brawl over.

I feel a rant about character education coming on.

That stuff I just wrote?

That wasn't it.


keywords: character education bullying no putdowns


keywords: good handwriting Write Now

---

MathLessonRepeatingDecimals 22 Sep 2005 - 20:01 CatherineJohnson




My neighbor showed me this yesterday. Naturally no one had ever taught me how to do this, which is par for the course. But she's a statistician & she'd never learned it, either.

I love this. It reminds me of the shenanigans I go through trying to force Microsoft Word to do graphic design.






I've entered this on the Math Lessons page.


other resources

Purple Math

Math Wizz on converting repeating decimal to fraction




update: Saxon meltdown (3-2-06)

Maybe I'm just tired, but I practically had a nervous breakdown tonight trying to convert 0.013333....(repeating decimal) to a fraction.

I just could not get it.

Finally Math Wizz saved me. Of all the websites I looked at, Math Wizz had the simplest, cleanest, & most follow-able explanation.

Math Wizz also has gigantic gifs.

---

LoneRangerOnHandwriting 21 Sep 2005 - 19:49 CatherineJohnson


I'm bringing Lone Ranger's advice on handwriting up front, because it's important.

For one thing, there's research showing teachers give higher grades to papers with good handwriting, whether they're supposed to or not. That makes sense. Any teacher who's spent more than 5 seconds in the classroom will have noticed that children with learning disabilities aren't the ones with the nice, neat handwriting.

Personal anecdote pause: Ed was giving me some grief about my handwriting lessons with Christopher. He thought they were silly. Everyone thinks they're silly.

So then we had a birthday party for Christopher, and one of the kids we invited was a boy who was in the multisensory class, considered 'at risk' for LD, etc.....the handwriting on his birthday card was so erratic and wild it was almost scary. And.....it didn't look all that majorly different from Christopher's handwriting.

Ed took one look at that birthday card next to all the other kids' birthday cards and got with the program.

(He has horrific handwriting himself, btw. He's a leftie.)

Back on topic: the other reason kids need good handwriting is the same reason they need good-everything: they need automaticity. Again, there's RESEARCH SHOWING that kids with good handwriting produce better content in writing essays. (I'm not going to look it up; you'll just have to trust me.)

Kids need to be able to write legibly and quickly.

Last but not least, this is another one of those curriculum decisions that I'm betting favors girls. Every boy I know has had handwriting woes; Christopher's handwriting was so bad he was being pulled out of Kindergarten for free O.T. services.

My understanding is that girls have better fine motor skills.....I could be wrong, but that's my impression.


Here is Lone Ranger:

To remediate handwriting buy some handwriting paper with a dotted center line. Miller Pads and Paper sells some for upper elementary aged kids and it is great stuff. www.millerpadsandpaper.com Now teach him two things. First, all his letters must basically be the same width (there are some exceptions here). Second, all letters must bump the top and bottom lines. Lower case would bump the dotted center line and the base. Upper case and numbers would bump the top and bottom lines. (For some reason kids like the expression "bump the lines") Have him practice on this paper until this new skill is internalized. He will see instant improvement and that is usually quite encouraging. Good luck!

update

I was Googling around, trying to find the terrific penmanship-paper software I had for my PC, and I found this instead: SpellWrite Books 1-4

It's a spelling and handwriting program from Oxford that sounds terrific. I've never seen it, obviously, but I like the idea, and I generally like Oxford Press. Offhand, and knowing next to nothing about the teaching of reading, writing, & spelling (now there's a caveat for you), I like the approach:

SpellWrite is a series of four workbooks for middle and upper primary that assist students to develop their spelling skills. It focuses on the four forms of spelling knowledge: Phonological, Morphological, Visual, and Etymological.

Features:
• Spelling is presented as an integral part of the writing process
• 25 units of three pages designed to provide a full week’s work for students
• Each book in the series includes: Words to Learn, Assessment for the appropriate year, Rhymes to read, Word Bank, Test pages, Revision units, and teacher ideas and suggestions for each activity
• Each unit begins with a rhyme, tongue twister, or word game designed to introduce the relevant sound and excite the children’s interest in words
• Allows teachers to explicitly and systematically teach students the four forms of spelling knowledge
• Covers a variety of text types with a focus on rhyme and poetry.

The books cost $12 apiece. I'm almost tempted to get one, just to see if I can kill two birds with one hand.

I love Megawords, but the student writes everything on the text pages themselves, which frequently don't have enough space.

Which brings me to another Personal Anecdote moment.

Ed's always been a tad skeptical of the Home Spelling project I've got going. Then, on back-to-school night, we were all handed class schedules written out by our kids. Christopher had spelled cafeteria cafitrea.

Ed has got religion

StartWrite software

I found it.

This is a dandy little program, that apparently works on a Mac.....wonder if I can find the original disk down in the basement?

review of StartWrite Handwriting

The great thing about StartWrite is that you can make the lines as dark or light as you like, and you can space them the way you like. You can also print any words at all for tracing. Extremely easy to use.

free online penmanship sheets

handwriting worksheets at Teachnology. These aren't bad. Upper case, lower case, printing, cursive, and numerals.

---

MathLessonsPage 21 Sep 2005 - 15:48 CatherineJohnson


I've started to get the Math Lessons page pulled together. I'm sure I've forgotten posts that should be indexed there, so if you know of any, let me know. (Any lessons you especially like from other people's sites, like MathandText, for instance, should also be added.)

There's a link to 'Math Lessons' on the sidebar.

---

TeachnologyFreeWorksheets 21 Sep 2005 - 20:07 CatherineJohnson


Teachnology seems like a useful site.

Here are free online word problem worksheets.

And here are lots of free math worksheets.

I like this addition and subtract equations worksheet.

---

BestMadMinutesBook 22 Sep 2005 - 04:06 CatherineJohnson


I keep forgetting to ask.

I'm teaching the Singapore Math after-school class again, and I don't want to use Saxon's 5-minute sheets.

I need a 1-minute sheet (or online source).

Thanks--

---

FunBrainNumberLine 22 Sep 2005 - 19:26 CatherineJohnson


Line Jumper, an online number-line competition at FunBrain.

The kids in my Singapore Math class LOVED the FunBrain site. They especially liked the Math Baseball game.

Normally I'm skeptical of online activities (because Christopher seemed to learn nothing from software math facts programs) but the kids I've known really did like these math facts games, and could play them for a lot longer than they'd do a worksheet.

You can also use Math Baseball to teach mental math, because the kids have to do the calculations in their heads, unless they pull out a pad of paper & a pencil.


I had Christopher do the integers worksheet from Saxon Math 8/7 last night. I'm going to have him keep doing it until he can finish it in 5 minutes & get everything right. That will help.

---

OnlineMathResources 22 Sep 2005 - 22:30 CatherineJohnson


I came across all kinds of interesting-looking math web sites last night while looking for:

• integers worksheets
• downloadable number line worksheets

I didn't find either of the things I wanted (and almost spent $29.95 to join some teacher site linked to by FunBrain just to be able to printout their number line sheet...).

But I found all of these:

• AAA Math (resources listed by grade thru gr8)
  also has a potentially interesting page called World Education Levels. Unfortunately, I can't tell what 'world education levels' are without spending a lot more time on the site than I want to spend. LOTS of online quizzes that are corrected by the site, and they seem to be selling a software program on arithmetic.

• Computer Lab: Math, Numbers, and Counting HUGE survey of 163 different online math sites for kids. Terrific collection.
  Item number 163: Disaster Math for Kids
  From FEMA! Interactive word problems graded by the FEMA site.

• the aforementioned FunBrain Math Baseball is a classic.

• FunBrain's teacher site, the page that almost sold me a $30 sheet of number lines. Has articles on behaviormanagement in the classroom that look good.

• Harcourt School Publishers' number line express Blecch. But maybe little kids would enjoy it. There's a talking lion railroad engineer.

• MacTutor History of Mathematics

• Math Cats how-to for teachers Definitely worth looking at.

• math clip art! possibly for autistic kids (I was on a major clip art tear a few years ago, when Andrew was in his PECS genius phase...)

• Maths Dictionary (British?)

• Mathsurf teacher's site word problems from Pearson Scott Foresman. If you're looking for story problems with multiple answers, this is the spot. Possibly (probably?) a good site to visit for problems your child may encounter in constructivist math courses -- worthwhile problems, as far as I can tell on cursory inspection.

• Mathsurf telling time worksheet (to print)

• NCTM Illuminations Looks decent. Lots of interactive 'tools': affine recurrence plotter and--Yay! nets!! I've been looking for nets!

• National Library of Virtual Manipulatives for Interactives Mathematics I've visited this site several times before. It's pretty good, as I recall. (If I'm remembering correctly, the pan balance problems are kind of cute & potentially useful.)

• Room 108 Looks decent. You can create online Mad Minute pages (must be answered & graded online)

• odd & even numbers possibly good for autistic kids? this site speaks the directions, although I don't think the directions are also written out in words. But any time an autistic child can hear the same words spoken by the same recorded voice it's a good thing, I believe. Site is simple and graphically compelling. Has a HUGE cursor (also great for autistic kids.)

• Primary Games good for autism? I have a feeling this might work with Andrew at some point in the near future. Very simple, has ONE moving image--'Squigly,' a little worm inside one of 10 apples who pops out of his apple and then disappears back inside every couple of seconds. The child has to tell which apple Squigly is in (first, third, fifth, and so on). The only bad part is that there's a lot of advertising crud at the top and the bottom of the page.

• Primary Games 'Diamond Mines' knock-off I spent a couple of years as a Diamond Mine addict.

• Primary Games fishy counting game good for autism? terrific. Very, very simple counting game (as nice as the counting game they used to have on the Barney web site....

• Primary Games Tetris bubbles Great! I've been meaning to post a TIME MAGAZINE article saying girls improve their spatial-visualization skills when they play Tetris. This is, I think, a somewhat slower version of a Tetris game. (Slower is always good for me....) Stupid music, though.

• Primary Games time clock Terrific! Very simple & cute. You have to be able to use a mouse (Andrew & Jimmy both have huge MOUSE difficulties, unfortunately.)

eureka

I will never, ever speak ill of the NCTM again.

They have FREE NUMBER LINES, 8 to a page!

Unfortunately, all 8 number lines start at 0 and contain only positive numbers....

update

I take it back.

I will carry on saying bad things about the NCTM.

They do not appear to have posted a single number line on their web site that includes negative numbers as well as positive numbers and 0.

keywords: online interactive math resources tools nets manipulatives

---

BestGrammarBook 15 May 2006 - 02:07 CatherineJohnson


I have appointed Susan grammar diva, because....she knows grammar! (And, more to the point, grammar books!)

Susan, what book should I order RIGHT THIS MINUTE?

Christopher got a 63 on his grammar test, because he 'mixed up subject and predicate.'

I can't take it.

He's ELEVEN.

And he doesn't know subject & predicate.

So.....which one of the books you told me about should I get NOW. I need something with MAXIMUM direct instruction, MAXIMUM coherence (if possible), and PRACTICE EXERCISES.

Sigh.


Another commenter once recommended the Shurley grammar series--how involved is this series?

(Does anyone know?)

Can I fit it in with everything else?

---

OwlPurdueUniversityOnlineWritingLab 23 Sep 2005 - 20:27 CatherineJohnson


For future reference -

The OWL - Online Writing Lab - at Purdue University is a fantastic resource.

I'm posting the link on the Math Supplements page.

---

GrammarSchool 14 May 2006 - 15:09 CatherineJohnson


So, yes, I am now in the grammar instruction business, too.

Ed asked Christopher last night what the subject and predicate were in the sentence, I ate too much food, and Christopher didn't have a clue.

He flat out couldn't say what the subject was, and he thought the predicate was 'too much food.' Then, when Ed corrected him, he sobbed for 15 minutes.

Middle school stinks.

We're only....3 weeks in? Already I've got at least 4 crying children stories, 4 that I can remember, anyway; there may have been more. Today Christopher's close friend M. started crying when the math teacher docked him a point on his math test for telling his twin brother, 'It's easy, you can do it.'

M. protested that he had only been telling his brother he could do the test, and the teacher said that didn't matter, he could have been cheating.

So back to grammar, Christopher has no clue what a subject and a predicate are. He rejected outright Ed's claim that 'I' was the subject: How can 'I' be a subject??????' Then collapsed into sobs brought on by the sudden realization that the reason he 'put the line in the wrong place' was that he didn't know where the subject ended and the predicate began. A classic example of a child not knowing what he doesn't know, which Willingham has written about. (Why Students Think They Understand—When They Don’t and How To Help Students See When Their Knowledge is Superficial or Incomplete)

I'm guessing Christopher probably thinks 'subject' means 'topic,' as in the topic of an article or book; and, by extension, 'predicate' means the topic of the second half of the sentence. Which would pretty much rule out pronouns & verbs as subjects & predicates, respectively.

Christopher is 11.

His school has two hours of 'English language arts' a day, TWO. And in two hours a day this teacher--this tenured, health insuranced, pensioned individual--did not manage to teach Christopher what a subject and a predicate are.

Teaching math is hard. I'm not going to be wildly critical of a math teacher who is trying. (A math teacher who docks a twin a point because he might have been cheating is another story.)

But teaching subject and predicate to a bright child with a good attention faculty whose strength is English language arts.......

Rolling off a log.

And I'm the one who's going to be doing the rolling.

I'm not happy.

update

I just thank God I started teaching Christopher spelling when I did.

---

FunbrainMadLib 23 Sep 2005 - 23:12 CatherineJohnson


Carolyn suggested I try Christopher on some Mad Libs, to teach him the parts of speech.

I'd never heard of Mad Libs!

OK, that's not right.

I'd heard of Mad Libs. Didn't know what they were; especially didn't know they were fun things that could teach parts of speech. fyi, I am aware of the fact that I have just written two incomplete sentences joined by a semi-colon. It's a secret technique of mine.

Turns out Funbrain has extremely fun Mad Libs.








Here's an Eleanor Rigby Mad Lib.

The Grammar Bible

I've mentioned this book before, but I'll do it again: The Grammar Bible: Everything You Always Wanted to Know About Grammar but Didn't Know Whom to Ask by Michael Strumpf is supposed to be the best book out there.

I heard about it from my editor at Holt, who said Strumpf ran a web site on grammar for years; grammar was his life. Copy editors all over New York would call him up on the phone to ask him how to edit sentences. Finally he wrote a book, and this is it.

I read the chapter on subjects & predicates and then taught it to Christopher--it was great.

He has a rhyme: the subject & the predicate are the name and the claim.

I always like rhymes.


I've got grammar stuff posted on the Math Supplements page for safekeeping.

Steps to Good Grammar

OK, I did it. I ordered Steps to Good Grammar. Has raves on Amazon & B&N.

I'm gonna get Rod & Staff, too.

Given that we've managed to miss THE FIRST TWO SUNDAYS OF SUNDAY SCHOOL, I figure we need it.

---

DougsNumberLines 25 Sep 2005 - 14:03 CatherineJohnson


I can't thank Doug enough for his number lines--and ALL OF YOU SHOULD USE THEM, TOO!

Adding & subtracting positive & negative numbers is one of those areas that can be severely procedural if you have a good memory, which most children do as far as I can tell.

Christopher was already becoming entirely 'procedural' with his integer problems: if he saw two minus signs in a row he automatically penciled in little vertical lines and turned them into two plus signs. Then he added.

ooops--must take Christopher to his playdate

will finish this when I get back

I love these number lines.

back again

Well, I'm back from my Excellent Adventure at Barnes & Noble with Andrew, who is obsessed with pulling Arthur books off of their shelves and lining them up on the floor, while I apologize to clerks & customers.

Now he's shrieking at the top of his lungs & jumping as hard as can on his bedroom floor upstairs, which has shaken loose all the lightbulbs in the kitchen light fixture, which means someone will have to climb up on a ladder, take down the fixture, and screw the bulbs back in.

I'm in a nuts-to-autism mood.

back on topic

as I was saying.....Christopher's memory is good enough that he's reaching the point of procedural fluency with integer computations, and that's got its bad side as well as its good side, because I'm sure he still has no idea how to do the problem I posted a couple of days ago, the one asking what the difference was between the boiling point of oxygen and the boiling point of nitrogen.


[pause]


This is grueling. I've just spent 15 minutes trying to deal with Andrew, who has slapped himself on both sides of the head so hard that he'll be bruised again. We're both trembling. I loathe this disorder.


I'm going to make one more stab at writing about Doug's number lines before I go have my own nervous breakdown.

What I'm trying to say is that it's clear Christopher is reaching the point where he's going to have procedural fluency with virtually no conceptual understanding, and Doug's number lines are the answer.

Number lines are to integer problems what bar models are to story problems. Perfect.

I'm going to have Christopher do a page of Doug's number lines every day for a few weeks, and I'm going to do them myself.

I was telling Ed about all of this, and he said number lines were essential in the GED math course he taught to high school drop-outs in Newark years ago. He was pretty successful with those kids, and number lines were a big part of it. These kids--young adults, actually--were years and years behind in math; they'd never, ever gotten it. Ed had to have visual ways of teaching math to them, he said, or he couldn't have done it.

I haven't got all of the number lines posted yet, but will get to it soon. Right now one page is here, at the top of the Comments thread.

number lines in your head

I'll have to track this down, but one of the neuroscientists who studies math argues that we have number lines--a kind of number line, though not a formal visual image of a number line--in our heads; number lines are essentially there already, along with basic counting & very simple fractions such as 1/2. (I'll have to see whether this particular researcher thinks animals have number lines, too.)

This is all the more reason to use number lines frequently, I think. Any time you can hook a new concept to something a child already has inside his head you've got an advantage.

Vision in Elementary Mathematics by W. W. Sawyer

While we're on the subject of visual models, I've been reading Sawyer's book, which my neighbor gave me for my birthday. It's challenging, but incredibly useful & rich.

Andrew is better

Lately Andrew seems to be having low blood sugar crises. Either that, or dehydration, or both. He has an autistic eating disorder on top of everything else, and won't drink water or milk, etc....and eats only a couple of foods. So he's chronically low on calories, nutrients, and fluids.

I forced grape juice down him 10 minutes ago, and now he's making cheerful noises. His face is bruised, and he's urinated all over his TV stand, videos, and whichever of my books he'd lined up as part of the still life.

BUT, he's OK.

I feel like Annie Sullivan after breakfast.

He folded his napkin.


(So is Kumon Math sounding like just the ticket for Andrew?? I say yes!)

---

GrammarQuestion 14 May 2006 - 15:10 CatherineJohnson


What is the complete subject of this sentence?

While taking the dog for a walk, she stepped in poop.

Thank you in advance.

---

WickelgrenOnPrealgebra 16 Jul 2006 - 20:48 CatherineJohnson




Gulp.

A student can learn a year of pre-algebra math in three to six months studying three to ten hours per week, depending on the child's math aptitutde.

I'm gonna have to pick up the pace around here.

I've been working my way through Mathematics 6 since the beginning of June.

It is now the beginning of October.

RUSSIAN MATH has, estimating conservatively, 10,000 problems. At least 10,000. I have now worked 8000. In the process, I've learned a huge amount, although, sadly, even Enn Nurk & Aksel Telgmaa have not been able to dissuade me from the conviction that 7 x 6 = 43. If they can't do it, probably no one can.

I've just begun the last of RM's six chapters, and I was getting excited about starting algebra next. I can't wait.

So last night I took Saxon Math's placement test (pdf file) for algebra 1.

I got a 72.

conclusion number one:

I am going to stop expressing reservations about the Saxon math series until I can actually take and pass a Saxon math test.

conclusion number two:

wow

There are a boatload of topics I still don't know after doing 8000 complicated Russian computation, geometry, & word problems.

They are:

• using four 'unit multipliers' to convert 630 square yards to square inches: I have no idea what a unit multiplier is, or how to use it
• what a decimal part of a number is (I got the answer right, but only because I made a blind guess as to what a decimal part would be)
• negative exponents
• how to find the volume of a cylinder
• 'the method of cut and try' to find the square root of 20: to my knowledge, I have never heard the words 'cut and try' in my lifetime
• how to use a straightedge (what's a straightedge? I still don't know) and a compass to copy an angle
• how to find the area of a triangle (all I remember is: hypotenuse)
• how to find the probability that a die will first roll a 6 and then roll a 2, in that sequence
• base 2
• update 7-16-2006: I know all these things now, and will finish Lesson 81 (of 120) in Saxon Algebra 1 today.

So my first reaction, in Western polarizing fashion, was: I know nothing.

I know nothing, and I need to work through all 857 pages of Saxon Math 8/7 with Pre-Algebra before I can even think about setting foot inside a real algebra textbook.

I was depressed.

But then I calmed down a little and thought, mmmmm....maybe not.

Maybe I can just go through Saxon 8/7 and do every single lesson & every single problem related to these 9 topics.

Is that wrong?

update 7-16-2006: I ended up working through the entire book. Every lesson, every problem, every test. Then I took the Saxon placement test and placed into Algebra 2, but decided to start with Algebra 1. I'm glad I did.

Christopher began teaching himself Saxon Algebra 1/2 this summer (he starts 7th grade in th fall) so I'm reading through those lessons to make sure I didn't skip anything I need to practice - and just for the joy of encountering John Saxon's take on topics I already know.

Algebra 1 integrates algebra and geometry, though without proofs. I'll start Algebra 2 in September.

In one year I will have worked through:

• final chapter of Russian Math
• all of Saxon Math 8/7
• all of Saxon Algebra 1

That pace seems OK to me.

---

AnyNumberCanBeAFraction 01 Oct 2005 - 05:52 CatherineJohnson









Steve, on the thread need for speed thread, pointed out that any number can be a fraction, and when I said I ought to put together a worksheet on this subject for Christopher, Dan directed me to this frame, DimWksheet010.ppt. of his dimensional dominoes!

It's wonderful.

I'm going to have Christopher do it.

Which reminds me, yet again, I have got to get Doug Sundseth's number lines attached. I've used them two nights in a row, and today I sent a bunch in to Christopher's teacher, in case she wants to use them with the kids.

math ed is a riveting subject

Obviously, I've become obsessed with math education. I'm constantly trying to figure out what it is about math that makes it confusing, and what one can do to make it less confusing.

Liping Ma talks a lot about fragmented knowledge, and cognitive scientists all wrestle with the problem of expertise, which means the ability to generalize what you know to novel problems and solve them.

I've noticed (I may be quoting others without realizing it) that one of the problems with the 'novice' stage of learning is a kind of over-solidity of numbers, a thingness.

Doesn't Freud talk about children first playing with words as if they were things?

Does he say the same of numbers?

I don't remember.

In any case, what I've seen in myself, and in Christopher, is that numbers are too-solid. Both Saxon & Singapore spend a great deal of time conveying the idea that numbers are fluid, in a away, blinking constellations that can be one thing one moment (-10, say) and another in the next (-5 + -5, or -20/2, or any of an infinite number of combinations & expressions).

The Everyday Math article called this 'number partition theory,' and I haven't been able to figure out whether it is or is not number partition theory, but for my purposes, at the moment, it doesn't matter. Just knowing that the number 10 doesn't have the stability of a chair or a tree or a car is a big help.

So I've been trying to convey this to Christopher.

Dolciani's classic algebra text, btw, opens with this idea. '6 + 4' is another expression for '10.' Ten is not the answer to '6 + 4,' but another expression of '6 + 4'. The difference is huge.

Saxon 8/7 constantly uses the word 'Simplify' to mean 'Find the answer,' which I think is excellent. One day Christopher actually said, 'When he says simplify, he means find the answer.' And I thought that was fine. He's getting the idea that simplify and answer are synonyms.

generalizing knowledge

I'm wondering whether making numbers less thing-y for a child might help him or her to generalize a bit more easily, or a bit sooner -- or at least help him to generalize when he's practiced enough that he/she ought to be generalizing.

---

DougSundsethNumberLines 30 Sep 2005 - 21:37 CatherineJohnson





blank number lines (pdf file)

symmetric number lines (positive numbers, negatives numbers, 0 (pdf file)

number lines: all positive numbers (pdf file)

number lines: all negative numbers (pdf file)

update

If anyone is interested in, or has time to, critique these study sheets, that would great. (There's no pressing need for this; I'm reasonably certain these are accurate, especially since the second document came straight from the pages of Mathematics 6.

addition & subtractions of integers review sheet

integers problems from RUSSIAN MATH

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MathmanOnPractice 01 Oct 2005 - 15:03 CatherineJohnson


from mathman:

So how many exercises should I assign? I can't possibly grade them all. This is not an easy question to answer.

It's much easier to say how many exercises the student should do although most students won't care for what I have to say. The student should work as many exercises as it takes to be able to do them correctly most of the time as fast as he can physically write out a complete solution. When informed that he has made a mistake, he should be able to find and correct his error quickly. When it counts, given time to review his work carefully, he should be able come up with the correct solution every time.

This level of mastery opens the door to calculus, differential equations, linear algebra and the quantitative elements of any science.

I'm going to print this out, ask Christopher to read it out loud to me, and then post it above the dining room table. (We're still waiting on delivery of the Ikea desk I ordered a couple of week ago.)

Willingham on overlearning

I re-read Practice Makes Perfect--But Only If You Practice Beyond the Point of Perfection every few months.

---

NumberBondsVersusFourFactFamilies 13 Nov 2005 - 20:07 CatherineJohnson



From the Comment thread about Lone Ranger's approach to teaching an 8-year old why it's OK to write the number 5 as 5/1: I mentioned that Saxon Math uses four-fact families to teach the operations of arithmetic, while both constructivist curricula and Singapore math seem to use 'number bonds.'

Here's an example of a number bond flash card:





You can download these cards from DonnaYoung.org, a homeschooling resource that looks pretty good, and has a page of mostly terrific paper math manipulatives, including lots of circular fractions, terrific large-print math facts drill sheets, graph paper, play money, scale paper for household furniture arrangements, and some cool-looking empty worksheets with number lines on top.

It also has triangular addition and subtraction flash cards (pdf file).

from the directions:

To use the cards, hide one of the corner numbers with your thumb or finger and let the child tell you what the hidden number is.

Saxon's fact families

Saxon Math does not use triangular flash cards.

Saxon uses four-fact families combined with Extreme Practice. If there is One Thing Christopher & I have overlearned from Saxon 6/5, it is FOUR FACT FAMILIES:

1, 2, 3

1 + 2 = 3
2 + 1 = 3
3 - 2 = 1
3 - 1 = 2

Same deal with multiplication and division.

Here's a typical four-fact family problem from Lesson 2 in Saxon 7/6:

23.
Rearrange the numbers in this addition fact to form another addition fact and two subtraction facts.
12 + 24 = 36

Christopher can do that in his sleep.

So can I.

I probably have done it in my sleep.

I've been doing so much grade school math I sometimes dream about it.

four weeks into Saxon 6/5

Quoting from a post I wrote on this subject awhile back:

About a month after Christopher and I began working with Saxon Math 6/5, he told me,

Multiplication and division are the big brothers, and addition and subtraction are the little brothers.

Then he said,

And multiplication and division are cousins.

This is a 9-year who, just 6 weeks earlier, had been flunking math.

You have to do a lot of four-fact fact families to come up with a thing like that.

I vote for fact families

Triangular flash cards and number bonds are everywhere these days, but I don't like them. Here's why:

• First of all, the potential for confusion is huge. An addition & subtraction number card looks extremely similar to a multiplication & division number card, and separating factors from addends in a child's mind is a challenge under any circumstances.

• Second, triangular number bond cards aren't all that easy to 'read.' Kids don't naturally undestand visual displays of data; far from it. There's too much info on these cards, IMO.

• Third, number bonds are incredibly static, and I don't think math is static. Math is something you do, not something you look at. Four-fact families are action-packed; you get so good at them you can whip one of those babies out in a couple seconds flat. They're fun, and they absolutely (I'd bet money on it) prepare kids for the time when they're going to start solving problems like 2 + a = 5. When Christopher segued to 2 + a = 5 in Saxon 7/6 he didn't have a second's difficulty. He'd been inverse-operationing 2 + 3 for a year at that point, so 2 + a was just obvious.

• Last & certainly not least, I haven't had any luck with flash cards, period.

Not nearly as beautiful as Doug's number lines, but a good idea.

oops

I've just noticed that Donna Young prefers sites not link to her printable forms, and in fact these links won't access the forms. Just go to her homepage, click on math, and then find what you're interested in. The math page is clear & easy to use.


Curricular Game Playing
Curricular Game Playing, part 2
number bonds vs. 4-fact families
Numicom Dominoes

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RonAharoniOnTheFifthOperationOfArithmetic 14 Sep 2006 - 14:53 CatherineJohnson


Carolyn has kindly left my two favorite passages in Ron Aharoni's What I Learned in Elementary School for me to blooki.

Here's the first:

What Arithmetic Should Be Covered in Elementary School?

The embarrassingly simple answer is: the four basic operations—addition, subtraction, multiplication, and division.

Yet, this seemingly simple answer is deceptive in two ways. One is that there are actually five operations. In addition to the four classical operations, there is a fifth one that is even more fundamental and important. That is, forming a unit, taking a part of the world and declaring it to be the “whole.” This operation is at the base of much of the mathematics of elementary school. First of all, in counting, when you have another such unit you say you have “two,” and so on. The operation of multiplication is based on taking a set, declaring that this is the unit, and repeating it. The concept of a fraction starts from having a whole, from which parts are taken. The decimal system is based on gathering tens of objects into one unit called a “10,” then recursively repeating it.

The forming of a unit, and the assigning of a name to it, is something that has to be learned and stressed explicitly. I met children who, in fifth grade, knew how to find a quarter of a class of 20, but had difficulty understanding how to find “three-quarters” of the class, having missed the stage of the corresponding process of repeating a unit in multiplication.

I've thought about this observation every day since reading Aharoni's article. I probably can't explain why. At least, I can't at the moment. (Good thing I'm not taking the Regents, I guess.)

But it reminded me of a post Carolyn wrote early on:

Catherine mentioned that she is a fan of tile fraction manipulatives over the more usual 'pie' manipulatives:

She said that her daughter didn't get anywhere using the more-common circular, 'pie chart' fraction manipulatives; she needed to see rectangular fractions. I have no idea why this would be, but it 'felt' right to me, so I searched for rectangular manipulatives and found these.

I prefer tile manipulatives too, for what I think are solid pedagogical reasons, and here is why: if you want to talk about improper fractions -- fractions greater than one -- with your kid, then the pie-shaped manipulatives add potential for confusion because you can't make a single connected object that represents a quantity greater than one. If you want to represent, for example, 3/2 with pie manipulatives, then you'll have one whole circle and a half circle. You can tell a kid that that represents a single object, the quantity 3/2, all you like; but to him it will look like two objects. Fractions are confusing enough without that.

Conversely, you can make a single line of tiles that is as long as you like.

So unless your child is really off and running with the pie manipulatives, I'd recommend the tile manipulatives.

These are the fraction tiles I like:




You can order extra tiles, too, which I have done. I've used these over and over again, with Christopher, and with at least two of his friends.

Worth their weight in gold.


Aharoni article, part 1
Aharoni article, part 2: America's 'new math' goes to Israel
Aharoni on the fifth operation of arithmetic
Ron Aharoni on teaching fractions & forming units
What I Learned In Elementary School by Ron Aharoni (AMERICAN EDUCATOR)

---

DistributiveProperty 13 Oct 2005 - 17:57 CatherineJohnson




I keep forgetting to post this story.

A couple of nights ago I was doing my Russian Math on too-little sleep plus a glass of wine, and I found myself drawing a blank when the text asked me to multiply 24 by 7. I was sitting there complaining, '7 x 24, what's 7 x 24, oooohhhhhhh' (More Sleep, More Exercise, Less Wine coming right up) when I heard, from within my fog, Christopher calling out, "Distributive property! Distributive property!"

I was really tired.

So I kept moaning about What is 7 x 24, and Christopher kept calling out Distributive property! until finally I said, 'What are you talking about?"

Christopher said, 'It's 168! Use the distributive property! 7 x 20 is 140, 7 x 4 is 28!'

I've spent practically a whole year trying to teach Christopher the distributive property.

I had no idea he'd learned it.

---

INeedAPlan 18 Sep 2006 - 17:21 CarolynJohnston




(blank Saxon answer sheets are attached in the Comments thread.)



Ben is not liking his new math plan. He's been doing Saxon math with an aide for around 3 weeks now, and is doing okay, but he complains a lot about wanting to go back to Ms. Math Teacher's class. She's a nice teacher, that's one thing, but also the other kids are there and he doesn't like feeling singled out. Especially not when the singling-out means he's working a lot harder than he used to in the regular class.

The other problem we are having is one we could be having with any math curriculum; Ben is trying to whip through his math homework, as fast as he can, in order to finish as quickly as possible. As a result, he makes a lot of careless mistakes. I really want to get him working more meticulously, because any work habit Ben acquires will be very hard to get rid of. Here is the plan I've implemented in order to get him checking his work more carefully. It's behavioral, a reward system; I've used behavior plans with Ben since he was a young spacey toddler because if I design them well, they work.

With Saxon 8/7, most of the homework on any given evening is review; it's mostly stuff that he could do correctly the first time if he were careful. So I've taken the risk of telling him that I expect him to get it 85% correct the first time through. If he does that, he gets rewarded (the current favorite reward is getting to watch The Simpsons on DVD when he's done with homework). If not, he does without. But I'm not crazy about this plan, and I'm looking for a replacement.

One thing I don't like is that the reward is tied directly to performance. If he ever gets a homework that is on a topic he finds more difficult than usual, the 85% plan isn't going to work very well.

The other thing I don't like about it is that it isn't working very well. He still makes careless errors the first time through his work. When he is done with that first pass through, and I say "you'd better double check your work now before you hand it in," he usually passes up the opportunity to check his work again. Checking Your Work Again is the brussels sprouts of schoolwork; I remember loathing it myself. Apparently it is SO loathsome that he'd rather risk losing his Simpson's reward than Check His Work Again..

I call this an almost-failed intervention. It's not a total failure; his error rate has dropped considerably since we started, but his first-time-through success rate is topping off at just under 85%. He still has a baseline careless error rate of around 10%, I'd say; he usually has one or two problems he's skipped over completely. You really want a behavioral plan, too, that the kid accomplishes successfully most of the time, not one where he's always just barely missing the target.

Can anyone think of a better metric for success?

And, clearly, Checking One's Work Again from the beginning, at the end of an assignment, is too disgusting to contemplate. How do you get a kid to Check His Work Again on a problem-by-problem basis?

---

OnlineLessonInUnitMultipliers 25 Oct 2005 - 19:36 CatherineJohnson



unit multipliers

---

AnotherDistributivePropertyQuestion 31 Oct 2005 - 04:21 CatherineJohnson



Quick question.

I mentioned Christopher has a wicked time trying to simplify this type of expression:

5 ( 6 - x )

Even worse is an expression like:

-5 ( 6 - x )

or:

-5 [ 6 - ( -x) ]

I've been trying to figure out how to teach and explain this. (I didn't get to show him either Doug's or J.D.'s graphics last night, because he had to study for his English test, and do math homework....which reminds me, I have a question about last night's homework, too.)

Back to the distributive property.

It's correct to say that we are distributing multiplication over addition, right?

We're distributing an operation?

That's what I had thought we were doing, but when I went Googling around about it, I found some dissenters.

                                  

Unfortunately, when I say we are distributing multiplication over addition, Christopher gets even more confused by the minus-minus aspect of 'addition' when what he's looking at is a subtraction.

I've written some 'Out loud' sheets on the concept of addition being subtraction of the opposite....but if anyone has other ideas, please let me know.

I'm having trouble breaking this problem down into its component parts.

Should I have him, at this point, rewrite the question as addition of the opposite?

That's what I'm thinking at the moment, but I'm not at all confident this won't introduce even more confusion and angst.

finding   x - 15 = 30

Here's my other question.

Christopher came home last night with a bunch of simple equations to solve.

He knows how to solve all of them using inverse operations, because he practiced that a lot in Saxon Math.

The teacher told them they couldn't do it that way. She wanted them to do it this way:


   x - 15 = 30
      +15  +15
____________
   x + 0  = 45

       x = 45

So naturally we had a whole battle royale about that. Christopher didn't understand the teacher's explanation, and forgot to bring his notebook home, so I had no idea what he was supposed to do. When I said he needed to call a friend and find out he exploded; when I called one of his friends to find out what he was supposed to do he triple-exploded.

His plan was to just find the answers the way he always does, write them in the blank, and take the half-credit.

Here's my question.

To me it seems like a good idea for Christopher to do a bunch of problems the way his teacher showed him.

But why is that?

How do I explain that using the inverse operation is different, sometimes, from isolating the variable?

And is that what we still call it?

Isolating the variable?

I just remembered

Last question:

a = b

b = a

Is this an official property?

Or is it just obvious?


I ask, because I have two Out loud sheets based on this principle.

The first one is full of problems like this:

5 + (-2 ) = _____

The answer is:

5 - 2


Then I have a second sheet filled with the opposite problem:

5 - 2 = _____

The answer is:

5 + (-2 )


I plan to ask Christopher why, if 5 + ( -2 ) can be rewritten as 5 - 2, then 5 - 2 can be rewritten as 5 + ( -2 ).

And I intend for him to answer that if a = b, then b = a.

All a & b have done is switch sides.

But is that right?

Or is this an Official Property?

update from J.D.

You know, it strikes me that this is another Out loud sheet.

I probably better write up a lot of simple multiplication problems, and have Christopher tell me how & where the distributive property is used in the algorithm.

keeping track of graphics

I'm trying to get all these incredible graphics stored where people can find them, which I have taken to mean stored in multiple locations:

Book-style index
Math lessons
Our favorite supplements

I also have a page devoted to Carolyn's math explanations (seriously behind, unfortunately, but I'm working on it).

I do need a Kitchen Table Math intern.

I bet I could rustle one up.

I'm not quite as behind on this project as I am on others (I realized today, I should just go ahead and post Dan's fraction-multiplication graphic now, before I've had time to sit down & study it...).

In any case, these contributions should all be findable.

---

IsSaxonPlusSingaporeTooMuch 07 Nov 2005 - 23:47 CarolynJohnston


We had a request today for some information about supplementing Saxon Math with Singapore Math...

I found this site several weeks ago and I LOVE IT! I started homeschooling my two sons last year after taking them out of public school. I have been using Saxon math. Last year they were in second and third grade and I had them in Saxon 2 and 3. This year, I have them both in Saxon 5/4. I like the Saxon program because it seems to be very thorough and they have plenty of practice. Neither I nor they are very strong in mental math and I have wondered about supplementing Saxon with Singapore Math. I'd like some advice on this. Would it be overkill? To let you know about where they are now: It takes them about an hour a day to do their math lessons. They are at lesson 28 in Saxon. (It's all pretty much review—nothing they haven't had before.) They have had four tests and have done well on all of them. (They both scored 100 percent on the first three.) My older son knows his multiplication facts through 12s pretty well. My younger son is shakier on these and hasn't learned sixes, eights and twelves. I tried giving them the Singapore 3a placement test and they just couldn't do it. I started giving them the Singapore 2a placement test and they are handling that fine (though with a lot of complaints because they have to THINK about what to do in the word problems.) They both like to have me walk them through problems instead of making a stab at it on their own. Thanks in advance for any help anyone can give me. Diane

First responders on the scene (with math tourniquets) were Susan and Dan...

Susan's response:

A homeschooler friend of mine once told me that many homeschoolers use both Singapore and Saxon at the same time. I'm presently using Saxon as the core supplement curriculum for my public school child, but I add Singapore problems to whatever chapter I'm on.

Singapore's word problems are better than any of the other books I've seen because they start with one and two steps and move up to 4+ steps by their level 5.

I don't know if you've seen The Well Trained Mind book, but it has an easy to follow schedule for homeschooling all subjects throughout the years of your child. You might get some ideas of how much to do from there. Since I'm an "after-schooler," as they call me, I haven't ever looked closely at the way they set up the teaching schedule, but it looks fairly thorough.

Dan's response:

I haven't homeschooled, so I feel a little uncomfortable commenting...but only a little.

I just wanted to ask if you were testing the multiplication (and, for that matter, addition) facts with timed tests. I'm pretty sure that timed fact tests are part of the Saxon school curriculum. It seems to be a consensus opinion here at KTM that these facts must be mastered to the point of automaticity. I certainly agree, and have found any lack of automaticity to be a major hindrance as students try to move forward.

And Diane replied..

DanK, Yes, I am using timed tests for addition and subtraction, and I use multiplication fact worksheets for drill, though I don't usually time them. We are just now moving into timed multiplication tests with Saxon.

SusanS, I have read "The Well Trained Mind" and I just revisited her suggestions for scheduling. An hour a day for math seems pretty typical for what most other homeschoolers I know are doing.

I am leaning towards getting Singapore and supplementing with it. Some of my friends who use Saxon with their kids just have the child work every other problem. I've been having my sons do every problem, and, as I commented earlier, it takes them about an hour. I don't want them to get overwhelmed by having an hour and a half of math every day, so I guess I would have to cut out some of the practice problems in Saxon.

So I'll weigh in now with a few thoughts...

I think an amalgam of Saxon and Singapore is a good choice for homeschooling. With Saxon, especially in the early grades, you can be sure that you're not missing out on any essential skills. I think Singapore has a good emphasis on word problems, and I like the way they get kids thinking algebraically very early.

I home-supplemented my son a lot the last two years (we had a constructivist curriculum in 4th and 5th grade—Everyday Math), and even though I'm knowledgeable about math, there were days when I felt up to the task of 'constructing his curriculum' (so to speak) and days when I just didn't. Saxon is a great support for homeschoolers who don't want to be carefully preparing their kids' lessons every day. Singapore takes a greater background knowledge of math, and is much harder for the kids to do independently than Saxon, so to do Singapore, you'll be making a commitment to get really involved with your kids' math. Not every homeschooler wants to do this.

I'd be reluctant to cut out every other Saxon problem on a regular basis, because I think those mixed practice problem sets are the genius of Saxon. They'll revisit a skill intermittently, and if your kids are only doing even problems, they'll miss getting the practice they need if the skill only appears in odd problems (it would be genius indeed if they had enough forethought to put a given skill alternately in even and odd problems!).

You could start by trying to add Singapore word problems to each math session, and see whether that worked; you might find the kids tolerate it pretty easily. If not, you might try switching off days. You wouldn't get through either curriculum as fast, but Saxon has a lot of repetition from one year to the next, so even if you didn't get all the way through a Saxon book you'd have little cause for worry.

Another thing you might consider doing is making Saxon your main text, and supplementing from one of the Singapore books that specializes in word problems, since that's where I think Singapore really has the most to offer. Singapore has a workbook series called Challenging Word Problems Books 1 - 6 ($7.80 plus shipping; 129 pages), in a U.S. (as opposed to British English) edition. You can start at the workbook that's at the level your kids placed into; the problems are marked at a mixture of difficulty levels. This is definitely what I would do if I were constructing a homeschool program.

One more thought—my son, who has Asperger's Syndrome, got balky in second grade about doing math timed tests. He would basically refuse to deal with them, in class; although he knew the facts, he wouldn't do the timed tests because he was reluctant to deal with the time pressure. We ended up doing some heavy bribing to get him to move on those tests (once he did, he was fine). I think adding the time pressure factor is important to nudge the kids toward automaticity. Rewards in the form of treats or outings or privileges are good, I think. Competition can also be good, if it's friendly competition and not cutthroat (and if they're siblings that close in age, it could get ugly).

---

HowToWriteAlgebraEquations 05 Nov 2005 - 03:08 CatherineJohnson



Christopher's friend Marc just asked me for help writing equations for word problems.

Here's the question.

Is it the case that you can't write something like:

3 + 5 = x


Russian Math says the convention is to have the variable on the lefthand side of the equation.

However, Prentice-Hall seems to want not only the variable on the left-hand side, but also one of the numbers.

To pass muster you'd have to write:

x - 3 = 5


That seems wrong to me, and in fact, Pre-Algebra: An Accelerated Course by Mary Dolciani has one equation in the answer key in which the variable is isolated on the left side of the equation.

What is the convention?

Meanwhile Marc's dad told him, 'Just write the equation in the most complicated way you can think how.'

Marc is good at math, but even he was a little befuddled by that.

I came up with: Write it whatever way makes sense, then flip it.

That worked for Marc, so he is now writing the equation the way it makes sense, then inversing it.

"I can inverse it," were his exact words.

I have a sneaking suspicion this is the kind of homework scene that led people to think Reform Math might be a good idea.....

---

EmailToMathTeacher 08 Oct 2006 - 22:14 CatherineJohnson

Hi—

I think Christopher probably did poorly on yesterday’s test, which is distressing. When the test comes home I’ll have him re-do all the problems he missed, and I’ll write worksheets containing similar problems for him to do as well.

We are very committed to Christopher learning to mastery every topic you teach.

Christopher says the test included a number of very long equations to simplify.

That’s great; the kids should be able to simplify long equations. But he hasn’t had any long equations to simplify in his homework, and unfortunately it didn’t occur to me to write such problems myself until Sunday night, when it was already too late. (I’ve written several sheets of practice problems for this chapter.)

I’m really hoping you can send homework at the difficulty level of the items that will be on the test. Kids only learn through practice, and a test isn’t practice!

Thanks—

Catherine

P.S. This is funny. I just pulled up my Chapter Two worksheets, and on the very first page I have written:

Distributive property to do list:

Write some long, complicated equations incorporating all the properties

Also—
I’m attaching my Chapter Two worksheets. Feel free to use them if you like, but be sure to check the answer sheets yourself—

Christopher was having a lot of trouble distributing a factor over subtraction, so I focused on the various permutations of distribution over subtraction.

I also used the technique used in MATHEMATICS 6 & in KUMON, which is to create problem sets in which a student does the same thing over and over again before doing any mixed practice:

The first column of problems distributes a positive factor over subtraction.
The second column distributes a negative factor over addition.
The third column distributes a negative factor over subtraction.
The fourth column distributes a negative factor over an expression with two opposites.

Last but not least, I'm sending my ‘Out loud’ subtraction sheets. Those were very helpful, so you might want to give them to the other kids. I’ve started doing ‘Out loud’ sheets, because it’s a technique used by Mathematics 6, the award-winning Russian textbook.

Enjoy!

to send or not to send, that is the question

Ed read this and said, 'Don't you want to wait 'til you see the test, and find out if Christopher is right about the long problems?'

I think normally that would be good advice.

But in this case I'm going to email first & ask questions later.

I've mentioned that there was a lot of parent furor over this course last year. A major part of the problem—perhaps the problem—was that the tests contained material far more difficult than anything the kids had seen or done in or out of class.

That may be fine in college. (I don't see why it's good there, either, but ktm readers will have informed opinions on this, and I don't.)

It's not good teaching in 6th grade.

Christopher is taking a class in pre-algebra, and the school's job is clear.

The school's job is to teach pre-algebra and make sure the kids learn it.

So my thinking is:

• Christopher is most likely to be right, which means the sooner Ms. Kahl hears from me the better.
• If he's wrong, that's important in and of itself, and is information Ms. Kahl should have. Why is a committed student who's clearly working hard perceiving the test incorrectly?
• Christopher's situation aside, the words 'teach to mastery' probably cannot be spoken often enough. Spoken, written, emailed, tattooed to one's forehead: Teach to mastery.
  This is The Message.

I'm hitting SEND.

question

Does it make sense to have the kids simplifying very long equations at this stage?

To me, it seems as if maybe we're getting ahead of the game, but I don't know. (I'm thinking the kids need more practice on the component parts of equations....but, as I say, I'm just not sure.)

I'm serious about having Christopher learn to mastery every topic the teacher covers. I don't question her authority to decide content—especially since the course content has been excellent so far, apart from the Extended Problems, that is, and even those are probably coming under control. They did their last extended problem in class, and the kids were able to manage it on their own. That's as it should be.

I'm curious what math-savvy readers & teachers think.

---

HomeschooledPreTeens 10 Nov 2005 - 15:41 CatherineJohnson



What are homeschooled pre-teens like?

Are they as hostile to their parents as public school pre-teens?

Does anyone know?

---

HomeschoolersTalkAboutPreTeens 10 Nov 2005 - 21:44 CatherineJohnson



My neighbor told me, back when we first met nearly 7 years ago, that every homeschooled child she'd ever met was a nice kid.

I never forgot that.

Now, having read Steinberg's Beyond the Classroom: Why School Reform Has Failed and What Parents Need to Do at the very moment Christopher is changing from child to adolescent, I'm remembering what she said.

Yesterday I asked what homeschooled pre-teens are like.

Here are some answers.


♥  ♥  ♥  ♥  ♥


My sons are 9 and 8 now; they were 8 and 7 when I started homeschooling them last year. My oldest son was acting a lot like what I remembered from the middle school years: his friends and teachers had more control and authority over him (in his mind) than his parents. What did we know about his life? He spent the best part of his day with other people. Homework was an (almost) daily battle from kindergarten through third grade with him. If I suggested a way of doing something that was different from what he'd learned at school, or what he thought he'd been taught, he would object that my way was not what his teacher told him. The implication was that SHE was in charge, not me.

I figured that if I homeschooled him, at least I'd be fresh and alert for our daily schoolwork battles instead of waiting until the end of the day for them when I was tired. I also figured he couldn't point an authority who wasn't there (the teacher or the textbook that he couldn't bring home) when he disagreed with me.

In fact, this has worked for our family. We attend a small co-op of about 10 families who meet once a week and do projects for science, history and study various fun electives. The other kids are not as sarcastic to their parents as the general public schooled population seems to be. (Of course, I'm looking at a very small sample.)

I think we've been releasing our kids too soon into the wide world. I know I did. Both of my sons were in daycare or with sitters 40+ hours a week from the time they were each about 3 months old until they started kindergarten. I was "outsourcing parenting" but I was working and didn't know what else to do at the time. My kids were spending their days with people who had no real stake in their lives.

I may not always be able to homeschool my kids, and it is absolutely NOT EASY, but, for now, I am grateful that I can do it and I think they will benefit academically, emotionally, and, yes, socially.

Maybe this goes without saying, but, you never know, so I'll say it anyway: I do not think myself or my children superior to anyone who does not homeschool. I am only able to do this by the grace of God. I'm just doing the best that I can do right now.

-- DianeAustin - 10 Nov 2005


I watched a homeschooled 10 year old come up to his mom and give her a big, snuggly, bury your head in mom's neck kinda hug—in public (McD's), AND in front of a dozen other homeschooled kids.

I've seen even older homeschooled kids enjoy playing cards with 6 and 7 year olds.

Being exposed to these types of kids really cememted the idea of homeschooling for me.

BTW, if you bring your child home from public school to homeschool, you need to read up on DE-Schooling.

-- NicksMama - 10 Nov 2005


Homeschooled kids are nowhere near as hostile. Not only are they less hostile in their pre-teens, but also less hostile in their teens. Not that it would be all smooth sailing for homeschooling parents, but having the kind of close relationship that you can really only get when you are together for a lot of the time really eases some of the tension.

Try reading John Taylor Gatto for information on the way school was designed to create disharmony between family members and contributed to the more extreme problems for teens today. The Odysseus Group

-- SamanthaRawson - 10 Nov 2005


Well, from what I've heard from the other moms at the Well-Trained Mind message boards, the kids are still spacey at that age, no matter where they learn. They turn 12 and act like their brains have rolled under the bed with the dust bunnies, not to be found again for 2-3 years. It's not uncommon for them to forget how to do stuff they mastered three years before. They discover the opposite sex. Some of them get moody, etc.

I have a friend IRL whose oldest is Mr. Know-It-All now that he's a teenager. He's very bright, and enjoys letting everyone else know it. :-P

I hope my kids won't be as insufferable as I was at that age. Of course, my folks hope for just the opposite to occur. ;-D

-- BrendaM - 10 Nov 2005



Steinberg on effective parenting
Steinberg is actually an expert on adolescent development, not education (which I think accounts for some of the ways in which he goes wrong, IMO).

I'm hoping to get around to writing about his study of effective parents, but for now the good news is that probably most of your ideas about what makes an effective parent have been born out by lots of research.

Steinberg talks about the 3 basic kinds of parents who turn up in study after study after study:

• permissive
• authoritarian
• authoritative

Judging by the Comments left here, ktm readers are in the 3rd category, and that's a Good Thing, as Martha would say.

Kids with authoritative parents are in lots better shape going into the Teen Peer Disaster Zone that is an American public school.

The horrifying thing, however, is that effective parenting is more effective for some kids than others.

Specifically, authoritative parenting for white kids packs a wallop. Not enough of a wallop, IMO, but a wallop nonetheless. You can actually define the difference in terms of a child's grades. The exact same child, in terms of SES, parent education, etc. will be getting Cs if his parents are either authoritarian or permissive, Bs if his parents are authoritative.

For black parents, the situation is completely different. The same black child with authoritarian or permissive parents earns Cs; the same child with authoritative parents earns a C+.

Asian parents, good, bad, and in between, have an even smaller difference on their children's grades, but in their case it doesn't matter. The Asian child of effective parents earns just one-quarter letter grade higher, overall, than the Asian child of ineffective parents. Asian kids have one peer culture open to them, and that's Brainy Asian Kid Culture.


the kids I know who've turned out well
I know a lot of them. These kids are glaringly from authoritative homes—and, I would add, from strongly authoritative homes.

They've been sat on.

Interestingly, all of Christopher's friends but one comes from an authoritative home (and the one who doesn't is the one we complain about!)

They've got seriously intense moms, that's for sure.

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CongratulationsBen 17 Nov 2005 - 18:44 CatherineJohnson









(I'm sorry. I know this is blinking. But I had to do it.)

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SusanOnBeingYourChildsSecretary 08 Oct 2006 - 22:14 CatherineJohnson



great comment from Susan


I have no idea what work you "show" for greater than/less that questions.

You might want to write down managable questions like what you put up above for your meeting with her, which I know you'll be having soon. That's perfectly legitimate and it will get you clear and perhaps make her realize that she's not so clear. She has to tell them what she means or the book must have had them doing it that way unless it is some standard way of doing it that everyone knows about.

We were having similar issues with not having enough homework for the work being asked to be done. We've had to use the other books I have for extra practice.


children don't know what they don't know

Again, children don't know what they don't know. They don't know about flexible/inflexible knowledge. They don't know how much is enough. An experienced teacher whose had children bomb on sections would probably anticipate problems with certain chapters. My son's algebra teacher is a veteran. He has stretched and redone some chapters with extra practice. After 25+ years of teaching math he knows exactly what's going to happen and when he can trust the text and when he can't. Even with that, some kids aren't going to make it and I still have the feeling it has more to do with not having enough practice.


the parent as personal assistant

I have had to become his personal secretary because of the school's expectations of him regarding homework and projects and deadlines. He is given all kinds of things to do with all kinds of deadlines and no real guidance on how to manage his time. Many of these things are lacking in specificity. I have to make him pull out his assignments and go through them one by one. If he can't explain something I ask why he didn't write down more so that he would understand it when he got home. We've had much whining and crying over this, but he's starting, finally, to realize that I am going to look at it when he gets home and it must make sense. Just my hammering away at the assignment book and his responsiblity to accurately get his work written down thoroughly has started to make him realize what he has to do to succeed, but that is a gargantuan assignment in and of itself.

I seriously don't remember this kind of juggling of assignments myself much before high school, so it irritates me that I have to take so much time to teach him how to even write it down properly.

I think as a parent you can point out these kinds of murky expectations by the teacher (like the show your work problem) and that they need to be clarified better.

Test-taking has been more difficult for my son, too. There's a stamina and a maturity needed that's a little different than is required for the quizzes. We were doing great on the quizzes, but tanking on the tests. We've talked it through with him and he's improving, but he still isn't as strong on them as he is on the quizzes.

It sounds like you are trying to turn it into a Life Lesson about perseverence and I think you are so smart to do so. Like you said, quitting soccer is no big deal, but he needs to see that some things he can't quit and that it will be alright. They really think it's the end of the world.

With all that blasted "character" stuff they're teaching, you'd think they'd include some of what he's going through.


the veteran

My son's algebra teacher is a veteran. He has stretched and redone some chapters with extra practice. After 25+ years of teaching math he knows exactly what's going to happen and when he can trust the text and when he can't.


This is exactly my concern with Ms. Kahl.

She is, I think, a 2-year veteran, and last year was a trial by fire.

Plus she's up for tenure this year, and while I don't know whether she should have tenure or not, I don't feel that she shouldn't. I know what a tenure year is like; we went through two years of he**. I'd have to feel strongly that she's in the wrong business to want to make Ms. Kahl's tenure year more stressful than it already is.

Christopher has said to me, several times, 'Ms. Kahl is a good teacher,' or 'Ms. Kahl is a pretty good teacher.'

Ms. Kahl isn't a crowd-pleaser; I'd be stunned to learn that she plays to the kids in any way, or grooms fans.

So if Christopher is telling me she's a good teacher, one thing he's not saying is that she's a narcisstic teacher winning love from kids. Plus he doesn't love her. He sees her as a good teacher who wants him to do well.

She's someone who might be a terrific teacher in 5 years' time.


chipperness restored

OK, Christopher just walked in chipper as usual; so far so good.

He's in particularly good spirits because they had another bomb threat today, so they had to walk down the hill to the Main Street School and mill around with their friends until The Danger Had Passed.

That's two bomb threats this fall, both at the middle school, and both, oddly enough, starting in the girl's restroom. "They always come from the girls' restroom," Christopher says.

I know my school didn't have bomb threats in the girls' restroom when I was a kid.

So we finished up with the bomb threat and segued to the subject of, "Do you have my Feature Story?"

"Yes, why?"

"Mr. Fried wants to see it."

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HelicopterParentsPart3 10 Jan 2006 - 13:43 CatherineJohnson








source:
Staying Within the Lines on Homework help


I spent years reading about how women (or blacks) internalized the culture's view of them.

Ed reminded me yesterday that this is called false consciousness.

Parents have false consciousness.

Here's an article, written by a parent, all about the Bad Things Parents Do when their children go to school. The author lives here in Westchester; she's in one of the river towns. Hastings, Dobbs, or Ardsley, can't remember which. That makes her a neighbor.

LISA JACOBSON runs a tutoring business, Inspirica, in Manhattan, and she has seen parents at their worst, their most enmeshed, their pushiest. Parents who do their children's art projects for them, so the third-grade classroom looks, she said, "like a gallery at MoMA." Parents who tinker with science labs and correct math homework and edit English essays until the child does not recognize more than a comma in an opening sentence.

Gee. It's those Pushy Parents again. The ones I keep hearing about here in Irvington.

I wonder why all those Pushy Parents are spending hours of their lives doing their children's art projects.

Might it be because if they don't do their child's projects the child will be given a large, prominently displayed 'D' for all the world to see, called up to the teacher's desk, asked loudly, 'Are you even trying to do the work?' and sent off to the cafeteria to be taunted by the entire 6th grade class?

I wonder.

Back when my sons were younger, the rule was that they did the "content" and I would help out with the cutting and the coloring. It just didn't seem worth the extra hours they would spend wrestling with scissors and crayons. So after my older son drew his poster for social studies intricately mapping the route from the school to his house, I colored the roads black and the treetops green. And once he had completed his essay for French about the Arc de Triomphe, I took a razor and cobbled a three-dimensional model of that landmark from foam-backed board. (For the record, he lost points for neatness on the map poster I colored, and while his French essay earned an A, my foam representation got only a B.)

Does this passage offer a clue?

A parent-created art project earns a B.

Question.

What grade does a child-created art project earn?

As it happens, I have the answer, since I've just run that experiment.

Here's how it comes out. Other parents stay up all night doing their child's feature story/persuasive essay/major research product. (Seriously. One mother told me she had to pull an all-nighter to get it done. Good for her. She's as furious at Mrs. Roth as I am, btw, and has been hovering on the brink of Going To The Principal for some weeks now.)

Your child writes his own feature story.

Your child receives a bright red D, is berated in front of his classmates, is taunted at recess, spends a week crying at home every night.

Meanwhile you drop work on your Actual Job, the one you need to pay your monster property taxes to support the school, in order to steal time to launch a major offensive against the school you're working so hard to support.

Question.

What was the smart play here?

Stay up all night writing your child's paper and be done with it, or let your child write his own paper, after which all he** breaks loose and you get to spend the next 6 weeks dealing with it. And that's 6 weeks if you're lucky.

On the one hand, I am well positioned to help with their writing. Not to do it for them, but to read what they write and send them back to revise. On the other hand, is that helping or hurting? Can a teacher, however well intentioned, possibly give scores of children the same attention that I can give my own? Am I cheating my boys more by stepping in or standing back? Should the roles of parent and professional ever be mixed?

False consciousness!

The Core Question is not Should the roles of parent and professional ever be mixed?

The Core Question is What is my child learning at school, if anything?

My fifth grader's teacher has specifically asked us not to help," said Jacqueline Ghosen, who also has a fourth grader, and who is more than able to help with math because she teaches business classes at the University at Buffalo School of Management. "Her thought is that if the children are not getting the concept, she is not teaching it well," she said. "But if our child gets it wrong, regardless of whose fault it is, he still gets a lower homework grade. Also, if he is the only one who didn't get the concept, she is not going to reteach it."

That's a problem, alright.

Two words: formative assessment

So every night Ms. Ghosen and her husband spend at least three hours reviewing their sons' math, one equation at a time, telling them how many problems are wrong and sending the children back to find the mistakes themselves.

A big, fat, red 'A' to Ms. Ghosen and her husband for logical reasoning.

If the teacher isn't teaching to mastery, somebody has to.

Who's it going to be?

Other teachers have the opposite request: they want parents to take the reins. Ms. Jacobson recalls a recent parent-teacher conference where she was told "that the only way to keep kids achieving at the high level expected by the school district is to teach at school and then have the kids go home and be drilled and helped and tutored by the parents."

Another big, fat, red 'A' to Ms. Jacobson's teacher for logical reasoning.

This teacher would no doubt thrive in a DI system.

She is not teaching in a DI system.

So she's leveled with the parents. If the school isn't teaching to mastery somebody has to do it.

Unless you have a live-in tutor (that's another story) it's going to be you. Us. The parents.

The real story here, the story that should have been written, is the story of why the schools aren't teaching to mastery.

She's looking at the symptom of school failure.

Not the source.


p.s.

I just spent a couple of seconds looking at that picture.

It's great, isn't it?

Totally undermines the article, something I've seen more than once.

Here we have an anxious child, bewildered by the indecipherable schoolwork he's supposed to complete at home, on his own, with neither competent instruction nor help. The teacher has written some stuff on the board, or the child and a couple of classmates have discovered some stuff in a small group, and now he's supposed to know it.

And here we have a mother glaring at the books her school has sent home—glaring from clear across the room. She's also looking semi-bewildered, but bewildered in a mad way, not a say way.

Wait! she's saying. Is it a 'feature story'? Is it a 'persuasive essay'? Is it a 'major research PRODUCT'?

Plus, she's so ticked off she has apparently acquired the ability to project herself across the room telepathically, double in size, and change colors; she's so ticked off she's turning into THE HULK.

I could send this out as a Christmas picture.


Of course the good news is that parents who possess supernatural powers terrify school administrators.


a personality change, too

Plus the mom was a happy, nice, non-hovering, non-helicopter parent before she got a look at the incomprehensible junk they sent home for her child to do.

I think the TIMES should forget about writing articles, and just have the artists draw the stories.


helicopter parents, part 1
helicopter parents, part 2
helicopter parents, part 3
helicopter parents at the AFT
news from nowhere, part 6 (AP students)
helicopter parents of the word, unite
helicopter parents of the world, unite part 2a (t-shirts)
MiddleWeb says hovering is good

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NewPlanForPractice 19 May 2006 - 16:31 CatherineJohnson



I've got some great Comments to pull up front, and will get to those ASAP.

But first, I wanted to put this out there in case any of you have ideas.

Christopher's math course is now officially a disaster.

For Christopher, it's pure memorization of fragmented procedures that have nothing to do with each other. That's how he's experiencing it.

We'll talk to the teacher and the principal, and they'll do what they can. But it won't be enough. We need a do-over.

So we've moved into the minimize-the-damage phase. We have to get Christopher through the course in one piece, so I can reteach the material next summer. We have to make sure he doesn't get a C, D, or F, and we have to prevent him from deciding he hates math, if possible. (Actually, he could take a C and stay in the track, I think. I'll find out.)

This weekend, trying to think what we need to do just to get through 'til spring, I decided to start giving Christopher timed practice. The tests are 'plug and chug'; they're about speed and accuracy and the ability to memorize huge quantities of (seemingly) unrelated material.

Here's what I came up with; I'd appreciate any feedback you might have.

I went through the sections of the chapter that would be on the quiz and pulled out each component task that was either assumed or taught by the book.

There were 21 separate skills in 4 Lessons.

Then I wrote out 5 or 6 problems in each of the 21 categories, and had Christopher do them while I timed him on my running watch.

Side note: on top of everything else, he's now developing test anxiety. Just what we need.

We pointed out he doesn't have test anxiety for KUMON, and he didn't have test anxiety with Saxon......so he won't have test anxiety for pre-algebra, either, if he knows the material cold.

So.

He did his 6-problem timed sets, and I checked them.

If he could do them top-speed and get everything right, we moved on. I'll have to figure out some way to fit in distributed practice, since this stuff is going to be out of his head the minute he finishes the test. But he looked like he was OK for the quiz.

If he made a lot of mistakes, we did another set.

We also talked strategy.

We told him he's very fast, much faster than he needs to be. He did one set of 6 calculations—reducing fractions to lowest terms—in 21 seconds. In fact he has close to two minutes per problem, and if he's doing 6 calculations in 21 seconds he's going to make mistakes he can't afford.

I did that with KUMON at first. I pounded through the worksheets as fast as I possibly could, and I made lots more mistakes than I needed to. Then I read somewhere, possibly in one of the TIMSS studies, that this is yet another difference between U.S. & Japanese students. U.S. students sprint through their tests and finish every problem, getting lots of things wrong; Japanese students apparently follow a systematic, and more deliberate strategy of doing problems they know how to do, and getting those right. I guess it's a quality over quantity thing...In any case, it's definitely a useful skill to learn how to pace yourself. I had no idea about this until I started doing KUMON worksheets. Sometimes, now, I deliberately slow myself down.

So we started coaching him on slowing down.

We also told him to look at the quiz when he gets it, find the questions he can do, and do them. Skip anything that stumps you; just go past it. Come back if you have time. Etc.

He's due home from school any minute, so I'll ask him how the quiz went. Then we'll see how he did when his teacher grades it.

But if any of you have thoughts on teaching a child to take timed tests on material he doesn't understand and learned only a few days before, I'm all ears.

Thanks.


existential question

Ed is champing at the bit to ask the principal exactly how he sees kids going from TRAILBLAZERS to this course.

I'm so horrified by the whole thing, I don't even want to watch a school administrator try to handle that question.


good news

Christopher just came in saying the quiz was "extremely easy."

'Extremely easy' means he knew the material and did well. At least, so far 'extremely easy' has always meant that he did well. His ability to judge his performance breaks down in the middling realm, but at the extremes, he seems to know.

We'll see.

The teacher gave him scratch paper.

um.....I mean scrap paper.

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CommentsToCome 15 Dec 2005 - 20:33 CatherineJohnson



I have a boatload of Comments to get pulled up front.....which means it's going to take awhile.

I thought I'd mention that the reason I pull Comments up front is that a) I don't want casual visitors to miss the super-meaty ones and b) once a Comment is on the front page it's part of the Category thread, so anyone reading that thread will be sure to see it. (All Comments stay connected to the original blooki posts, but a person reading through the KUMON category, say, isn't necessarily going to have the patience to click on each post individually so he/she can read each Comments thread individually.

So these things need to come up front.....

I've finally begun disciplining myself to KEEP A LIST, and here's what I've got at the moment:

• boys hate journaling

• JD (& others) on Houghton Mifflin Math & long division

• Susan on grading handwriting (Christopher is going to be reading this one out loud)

• Steve on epiphany

• Suzuki

• teaching to mastery

• Rudbeckia Hirta on finding stats on colleges "Random factoid (before I disappear into a cloud of office hours, reviews, calming of panic, and then grading): if you want a statistical profile of a college/university (like graduation rates, etc.) search their web page for the Office of Institutional Research and look for the Common Data Set."

• Doug on 'the margins'

• J.D. email

• Verghis on KUMON honor roll

If there are things I've forgotten, let me know.


other

Since I'm posting a public to-do list, I also need to:

• locate Ken's reading test & post links everywhere

• post links to FERPA (thank you, Rudbeckia)

• post links to the Rewards Reading Series, which both Dan and Smartest Tractor have mentioned (Smartest Tractor has purchased SOPRIS' writing program, IIRC)

• post ALL links to reading/writing materials on the how-to-teach-writing page

• collect the science-teaching links from.....was it today? (it's all a blur!)

I should probably go ahead and buy DON'T MAKE ME THINK....

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ThankYouKtmContributors 17 Dec 2005 - 22:23 CatherineJohnson



I was telling Carolyn the other night how rhetorically powerful it had been to open our meeting with the principal by contrasting IMS's Grade Contract to the contracts posted by Ken and Smartest Tractor.

Those documents anchored & defined the encounter.

Carolyn said, 'Well, you've been putting a huge amount of energy into Kitchen Table Math [true], and it's coming back to you."

It sure is.

If I remember to do it, I'll start taking notes on my daily experience reading Contributors' notes. Offhand, I'd say I learn something new every day. Frequently, I find a new way of seeing something I already know, which is exactly what I need, and what I'm looking for.

By the way, I've given everyone a promotion from Commenter to Contributor. Congratulations! (ummm....Carolyn, OK with you?)

I'm guessing the answer is yes, but since I have a Rule against making Unilateral Decisions, I should say that in my own mind I've given everyone a promotion from Commenter to Contributor. I'm an expert on this kind of promtion, btw. This is the kind of promotion where you get to do even more work for the same amount of zero-money you were already pulling down to do the work you were already doing. (Have I mentioned I spent 7 years as a trustee of the National Alliance for Autism Research?)

In other words, this is the kind of promotion your basic PTSA-Mom spends a lot of time getting, the difference being that you guys get way more appreciation than PTSA moms ever get. Trust me. The world of Volunteer Moms is the world of No Good Deed Goes Unpunished. Like, um, agreeing to teach Singapore Math because the chair of the After-school program wants her son to take the course and then having the Superintendent tell the president of the PTSA that you're undermining TRAILBLAZERS.

oops!

off-topic!

A tiny riplet of suppurating rage escaped me there.

Sorry.

I'm joking. (I really am. Today is a very good day.)



Rudbeckia and Susan J on the greater-than and less-than signs

It just happened again.

I asked for thoughts about assessming flexible/inflexible knowledge at home, and Rudbeckia and Susan J left these comments:

I'm wondering if Christopher is having trouble with the comparisons (deciding which is bigger / smaller) or with the notation (which symbol to use).

[and then:]

I'm asking if he has trouble deciding which symbol to use while simultaneously remembering which number he had decided was larger.

[here's Susan J:]

I'm with Rudbeckia. My sister is an experienced OT and a generally sane and competent person who is required to use > and < in her reports of patient progress. She cannot remember which one means which and she starts screaming if I try to tell her how to remember. She's solved this problem with a sign over her desk with the these two symbols matched to what they mean in words.

By the way, if I call them "left angle bracket" and "right angle bracket" when I'm talking about some computer terminology, she has no problem at all telling them apart.

I'm blown away by both these observations.

Seriously.

I've known what the greater & less than symbols mean for so long, they're devoid of meaning, mystery, or possibility. (Though I expect that to change as I move into algebra.)

The idea that anyone could see them as anything other than mundane and obvious is new to me.

My favorite definition of art, btw, came from the Russian constructivist (any relation to our current constructivists? I have no idea).

They said art was the familiar made strange.

I often have that experience reading Contributors' posts.

I love it.



greater-than, less-than, the mnemonic

In case there's anyone who doesn't know this (I didn't), these days they teach kids that the 'big' part of the greater-than/less-than signs always points toward the big number, while the point of the sign points to the small number.

2 < 3
3 > 2

That has worked well for Christopher, though now Rudbeckia's got me wondering....



learned something new, too

Susan J also said:

BTW, being a programmer, I'm not at all sure whether 0.9066 and 0.906600 are equal or not. They may look equal on a print-out but not be equal inside the computer.

[here's Doug:]

Whether 0.9066 and 0.906600 are equal or not, they aren't equivalent. The second implies two orders of magnitude better precision. I'd probably use ≅.

Of course, in a math class, numbers are all presumed to be precise unless explicitly noted otherwise, so = is the correct symbol here.

Cool.

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AnneDwyerOnTutoring 16 Dec 2005 - 21:44 CatherineJohnson

What I've noticed with my tutoring students is this: if they don't understand something in math class, they try to find a procedure or "trick" that works everytime.

Since they don't really understand it, when they have to go back and do it on a test or later, they don't remember the "trick" exactly and their answers are consistent, but wrong.

For example, I was tutoring a student in basic math. He didn't really understand that a whole number has an implied decimal after the number (e.g. 3 is really 3. for a decimal problem)

When he first learned to divide decimals and he was following the teacher's examples, he was doing the problems right: So if he was dividing .045 into 15, he moved the decimal over three places for the .045 and three places for the 15. He even managed to get it right on the first test.

But he did them wrong on every test after that. When we were studying for the final, I was able to watch him do the problems.

Since he really didn't understand, he made up his own "trick". In the problem above, he would move the decimal over for the .045 correctly, but he put the decimal point in front of any number inside the divisor sign. So .045 into 15 became 45 into 150 instead of 15,000. And, because he had taught himself this trick, he ignored all decimal points inside the divisor sign. So even .045 into 1.5 became 45 into 150.

Needless to say, it took a while to find the problem and then to correct it.

IMO, with Christopher, because the class is going so fast and he doesn't always understand what he is doing, he will figure out his own rule and then apply it. You have to go back and see exactly what he is doing when he does the problems so you can identify the error he is making.

We are in fraction & decimal he** around here, which is annoying because I don't think we would be with Saxon or Primary Mathematics—and we weren't going into this course.

This is part of what I mean when I say Christopher is 'losing knowledge' he already had, or experiencing 'math regression,' or just......getting all jumbled up. I think he is becoming uncertain of procedures and knowledge he used to have fairly well nailed-down. (Though I don't know.)

Anyway, both of the ideas here strike me as excellent ideas.

First of all, I'm going to start writing whole numbers with a decimal point and some zeros to the right. I know that will help.

And second, I'm going to keep my eye open for 'invented shortcuts.'

One strategy I've begun, which I think is going to improve matters, is that I'm continually telling him that 'math shortcuts' come from the longer equations he's learned in the past. His teacher seems to be teaching only the shortcuts—either that, or he's only picking up the shortcuts, not the explanation for why they work. Either way, the result is the same: he's learning math tricks.

Last night, when I insisted on showing him why you could invert and multiply, he got his 'eureka' smile.

I'm sure he will have forgotten what I told him by today, but I'm going to keep hammering away at this.

I do think that the basic principle—that math shortcuts come from general principles he already knows—will stay with him, and will help.










source:
reciprocals

---

AnneDwyerIsObsessed 19 Dec 2005 - 17:20 CatherineJohnson



from Anne Dwyer:

How do you know you're obsessed with mathematics education?

When you walk into a used book store and have to buy a Grammar School Arithmetic book published in 1892 because you want to see what math education was like before the progressive movement got involved.

Here are some cool things that I hadn't seen before:

The book teaches how to divide by a fraction (flip and multiply) but it also teaches this method for simplifying a fraction: Reduce 3/4/5/6 to a simple fraction (of course it was written as three fourths over five sixths) The answer: divide the top and bottom by 12 which is the lowest common multiple of 4 and 6 and it reduces to 9/10. I like this method because it works just like getting an equivalent fraction.

A number is divisible by 2 if the last or right hand digit is even.

A number is divisible by 4 if the number denoted by the last two digits is divisible by 4.

A number is divisible by 8 if the number denoted by the last three digits is divisible by 8.

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisble by 9 if the sum of its digits is divisible by 9.

A number is divisible by 5 if its last digit is a 0 or 5.

A number is divisible by 25 if the number denoted by the last two digits is divisible by 25.

A number is divisible by 125 if the number denoted by the last three digits is divisible by 125.

A number is divisible by 6 if its last digit is even and the sum of its digits are divisible by 3.

A number is divisible by 11 if the difference between the sum of the digits in the odd places is either 0 or a multiple of 11.






Well, I have a roped-off pew in the church of my heart for the obsessed.

Edie: An American Biography by Jean Stein


key words: divisibility

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HomeschoolCurriculumForAProdigy 19 May 2006 - 21:18 CarolynJohnston


Here's a letter that LoneRanger found on another list and posted on our requests page. It's an interesting story about a homeschool mom with a brainy kid who sort of rolled her own math curriculum. My advice would be "don't try this at home". I don't really like the bit about 'real math not being sequential little increments' and 'the usual order is arbitrary pedagogy', either; it's a mistake to try to make broad sweeping generalizations from your experience with a single child.

But with those caveats, it's kind of interesting to see what she did.

My son is now 19 and a freshman at MIT majoring in math and computer science. He is extremely talented at math. He has never been to school. We've never worried about doing anything sequentially. I've always used the Tetris model of homeschooling with the random pieces falling from the sky, never the traditional beads-on-a-string approach. Here's what we did for math. It might not work for less-mathy kids, but it sure worked for us. It is sort of like learning a foreign language by moving to the country and having to survive, rather than learning a foreign language by studying 10 new vocabulary words a day and introducing 2 verb tenses per semester. I think S would have done much less if we had insisted on a sequential approach. "Real math" is not sequential little increments. "The usual order" is something totally arbitrary that pedagogues came up with.

Elementary PK-5
I used to say we had a "game-based curriculum". We played a lot of dice, card and board games that involved math. Get "Games for Math" by Peggy Kaye for ideas. We owned every math computer game on the market back then. The best ones are the ones where you need to use math to play the game. I avoided the ones where you are drilled for a few problems, and then "rewarded" by shooting a few spaceships or something. We talked a lot about mathy stuff in the car or waiting for food in restaurants. There was no agenda to it. We would just talk about anything off the top of my head to keep him entertained. We did not use a traditional math textbook with formal homework assignments until 9th grade, when he did AP calculus. But we used a lot of children's math books from the library ("Number Devil", "Al Gebra", etc). I also had all of those "What Your Nth Grader Should Know" books, and I went thru the math sections like a check list to make sure he had all of it. We bought all the Doug Downing "Easy Way" books (algebra, trig, calculus) and I read them to him like story books. Whenever he got bogged down in the explanations, I just skipped ahead to where the story picked up. A year or 2 later I would go through it again, with the explanations, a year or two after that we would make the final pass and include all the footnotes and end-of chapter problems. These all overlapped. We did the first pass on the algebra one in 3th grade, and the first pass on the trig and calc ones in 4th grade. We did all the teaching company videos. But I never asked him to do any problems with them. He would just watch them. Also the old Square One on PBS. He never memorized the multiplication tables (neither did I). I taught him the little tricks I figured out as a kid to compute them on the spot, and he invented some new ones. The tricks involve a much higher level of mathematical understanding than memorizing the table, plus they also work for bigger numbers than 12X12.

Middle School 6-8
At the beginning of 6th grade we discovered Mathcounts, and our lives changed. The math was an exact match for him. The problems are extremely challenging, varied, interesting, and combine multiple areas of math in one problem. They sometimes require stuff like combinatorics and number theory that I didn't see into college. Competition math is totally non-sequential. When newcomers start on Mathcounts, they just jump in the stream wherever everyone else is working. At first they can't do it. It takes about 100 problems of a solution book or person walking them through how to do it before they start to get the hang of it. Then, the first years can maybe get 20% of the problems. The second year, the problems don't get any harder, but the kids are better at it. Maybe they can get 50%. Third year maybe 70%. There is a tremendous amount of preparation material out there for contests. We have a huge supply of problem books with solutions, for contests at various levels. S learned by doing problems, with all the math mixed together.

High School Camp
- the summer after 8th grade S started attending USA-Canada Mathcamp. 5 weeks of math-nerd paradise! A huge smorgasbord of offerings at all levels. Kids pick and choose what they feel like doing every day. Some classes are one-lecture long, others might be 2 weeks, or the entire 5 weeks long. Topology, Field Theory, Optics, Problem Solving, Cryptography. A total mish-mash of subjects that the staff is interested in (often has Ph.D.s in) and makes available to the kids. It is totally non-linear. No pre-reqs, homework sets, exams, grades. The kids just jump in it and play around. Everyone is thrilled to be there and looks forward to it all year. 9th Grade - S had already had 3 passes thru Calculus the Easy Way spread over 5 years, plus watched some calculus videos. I got a bunch of AP review books and old AP problems. He worked through those, then took the AP Calculus BC exam at the end of 9th grade. I bought a calculus textbook, but he never used it. 10th grade - he did distance learning courses for Multivariable Calculus and Linear Algebra. This was his first experience actually working through a math textbook and dealing with homework sets and exams. He HATED that aspect of it (too much drill-and-kill even at this level). I had to force him to sit down and do it while he bitched bitterly, particularly on the multivariable which didn't involve as much new material as we had assumed. But he got through, and made As. He also read an AP Statistics review book and took the AP exam. 11th grade - started auditing grad level math courses at UT (Abstract Algebra, Algebraic Topology). 12th grade - Audited 4 grad courses. Because of conflicts with college visits, he was able to do varying amounts of the work, including attending. But he got something significant out of each of them. Also self studied differential equations using lectures and materials from MIT's OpenCourseWare site (free).

College Applications
We ended up with 10 AP scores (all self-study), 4 scores on SAT II subject tests (in addition to the regular SAT I scores), 3 grades from UT distance learning courses, 2 letters from UT profs stating what his grade would have been in their grad course if he had been allowed to register. I put everything together on one big master transcript. I included the things he studied at home, sort of arbitrarily bundled into "courses". I did not include any parent assigned grades. The transcript is 2 pages. There is an additional 5 page document with course descriptions (textbooks used, etc. Max few lines per course). There is also a one-page "school profile" describing our general educational philosophy. It makes it clear that we were homeschooling in order to attain the highest possible level of academic success, not for any religious reason. It also makes clear that the student had plenty of opportunity for social interactions. We got a rec letter from one of his math profs at UT, from one of the coaches of the USA Computing Olympiad, and from a homeschool parent who taught several classes that included my son. He also had an extensive list of national and some international awards in math, physics, computer science.

At MIT
We had a transcript and copy of the syllabus for the two UT distance learning courses he took, but he did not get automatic credit for any of the college level math he had done other than AP calculus. He was able to get credit for multivariable calculus by taking an MIT exam during freshman orientation. He expects to get credit for differential equations the same way, but they require kids to submit a semester's worth of homework assignments before they allowed to take the exam, so he hasn't gotten around to it yet. There are other courses that he has covered and could almost certainly get credit for by taking MIT's exam (linear algebra, topology). But he has decided not to bother since they are not required for the particular math major he is going for, and he expects to have plenty of credits. MIT is fairly loose about prereqs, so he won't have to repeat anything he has already covered.

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SteveOnTeachingWritingPart2 10 Jan 2006 - 14:00 CatherineJohnson



I'm trying to pull together the Writing thread for my neighbor, and just re-discovered this Comment from Steve:

I just helped my son (4th grade) complete his report/map/craft project on Chirstmas in Greece. (All of the kids had a different country.) As with his other projects, the problem is that the school doesn't prepare them to do the job. They may talk a little bit about what to do, but they don't see what goes on at home. The kids just can't do the project by themselves. If I let him do the project all by himself, it would be horrible, take FOREVER, he would learn very little, and he would get a poor grade. I end up doing the teacher's job. I don't do it for him, but he needed major help in organization, reducing the information down to a reasonable size, and putting it all into his own words. No parent I know likes school projects like dioramas, research reports, and other thematic displays of educational pedagogy and feel-good-ness. Perhaps they expect and want parental involvement?!? I'm more than willing to do my part, but, I really don't want to do their job. Please don't ask me again to practice basic math with my son at home.

There are so many fantastic Comments on this site. I've got a list to pull 'up front,' and am going to carve out some time today to get started, at least. The archived entries on how to teach writing are here.

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MathWarsAtHome 17 Jan 2006 - 20:36 CatherineJohnson



Christopher is sitting witih his dad practicing math & screaming & shrieking.

I just heard him shout, 'I thought you were nicer than Mommy!!!!'

Yeah. That's what everyone thought.

-- CatherineJohnson - 15 Jan 2006

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ConstructivismAtHome 16 Jan 2006 - 21:24 CatherineJohnson



You will all want to order this book right away.

Teaching Your Child to Love Learning: A Guide to Doing Projects at Home






-- CatherineJohnson - 16 Jan 2006

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SentenceCombining 18 Jan 2006 - 16:43 CatherineJohnson



....speaking of books coming in the mail, my copy of Don Killgallon's Sentence Composing for Middle School arrived today. (Killgallon's website)

I don't exactly know what sentence combining is, but I have a Bayesian conviction it's going to be the answer to my Writing-Instruction problems at the sentence level, thanks to this fellow:

Grammar teaching and writing skills: the research evidence

Richard Hudson (dick@ling.ucl.ac.uk)

Dept of Phonetics and Linguistics, UCL, Gower Street, London WC1E 6BT

Does a training in 'formal grammar' improve a child's ability to write? At one time it was taken for granted that the answer was yes, so children were taught grammatical analysis as part of the effort to improve their writing. However when educational researchers sought evidence for the expected effects, the results were negative; for example, one of the classic experiments concluded: "It seems safe to infer that the study of English grammar had a negligible or even harmful effect upon the correctness of children's writing in the early part of the five secondary schools." (Harris 1962) A number of studies in the 60s and 70s have since been accepted as 'classic' support for the view that grammar teaching does nothing for children's writing. By the late 60s the dominant view in both the UK and the USA, and possibly throughout the English-speaking world, was that "most children cannot learn grammar and ... even to those who can it is of little value." (Thompson 1969) No doubt this view fitted the spirit of the times both in English teaching (where grammar was seen as a shackle on children's imagination) and in linguistics (where Chomsky was arguing that grammatical competence develops 'naturally' according to an innate programme, so teaching is simply irrelevant).

Since then much has changed in both the UK and the USA, and the pendulum seems to be on the return swing. It would be naive to think that the pendulum is driven by academic research - indeed, there has been very little research on grammar and writing since the flurry in the 60s and 70s; rather it reflects very general attitude changes in education and more generally throughout society. However the result is that there is now much more enthusiasm in some educational circles for the idea that conscious grammar (resulting from formal teaching) could have the useful benefit of improving writing.....

What, then, does the published research really say about the effects of grammar teaching?

[snip]

Grammar teaching could be surreptitious, as it were, with a clear underlying theory of grammar but minimal use of grammatical terminology. This is in fact how a lot of grammar teaching has been done; and in particular there is a well-recognised activity called 'sentence combining' which seems to be widely used in the USA. There is some evidence, apparently good, that this kind of activity benefits children's writing (Abrahamson 1977; Barton 1997; Hillocks 1986; Mellon 1969; O'Hare 1973), and in some studies it turned out that this kind of grammar teaching produced better results than more traditional teaching of grammatical analysis. For example, " Hillocks surveys the many studies of the effects of sentence combining, and finds them overwhelmingly POSITIVE at all levels (grade 2 to adult). 60% show significant gains in syntactic maturity; 30% non-significant gains; 10% no gains." (Weaver 1996, reporting Hillocks (1986)).

Why should these exercises be so much more successful than traditional analysis? It seems reasonable to assume that it is at least in part because they are exercises in the production of language, and specifically in the production of written language, so they feed much more directly into the child's growing repertoire of productive skills than exercises in grammatical analysis do. In short, they are more closely integrated into the teaching of writing, so the skills acquired in isolation are more likely to transfer directly into a usable skill. However this conclusion does not necessarily rule out the possibility of transfer from grammatical analysis under the right conditions.

This makes sense to me, so I'm going with it.

5 reasons:

• it makes sense

• I'm a writer, so my intuition about what works in writing instruction is probably worth listening to

• I used to teach writing, so my intuition that sentence combining makes sense is, again, probably worth listening to

• KUMON Reading uses sentence combining

• sentence combining seems somewhat analogous to the way Ben Franklin taught himself to write

We need a Bayesian Rating Scale

That way, we could assign numerical values to the question of, Just how strongly do I think I guessed right?

Here's a possibility:

On a scale of 1 to 7, 1 being 'no clue' and 7 being 'death and taxes, how certain do I feel that sentence-combining will make Christopher a better writer?

6

or

6.5

I'm not feeling a lot of doubt here.



I love this

back to Hudson:

In conclusion, the idea that grammar teaching improves children's writing skills is much better supported by the available research than is commonly supposed. However there is no denying the need for more research in this area, so we finish with quotations (from Walmsley 1984) by two of the twentieth century's most distinguished psychologists who have taken an interest in this question.

Robert Thouless (1969:211):
"If a small part of the research effort that has been put into demonstrating the uselessness of grammar ... had been distributed over a wider field, more might be known about how skill in the use of English can best be developed."

John Carroll (1958:324):
"I am reasonably sure that unless the student gets a feeling for sentence patterning ... his own sentence patterns will show many obvious defects. Research on the effectiveness of teaching English grammar in improving English composition has been mainly negative, but until this research has been repeated with improved methods of teaching English grammar, I will remain unconvinced that grammar is useless in this respect."

I went on a Sentence-Combining treasure hunt on Amazon, and came up with Don Kilgallon as the likeliest prospect. Just glancing through the middle school book, it seems like exactly what I want.

From the back of the book:

With the first edition of his book, Don Killgallon changed the way thousands of high school English teachers and their students look at language, literature, and writing by focusing on the sentence. In this revised edition, Killgallon presents the same proven methodology but offers all-new writing exercises designed specifically for the middle school student.

Unlike traditional grammar books that emphasize the parsing of sentences, this worktext asks students to imitate the sentence styles of professional writers, making the sentence composition process an enjoyable and challenging one. Killgallon teaches subliminally, nontechnically--the ways real writers compose their sentences, the ways students subsequently intuit within their own writing.

Designed to produce sentence maturity and variety, the worktext offers extensive practice in four sentence-manipulating techniques: sentence unscrambling, sentence imitating, sentence combining, and sentence expanding. All of the activities are based on model sentences written by widely respected authors. They are designed to teach students structures they should but seldom use. The rationale is that imitation and practice are as valuable in gaining competence and confidence in written language production as they are in oral language production.

Since the practices have proven successful for the great majority of students who have used them in all kinds of schools, it's demonstrably true that Sentence Composing can work anywhere--in any school, with any student.

I believe it.

Kilgallon has written books for all grade levels.

















Bayesian statistics & false positives
Bayes & the human mind
Bayesian reasoning, intuition, & the cognitive unconscious
most bell curves have thick tails
ECONOMIST explanation Bayesian statistics
Bayesian certainty scale

sentence combining
Smartest Tractor on Killgallon & 5 ways to combine sentences

Bayesianprobability


-- CatherineJohnson - 17 Jan 2006

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AProblemForCarolynAndBen 21 Jan 2006 - 15:17 CatherineJohnson



I've been thinking about Carolyn's at peace with cross multiplication post:

...lately we've been dealing with problems like d/36 = 7/4, and whatever he learned about cross-multiplication last summer is gone.

I've wanted to teach Ben to do them using isolating-the-variable methods. It's difficult to get Ben to take this step-by-step approach. One problem is that he always wants to do the problems in Saxon 'the easy way' -- and I can't tell you what the easy way is, for Ben, because from where I sit, it looks as though the answers just come to him. It's a bit uncanny. I think he visualizes the proportions, somehow.

doing things the easy way

First of all, there's one thing to be said for sending your child to a school that will stomp him with D's and D+'s.

If you don't reach the point of actual School Refusal (we were getting close there), the kid is motivated not to get more D's and D+'s. Brute force has its uses.

Once your child has had his ego mulched, there's a chance he'll listen to reason.

For all of you parents-of-little-ones, let me add that it's not much of a chance.


here's the sequence:

1. big test coming up on material not taught to mastery, not learned, and not comprehended in any way, shape, or form

2. parent points out, logically, that child has not mastered, learned, or comprehended material; therefore he will need to study a lot

3. child rolls eyes, screams, yells, sobs, claims stomachache, headache, exhaustion, etc.

4. parent persists in patient, logical explanation

5. child rolls eyes, screams, yells, etc.

6. parent persists

7. child screams, yells

8. parent loses control of patient, logical tone

9. child screams, yells

10. parent levels threat to take away allowance/PlayStation/TV

11. child says, 'I don't care'

12. parent asks 'do I need to tell your father?'

13. child says, 'Daddy never yells'

14. parent, etc.

15. child, etc.

16. parent, etc.

17. child, etc.


Talk about scripted instruction.

Notice that throughout this exchange, no actual math is getting done. In our house we call this running out the clock.

My point is: the day the 'D+' comes back on the test we have crying.

By the time the next test is upon us, the D+ is history.

Ed and I are still traumatized; Christopher has moved on.

Nevertheless, since Christopher got his D (make that D's plural as of yesterday) he is willing to listen to us when we tell him to write out each step of the solution.



I love this problem:

-x = -5



I don't know where I found it; not Prentice-Hall, I'm sure. I think it was in a workbook — maybe Instructional Fair or Kelley Wingate.

I'm wondering whether this might be a good problem to do with Ben.

Here's what I love.

• First of all, it's incredibly simple visually and mathematically. The load on working memory has to be small.

• Second, you can show, in just one problem, that adding, subtracting, multiplying, and dividing are still related even though you're solving equations, not learning inverse operations.

• Third, you can almost use it the way people use simple proofs and demonstrations; it's so simple and pristine you can ask your child to write out the steps on more than one occasion - and to justify each step, and to solve it using addition/subtraction AND multiplication/division.

• Fourth - somebody else will have to fill this in. There's something about this problem that starkly shows the 'equalness' of equations, as well as the do-the-same-thing-to-both sides principle. I can't express it, but I can see it.

• Fifth, it demonstrates the fact that a 'minus sign' is the same thing as a coefficient of -1.

Christopher can't write out the steps to solve this problem — although he does now 'see' that the answer is x = 5 — but I'm going to see to it that he can.



solving via addition & subtraction:

-x = -5

-x + x = -5 + x

0 = -5 + x

0 + 5 = -5 + x + 5

5 = x



solving via multiplication and division:

-x = -5

(-1)(-x) = (-1)(-5)

x = 5



Wal Mart homeschooling

wow

Wal-Mart has a huge selection of books for homeschoolers.

They have a bunch of Instructional Fair books. I like the pre-algebra workbook.






Illinois Loop likes Kelley Wingate's workbooks, and I see that at least one Core Knowledge course uses her series.

Wal-Mart is apparently selling a cheaper version of the IF workbook I have, which costs $12.99. Wal-Mart's is $2.81.

You can find Kelley Wingate in various places. Homeschooling Supply has the pre-algebra book for $12.31.

These things aren't cheap.

I should talley up all the money I've spent on materials for re-teaching math.

Not to mention the cost in lost work time.

-- CatherineJohnson - 21 Jan 2006

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StickingPointsInMath 30 Jan 2006 - 20:09 CarolynJohnston


Rick Garlikov, the subject of the other day's post on TeachingBinaryLikeSocrates, has a mentoring service for students and parents in Alabama. You can pay to have your child mentored and tutored, or you can pay to be mentored in teaching your own kid. I love the latter idea, actually. Teach a parent to fish, and he'll eat for a lifetime.

Anyway, on his web page about parent mentoring, Rick has a section in which he discusses the areas in math where kids tend to flounder (you have to scroll way down to see it). He also has a section about verbal subjects where kids tend to flounder, but we'll cover that in a different post. Here's Rick's list of sticking points in math education:

• Understanding counting by groups, such as groups of two, five, and ten
• Seeing numerical relationships in general and knowing to look for them
• Place-value and adding/subtracting that requires regrouping or what used to be called borrowing and carrying
• Understanding multiplication and division
• Fractions
• Decimals rate/time/distance problems
• What algebra is about; how it works in general
• Geometry proofs and theorems and their point

Although certainly this is a largely correct list, is it the most useful possible list for parents and teachers to be on the lookout for difficult spots in their kids' math educations?

Can we narrow it down more precisely than saying (in effect) "everything about fractions"? For example, I've noticed that kids tend to have no problem at all multiplying fractions; they do the obvious thing, and it's also the correct thing. It's adding and subtracting fractions that's difficult for kids, because the obvious thing is not the correct thing.

Can we narrow down more precisely what's hard for kids, and what isn't, about algebra?

What does he mean by 'seeing numerical relationships in general', and do we agree that it's a sticking point? My experience was that counting by groups was not especially difficult for Ben, and I never got the impression it was hard for his compatriots, either.

Are there topics that didn't make it onto Rick's list?

Weigh in, and I'll collate all the input and try to put together a comprehensive list.

-- CarolynJohnston - 25 Jan 2006

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ParentsMentoringChildrenInSingapore 16 Sep 2006 - 20:27 CatherineJohnson



OK, I know I'm supposed to be typing Steve's algebra lessons into Equation Editor so mere mortals like me can read them, and also doing the same for my own Comment for Carolyn's Sticking Points post.

Plus I've probably got a civil servant or two who need bullying this afternoon (where does David Allen say to put 'bully civil servants' on the Master List?)

But all of that can wait!

BECAUSE FIRST I HAVE TO WRITE MY SLAVE PARENTS IN SINGAPORE POST!



don't encourage me

brief pause for Character Analysis

My mom used to always say something funny.

She is stubborn as a mule, and she used to say, 'I can be led, but I can't be pushed.'

That's me to the nth.

I can be led. In fact, I like to be led; I make a good second in command.

But don't push me.

Until last night, I hadn't thought of myself, not consciously, as a person who gets her way by bullying civil servants. Sure, I was willing to raise holy he** if I thought my kid was being hurt. But I hadn't thought of this as bullying civil servants. Given the relative unequalness of the match — me against a small school district — it seemed more like.....um........

hmm. The only image coming to mind is Butch Cassidy and the Sundance Kid deciding to shoot it out with the entire Mexican Army.

Sure, you do it. They're out there shooting at you, you're inside your cave bleeding to death, so what the hell? You go down fighting.

I'm joking.

Anyways, now that ktm guest has put it this way I'm thinking......bullying civil servants.

Bullying civil servants to get my way.

yes

I like it!

I want to get my way!

Until last night, I didn't know I was the bully.

I thought I was the helpless parent-victim getting clobbered by fuzzy math & ZERO teaching to mastery.

If I can be the bully and get my way — THAT IS FANTASTIC NEWS!

YAY, ME!

Now all I need is somebody to tell me who I need to bully to get Direct Instruction, Formative Assessment, and Teaching to Mastery established as the formal educational policy in the Irvington Union Free School District.



speaking of getting my way

This is funny.

We're back at tennis lessons, and I ran into the mom I always see there who has a daughter in Mrs. Roth's class, and who's had the same view of her we had (and knew other parents in our boat as well.)

She said, 'You guys must have really done someting. Mrs. Roth is completely changed. All the girls who didn't like her love her now.'

That's what Christopher's been hearing, too.

His chums are constantly telling him, 'Mrs. Roth's so much nicer now that you're gone. She's so much happier.'

He's been hearing this every day, poor thing.

I finally told him, 'Mrs. Roth's not nicer because you're gone. Mrs. Roth is nicer because the principal told her to be nicer.' Then I told him not to be saying this to all the other kids. It's time for them to go back to beating each other up about who has a crush on who. Either that, or just resume milling around randomly calling each other names like they used to.

This is my cue to say again how much we like our principal, Scott Fried. I think I mentioned that Ed said, after our meeting about Mrs. Roth, 'He handled the situation perfectly.' I quote that because Ed's been an administrator for so long himself.

After the meeting, Scott made the call the next day.

Christopher has been moved to a teacher — Mrs. Kozak — who is lovely, and who seems to be making a special effort to get him perked up and de-traumatized. It's working. Christopher comes home every day and reads his notes from her class out loud to me! Plus Mrs. Kozak is teaching spelling, grammar, and writing-as-a-process; they write drafts under supervision, get comments on their drafts, then revise. She even told Christopher he has to come in for extra help with his handwriting. Glory Hallelujah.

Another thing: from a distance, it appears that Mr. Fried worked well with Mrs. Roth, too. The fact that children who were unhappy in her class now have no complaints at all is very impressive. How often do you see a bad situation turn around on a dime?

Seeing as how Irvington teachers & perhaps administrators may be reading this site, I'll say one thing more.

Other parents have been told, by their children, that Mrs. Roth typically chooses one child to pick on.

A child in Mrs. Roth's class has told Christopher that he has become Mrs. Roth's target now that Christopher is gone.

I don't know whether that's true.

But I imagine Mr. Fried is keeping an eye on the situation.



next up

So that was the story at tennis.

Next thing, I heard from my friend J., who called to chat. We hadn't talked since summer. One thing led to another, and she told me Christopher had been called a 'BOCY' at school. She was aghast.

I already knew Christopher had been called a BOCY, and, frankly, I don't care. The kid who called him a BOCY is one of his best friends, and the two of them are going to have to figure it out for themselves.

I did mention to Scott that he may want to take a look at how much BOCY-calling is going on, if only because Andrew will be there next year, which means IMS is going to have some INTENSE BOCY BEHAVIOR HAPPENING ON A DAILY BASIS.

Forewarned is forearmed.

Anyways, I already knew about the BOCY business, but it turned out J. didn't know that her own son had been called the n-word.

Her son told Christopher about it, which is how I knew, but hadn't told his mom because he figured she'd go ballistic.

He was right.

J. called up the principal, and the conversation went something like this:

J.: My friend Catherine told me so-and-so called my son the n-word.

PRINCIPAL: 'Catherine? Catherine Johnson?'

J.: 'Catherine's a good friend of mine.'

PRINCIPAL: 'Did she call you?'

J.: 'No, I called her because we hadn't talked in a long time. If I hadn't called Catherine, I wouldn't have even known it happened!' [J. is very cool.]

PRINCIPAL: etc.

So the next day the principal called J.'s son, M., into his office to interview him about what had happened:

PRINCIPAL: What happened, exactly?

M.: tells story

PRINCIPAL: Who did you tell?

M.: Chris Berenson

PRINCIPAL: Why did you tell Chris Berenson?

M.: Because he's my friend.

PRINCIPAL: etc.


J. told me, 'You guys must have really shaken things up around there.'

I love it!

We're everywhere!

There's no escaping us!

THERE'S NO ESCAPING US BECAUSE WE LIKE TO GET OUR WAY BY BULLYING CIVIL SERVANTS!



is it still Wednesday? not Friday?

That's hard to believe.

This is the kind of post I write on Fridays, after a week of Maintaining Composure & gobbling up so many frontal lobe resources there's nothing left.

OK, back to business.

That being:

SLAVE PARENTS IN SINGAPORE

Carolyn mentioned the subject of parent mentoring, which reminded me of an LA Times article I read about Singapore way back when, before there was Kitchen Table Math.

So if we were to crib from the valedictorian of nations, what would we find? A school system based on two credos: one very American—competition—and one unimaginable in the U.S.—total government control. For students, this means high-pressure exams at the end of grades four, six, 10 and 12 that help determine not only what classes they take but, ultimately, whether they will wind up as doctors or cabdrivers. For schools, the pressure is to attract the best students—who have their pick of campuses.

Then there is:

A national curriculum. In Singapore, there are road maps for instruction at every level, molding tests, tutoring and teacher training. The documents are amazingly concise—eighth-grade math is covered in 10 pages, listing 19 topics within algebra, geometry, etc. (Students, for example, must be able to calculate the "volume and surface area of sphere, pyramid and cone.") By contrast, American eighth-graders race through 30 or more topics, learning them so superficially that they have to be repeated over and over.

Involved parents. Here, that doesn’t mean just showing up for Back to School Night. Parents get on waiting lists for the best tutors, who charge $300 a month. They buy two sets of books to ensure that one is always available for homework. Hundreds pay $300 to attend 30 hours of weekend training so they can understand changes in math instruction. "As parents, we think of always buying the best computers, giving them the best tutors, to play it safe, you know, so they can score high on their examinations," says Siew Yok as she purchased software so her 12-year-old daughter could cram to qualify for prestigious Raffles Girls School.

So here we have it, the Secret of their Success:

• parents get on waiting lists for the best tutors

• parents pay $300 to attend 30 hours of weekend training so they can understand changes in math instruction (now there's a potential revenue stream the folks at EVERYDAY MATH haven't thought of)

• parents buy 2 sets of books

That pretty much describes me to a 't.'

• hiring the best tutors = KUMON

• spending $300 on a weekend seminar = writing Kitchen Table Math so I can learn math & how to teach it from Carolyn & the resident KTM Math Brains

• buying 2 sets of books = buying 2 sets of books, one set via taxes, one set via American Express payments to Amazon.com

Assuming this article is true, in Singapore the job of seeing to it children actually learn what the teachers are teaching belongs to the parents.

Good thing I live in America.

If I lived in Singapore I'd be getting caned on a regular basis.


Asians in Great Neck



-- CatherineJohnson - 25 Jan 2006

---

SteveOnWhyKitchenTableMath 16 Sep 2006 - 20:28 CatherineJohnson

The only kids who are prepared to take a proper college prep math (esp. honors or AP courses) track in high school are those kids who are very smart or get help outside of the school. The current crop of fuzzy, low expectation, no mastery, discovery, spiraling math curricula are HARMFUL to kids. In the old days, traditional math may have been taught very poorly or inconsistently, but I don't think that was on purpose (perhaps incompetence and neglect played a part). Nowadays, perhaps there are more controls and teachers are more consistent (with the program), but the math curricula do not get students from point A (counting numbers in Kindergarten) to point B (a full course in algebra in eighth or ninth grade). This IS on purpose.

The problem of education is not some myopic teacher-perspective view of the problem. It is not "if only". If only we had more money. If only we had smaller class sizes. If only we didn't have to meet (trivial) state standards. If only the administration would get off my back. If only parents would get off my back. If only we had a better school culture. It is much more fundamental than that and it's not just about the teachers.

KTM exists because schools are not doing their jobs. Parents have to do it at home at the kitchen table. KTM is not ranting. It contains specific help for parents that they cannot get from the teachers, administration, school committee, or parent/teacher groups. Most of the regulars here have spent a whole lot of time working within their systems. It doesn't work.

After Christopher failed 2 of 6 units in 4th grade math, I had the Bayesian perception that unless I learned math myself, he would be out of the running for any career involving math in any way.

That perception may have been wrong. I'll never know how things might have turned out if I hadn't plunged into re-teaching Christopher his math, plunged into re-learning math myself, and ultimately plunged into writing and, more importantly, reading Kitchen Table Math.

Looking back, I think it's right to say that I myself was locked out of any career involving math in any way.

In my own school days, I was taught to mastery. That teaching stood me in good stead. I had 'shopkeeper's arithmetic' down cold, and I was able to start over again learning math in mid-life, and make quick progress.

But it wasn't enough to let me take math in college. And at that age, in college, I didn't know what I didn't know. I didn't know whether I liked math or not, whether I might be reasonably good at math or not, whether I should be doing something related to math or not....I didn't know anything. if I thought about it at all, I just figured I wasn't a 'math person.'

As one of Carolyn's old professors says, the last person you want making life decisions is a 19-year old.

When we were in Los Angeles over vacation, I spent time with the now-grown children of friends.

These kids have had fantastic educations, every one of them in private schools, including Catholic schools.

None of them is headed toward a math-related field at the moment (these kids are high school seniors & college freshmen) but each one of them could choose a math-related field if he or she wanted to do so. The door is open.

That's what I want for Christopher (and for Andrew, obviously, if I can get him there). I want the door to be open.

We've chosen to live in a high-tax suburban town with good schools. This was our version of choosing a private school. Talk about not knowing what you don't know.

The Irvington math track, thus far, isn't going to put Christopher in position to choose a math-related career.

Everyone says the high school is fantastic, and given the principal there I'm sure it is.

But when I talk to parents whose kids have taken AP calculus at IHS — and those kids are the only American kids who are competitive with their peers in other countries — what I hear is this:

His dad is really good at math, so he helped him all the way through.

In other words: my son made it through AP calculus because his dad knows calculus.

I have also heard this:

My son couldn't find a calculus tutor anywhere. He had to get through it on his own.

The woman who told me this has an advanced degree in math herself.

Carolyn says she finds it hard to believe that there could be no calculus tutors in all of Westchester County, and I agree.

But — and here's the point — I can't take the chance.

Maybe there'll be calculus tutors in Westchester when Christopher gets to Irvington High School, and maybe there won't.

Maybe Christopher would have gotten back on track without my turning into Math Mom, and maybe he wouldn't have.

I don't know.

I couldn't take the chance.

-- CatherineJohnson - 26 Jan 2006

---

FormativeAssessmentAndRichardNixon 16 Sep 2006 - 21:05 CatherineJohnson



I was trying to pull together the various posts & comments on gaps and gapology when I discovered that one of the many benefits of formative assessment is that FA allows you to:

a) discover gaps

and

b) get rid of gaps

Feedback given as part of formative assessment helps learners become aware of any gaps that exist between their desired goal and their current knowledge, understanding, or skill and guides them through actions necessary to obtain the goal (Ramaprasad, 1983; Sadler, 1989)

The importance of this idea should have been obvious, yet I wasn't thinking about gaps when I first began looking into formative assessment.

So I was sitting here thinking about formative assessment and gaps when I flashed on the famous Howard Baker line about Richard Nixon:



What did the President know, and when did he know it?


That's formative assessment for gaps.








key words: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
formative assessment in a nutshell
formative assessment and Richard Nixon
Terminator



-- CatherineJohnson - 31 Jan 2006

---

GoodAdvice 01 Feb 2006 - 20:53 CatherineJohnson



I was just straightening up my computer files, and I came across this piece of fantastic advice on how to work word problems in algebra.

Unfortunately, I didn't record the author of this advice.

I think this is the text of an email Carolyn's husband, Bernie Johnston sent me back before we started writing ktm. But it may have been posted by Steve....(I'm inclined to think it's Bernie, not Steve, because Steve prefers 'isolate the variable' to 'undo what's been done to X,' assuming I read his response to Carolyn's post on the subject correctly.)

I'm sure one of them will recognize this. [update: Bernie wrote it]

This reminds me of a thought I had last week. For many many algebraic or calculus computations I have a phrase that runs through my head and tells me how to proceed. If I forget what to do I simply conjure up that phrase in my head. When I've tried to tutor people I've noticed that they frequently get stuck at exactly the point where the phrase would be useful but they have no phrase in their heads. When I think back upon where the phrase came from I realize that in many cases it came from my high school algebra teacher.

For example, when you start an algebra word problem, it's very difficult to know where to begin. There are a lot of words and the potential complexity of the problem is enormous. If you spend a lot of time using the front part of your brain to search for an appropriate path you may never find it. The phrase "when you don't know something, give it a name" is essentially the secret of algebra. This allows you to mentally grasp a particular thread of the problem which you can then follow through to the proper conclusion: the problem space has been cut way down in size.

Another one he gave me:

"When you have an equation with variables on the bottom, clear the denominators".

"Put the x's on one side and the numbers on the other."

"Undo whatever has been done to x."

These phrases are not singing rhymes but they are quite useful. The idea that certain procedures must be memorized or learned by rote is highly unfashionable these days but I think absolutely necessary.

words to remember

When you don't know something, give it a name.

When you have an equation with variables on the bottom, clear the denominators.

Put the x's on one side and the numbers on the other.

Undo whatever has been done to x.



words to remember from Vlorbik

Include the units.

Word problems have word answers.




V is right; including the units & writing word answers to word problems this is a VERY good habit to get into, right up front. I'm forcing myself to remember to do this.

Interestingly, Christopher isn't hugely resistant to including the units. I thought he would be, because he's resistant to everything.

Just goes to show how distant the middle-school brain is from the grown-up brain. Christopher seems to view 'including the units' as Obviously Something A Person Should Do.

I wonder if it's the relative hyperspecificity of the child's brain. He may feel like an answer of '5,' when what is meant is '5 cents,' really truly isn't 5 cents.

Don't know.






key words: good advice on algebra word problems good advice on how to solve algebra word problems
understanding basic algebra moves (& Comments)
good advice on solving algebra word problems

-- CatherineJohnson - 01 Feb 2006

---

TimeTimer 08 Feb 2006 - 19:59 CatherineJohnson



My Time Timer came today.

So far, I love it.

I ordered it because I've always been drawn to Time Timers in special needs catalogues, and because The Organized Student, by Donna Goldberg, says students need to be directly taught what time is.

That struck a chord. Like your basic middle schooler, I don't really know how much time any given task takes to do, either.




my problems and welcome to them

One of the Stupid Things I've been doing for — oh, the last year or so — is going to bed too late because I start doing math too late, and can't stop.

Many people would look at this problem and say, "Why don't you start doing your math earlier?"

Good question.

For some reason, I always plan to start doing my math earlier.....and sometimes I do do my math earlier.

But then, somehow, even when I do start my math earlier, I still end up going to bed too late.

This is why I need a Time Timer.



how long is a nap?

OK, so there I am, sleep-deprived & sitting at my desk facing massive piles of Stuff that needs managing.

And I'm tired.

I'm so tired I obviously need to take a nap, BUT I don't take a nap because I DON'T HAVE TIME TO TAKE A NAP....

And so, tragically, I remained rooted at my desk, getting nothing done, because I'm too tired to get things done but I don't have enough time to take a nap because I have too much stuff to get done, etc.

So today, contemplating my groovy new Time Timer, I decided: let's just SEE how long it takes to take a nap.

I took it upstairs with me, set the dial for 30 minutes, got in bed & went to sleep.

Fifteen minutes later I woke up.

Fifteen minutes.

That's not very long.

I can easily spare 15 minutes to take a nap when I'M NOT GETTING ANYTHING DONE ANYWAY.



why do I need a Time Timer for this?

In theory, I could use an ordinary analog kitchen timer, as Google Master pointed out.

Sure, a Time Timer has obvious advantages.

A Time Timer is almost silent; a kitchen timer ticks loudly.

A Time Timer has no alarm when time runs out; a kitchen timer is designed to blast you out of your skin.

Still, these are details. There's no logical reason I have to have a Time Timer instead of a kitchen timer.

Except: the very fact that I have not been able to bring myself to use a kitchen timer as a Time Timer is undoubtedly evidence that I belong to the class of persons who would benefit from the purchase of a Time Timer.

(key words: environmental dependency; frontal lobe function; ADHD ... in case you were wondering)



snippets from the Time Timer materials:

"Since using the Time Timer, my meetings have never been more efficient or effective. People actually want to attend because I don't waste their time."
- Corporate Department Head

"...perfect idea for people with alzheimers disease who constantly ask their caregivers 'how much longer' type questions..."
- Family Member/Caregiver

"I have seven students (six with autism and one who has Downs Syndrome.) I like using the Time Timer with my students because it does not disturb the others, some of whom are extremely noise sensitive."
- Special Education Classroom Teacher

"The Time Timer really helped me keep track of time at my AP tests."
- High School Student

The booklet says Time Timers are good for timing time-outs, transitions, and 'how much play-time is left.'




Time Timer and motivation

I think the Time Timer is going to help.

Christopher definitely has no concept how much time things take. He'll tell us he has 'nothing' for homework, when it's really 'something'; he just has no clue. I have no clue, either, but I'm at a higher level of cluelessness, to paraphrase Charles. THE ORGANIZED STUDENT suggests using the Time Timer to teach kids how long homework takes, and that's what I'll do, for Christopher as well as for me.

So far today I've seen that the Time Timer has a useful anti-procrastination effect.

I'm in 'waiting' mode at the moment — waiting for phone calls, waiting for feedback, waiting to see what comes next — it stinks.

While I'm always inclined to do what I want to do instead of what I'm supposed to do, Waiting Mode makes everything much, much worse. Waiting Mode makes even structured procrastination hard to do. Since half my productivity is based on Structured Procrastination, this is bad.

So this morning, I set the Time Timer for half an hour.....and then I did productive stuff for half an hour.

The reason I could do productive stuff for half an hour, instead of spinning my wheels NOT thinking about the telephone, was that I could see how fast that half hour was passing me by.

I didn't want to lose it.





My Time Timer isn't nearly this beautiful.



some books that have changed my life
the answer to all of Doug's problems
productivity question
what is an hour? Time Timers
my Time Timer came - how long is a nap?
Time Timer says no!



-- CatherineJohnson - 08 Feb 2006

---

AlphaSmartReducedPrice 23 Jul 2006 - 11:18 CatherineJohnson



I talked to the folks at AlphaSmart today & learned that the price has been reduced 30%. $199 (which is what I paid for mine years ago) down to $139.

The price is reduced because the company may discontinue AlphaSmarts; the woman on the phone wasn't sure.

This news prompted me to buy one for Andrew on the spot. (Impulse purchase alert.)

I hope they don't discontinue the AlphaSmart, but the possibility that they might is reason to buy one before they do, not reason to move on to the new, improved Neo or Dana (though the Neo probably is an improvement).

Ed bought a Dana as soon as it came out and has had problems. I can't remember now whether his problems — losing his research notes from a trip to France — were the machine's fault, or his, but I have a memory the problem was in the machine...

UPDATE 7-23-2006: The original AlphaSmart is no longer shown on the site. Now they're just selling the Neo for $249 and the Dana for $429. I should have bought another AlphaSmart while I had the chance.

When I turned on my AlphaSmart for the first time in at least 2 years last weekend, everything was still there where I left it.

I'd guess that whatever bugs the Dana had at first have been worked out, but I know the AlphaSmarts can live in a backpack.

I also got a new keypad for 25 bucks, AND — once you get going with a completely un-thought-through semi-major purchase, you may as well go for broke — I also purchased two 10-dollar cloth slip covers so as to avoid a repeat of the gummy keyboard mishap.

I'm thrilled Andrew will have his own machine. He can be liberated from doing his addition problems at school with stamps and inkpad. Talk about inefficient.



Neo

from the website:

Features:

Neo is a rugged and lightweight tool that can be used anywhere, with 700 hours or more of operation on 3 AA alkaline batteries or 200 hours on a charge. Instant on/off and autosave eliminate startup delays and accidental data loss.

Affordable and expandable.

Neo offers the lowest cost of ownership compared to other computing technology. Plus, with the extensible SmartApplet architecture, new functionality can easily be added so you can get more from your Neo investment.

Connectable.

Easily synchronize data with a home, classroom or office PC.

Built-in word processor.

Easily synchronize data with a home, classroom or office.

AlphaWord Plus, a full-featured word processor that provides:

• Eight active file spaces for one-key file access
• Named files for convenient file management
• Spell-Checking and Thesaurus
• User dictionary for adding additional words and terms
• Linked files for rubrics, homework instructions, or reference materials
• Find/replace and word count
• Spanish-English word lookup
• Built-in help system for quick access to command reference

The large screen and new font technology display up to twice as much text as the AlphaSmart 3000. Students can save hundreds of pages of text with room for SmartApplets “ software programs extending classroom versatility.

prices

• AlphaSmart $139
  
• Neo by AlphaSmart $249
  
• Neo Rechargeable $269
• Dana by AlphaSmart $379 new price: $429
  
• Dana Wireless $429
  

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue
the joys of primitive computing
the joys of primitive computing



-- CatherineJohnson - 10 Feb 2006

---

PrimitiveComputing 15 Feb 2006 - 01:44 CatherineJohnson



At least 2 ktm Contributors have ordered AlphaSmarts since I started obsessing about the things last week.

No question I missed my calling in life. I was supposed to be a Travelling Salesman.

This reminds me of the time my mom and I interviewed her Uncle George, who was the patriarch of the family, to the extent that we had a patriarch, which we didn't.

Uncle George was an engineer. He worked all over the world, in Saudi Arabia, South America — everywhere. He has incredible stories of his wife giving birth in the middle of South American revolutions.

Anyways, we were talking about his father, my Grandad McCammon, a Methodist minister who was president of the first Methodist college in Illinois.

Uncle George said (paraphrasing), 'Dad wasn't really a religious man. He was a salesman.'

I just about fell out of my chair.

I'd been wondering about that.

I like religion myself, and try to 'be religious,' but it doesn't come naturally. It's something I have to work at (and it tends to be something I put off working at.)

Tearing around the internet grabbing folks' arms and urging them to BUY THIS REDUCED-PRICE ALPHASMART NOW! is what comes naturally.

Blood will out.

In case you're wondering, the reason my Granddad McCammon became president of the first Methodist college in IL was that he'd raised enough money to build a Methodist Fellowship Center (I think that's what it's called) at the U. of Ill. Folks had been trying to raise the funds for awhile without much luck. When my Granddad took over, he got the money.

That's selling.

His reward was to be named president of the Methodist College.



On the Joys of Primitive Computing: The AlphaSmart Neo

While I was hopping from one AlphaSmart website to the next, I found this terrific essay on the joys of primitive computing by Kendall Clark.

I agree with every word that a) applies to me and b) I understand.

Part of being a savvy technologist includes staying on the perpetual hardware upgrade habitrail -- or so people too often assume.

Some of us, however, are done with hardware. I put myself through college, back in the day when Intel' 80386 CPU was a big deal, by building computers for aeronautical engineering students at the University of Texas, where I wasn't a student.

I am so over hardware, and I have been for more than a decade. I take pride in making my living from technology and doing so with very old, even decrepit hardware. My main server for five years has been an IBM Thinkpad I found in a dumpster. My only extravagance was to max out its RAM at 512 MB. My everyday system is a nice 15" Powerbook supplied by UMD. While OSX is nice, it's not exactly Linux on an Opteron.

I'm bored by hardware and a bit cheap about it, too.

All of which makes the fact that I've fallen in love with a new box (and a new kind of box) all the more curious. I'm talking about my new Neo by AlphaSmart, upon which I'm typing this weblog entry. Before saying more, thanks to Paul Ford for telling me about the Neo. Paul rocks.

Oddly enough, the Neo is basically a computer for school children. It's stunningly stupid and, well, primitive. I'm enjoying it so much, and being so productive with it, that it's got me thinking about what I'll call Primtive Computing and Power User Devolution.

The Neo is interesting not because of what it does or what features it has, but what it can't do and the features it's missing. It's all about one thing and one thing only: writing. [ed.: I wrote a huge part of the ANIMALS IN TRANSLATION proposal on my AlphaSmart, sitting at the picnic table outside the kitchen.] I'm most comfortable turning any task into a writing task (when all you have is a hammer...), which means I'm super comfortable with a primitive device that's really only good for writing.

Specs? I don't even know what kind of CPU this thing has, and I couldn't care less. The OS is some homegrown thing, apparently, I think the OS is some variant of PalmOS, but I don't really know. Or care -- cultivating ignorance about irrelevant details is part of the ethic here, I think. The word processor, the only app it has, is brain dead. Which means no distractions; it gets out of my way as well as venerable Word Perfect 5.1 for DOS used to -- a writerly experience I've only come close to replicating with Emacs.

The keyboard action is passable; not great, but no impediment. The screen is a measly six lines, and I'm finding it perfectly acceptable. Especially when it meaans that battery life -- powered by 3 AA batts -- is a remarkable 700 hours. Yes, 700 hours! The damn thing weighs all of 2 lbs, though it feels lighter. It's the ultimate road warrior's tool, at least if you think of a road warrior as a writer.

My joy at the sheer utlity of the Neo -- even at the rather inflated price of $250 [ed.: the original AlphaSmart is on sale for $139! Not $250!] -- leads me to wonder whether Primitive Computing is a trend of larger significance. Maybe the sign of a real power user is someone who's happy to get by with less, rather than ever insisting on more. Using the Neo is of a piece with the Hipster PDA and with Danny O'Brien's ethnographic observations about the ubiquity among the power set of text files as a first class organizational tool. [ed.: no idea what he's talking about]

The Neo is the closest I'm going to get to the kind of intentional simplicity that could lead to something like Walden on the job. (A chimerical goal, to be sure, since Walden was mostly about not working for The Man, rather than doing so sanely. Oh well!) ....

[snip]

As the man used to say back in the day: Highly Recommended.

The best thing about the AlphaSmart & the AlphaSmart Neo?

You can't hook them up to the internet.

Kendall Hunt
Mind Swap - Maryland Information and Network Dynamics Lab Semantic Web Agents Project
(Kendall Hunt is part of this)





AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue




-- CatherineJohnson - 14 Feb 2006

---

NewYorkStateMathTestGrade6Part2 30 Jun 2006 - 11:07 CatherineJohnson



update: oops

Ms. Kahl did send home state test prep material (see below). Apparently, Christopher has a PACKET.

Good!

He and his dad are working on the scale drawing right now. (see below) They're having a blast.

fyi, I think scale drawing is a fabulous assignment. Christopher is finally getting some extended practice using a ruler, and of course a scale drawing means fractions, ratios, & proportions.

It's true Christopher couldn't do this assignment on his own. (I'm feeling smug today because my fiercest competitor-mom, aka the 'Homework Nazi,' could not do this assignment. She told Ed, 'I didn't even know where to start.' Hah! I say Hah! because this woman is good. She's blowing me out of the water.)

However, Ed isn't doing this assignment for Christopher. He's helping.



update update

Ed is grumpy.

The scale drawing was fun for the first two hours.

The last two hours weren't fun at all.

"This is vacation."

"I don't see why they're giving this much homework on vacation."

"I have a huge amount of work to do myself; this took 4 hours."

"Christopher doesn't know anything about ratio."

"He doesn't have any conceptual understanding at all."

"He kept looking for formulas to do things."

"He didn't even know where to begin."

"He doesn't have a lot of natural ability in math." [ed.: Any assignment that ends with the parent deciding his child doesn't have any natural ability in math is the wrong assignment a far as I'm concerned]

"She has no idea how to structure an assignment." [ed.: ditto]

Over dinner Ed was pondering the 'packet,' which turns out to be a special Glencoe-produced 58-page booklet called "Mastering the Intermediate Level Mathematics Test: Diagnose — Prescribe — Practice Workbook."

Fifty-eight pages of items aligned to the New York state test, with no answers or solutions.

Apparently our job over 'break' is to Diagnose — Prescribe — Practice and also create our own answer key.

Well, thank God I've got Smartest Tractor lighting the way (pdf file).



back again

I've been off doing Career Stuff that's actually been quasi-fun.

I say quasi because my particular career seems to involve heaping loads of crapola^* (not a nice word on Sunday!), not to mention the occasional bolt from the blue.

The other day I called my agent and, when her assistant answered the telephone, said, 'Hi, this is Catherine.'

The assistant said, 'Who?'

That's the crapola aspect; I'll spare you & me both an extended account of the bolt from the blue part (though poor Caroline is slated to get an earful today....)

Anyway, I've been off because I was doing Career Stuff that was actually a blast.

This involved going into the city to meet with our kids' psychiatrist, Eric Hollander (that was the fun part), after which I decided to surprise Ed in his lair. (What is that woman in white doing in the picture?)

It had to be a surprise, because I didn't have my cel phone with me. I didn't have my cel phone with me, because I forgot my cel phone.

I need WAY more exercise.

So I decided to drop in unannounced.

Naturally that didn't work out; Ed wasn't there, and when he finally did get there he had five minutes to get to a faculty meeting.

So there was nothing left to do but visit the NYU bookstore and look at every single education title on both floors.



what are graduate students in Diane Ravitch's department reading?

Nothing by Diane Ravitch, that's for sure.

It was all constructivism all the time. Every last textbook.

That and feel-good books about heroic white teachers teaching poor black children — books like Small Victories: The Real World of a Teacher, Her Students, and Their High School. (I'm thinking a 'small' victory probably doesn't include teaching kids enough algebra to graduate from high school, but I don't know.) There were many of these books.

Until that visit, I hadn't realized that heroic white teacher saving poor black children must be an important fantasy element in ed schools today. I say fantasy element, because I'm pretty sure all of the teachers in all of the books were white, while all of the kids were black. Certainly Jaime Escalante was nowhere to be seen. (Of course, neither was Rafe Esquith, and I don't expect to see Our School turn up on the assigned reading lists any time soon, either.)

Perusing the offerings, you wouldn't know teachers teach math. Everything was about 'literacy' and 'authentic assessments' of literacy and the like. Which is probably just as well, considering.

There was one book that stuck out like a sore thumb: Techniques for Managing Verbally and Physically Aggressive Students. I think that was the title. This book was so unadorned by photos of Beaming White Teachers surrounded by Adoring Black Children that it was refreshing.

Leafing through the pages I found instructions on what a teacher should do when he is being strangled by a student.

The 2 or 3 books that did address math were constructivist all the way. Liping Ma was absent; John Van de Walle's now-classic hundred-dollar tome Elementary and Middle School Mathematics: Teaching Developmentally, Fifth Edition was present in abundance.

The funny thing was, the store management had stocked a bunch of food business textbooks just across the aisle from the ed books. There was a book on restaurant math — I think it was Math Principles for Food Service — that was pure direct instruction. No photos of smiling white teachers surrounded by black students yearning to succeed in food services, just stuff you need to know. Chapters on 'weights and measures,' 'portion control,' 'converting and yielding recipes,' 'production and baking formulas,' and 'using the metric system of measure.' If you're going to make it in food service, you're going to need some math. Seeing as how the first chapters cover addition, subtraction, multiplication, and division, apparently you're not going to learn any of this math in grade school.

Part 1 is titled: Using the Calculator.



upstairs, downstairs

So those were the texbooks, which are housed downstairs in the basement.

Upstairs, in the 'commercial' section, I found:

• Getting It Wrong from the Beginning: Our Progressivist Inheritance from Herbert Spencer, John Dewey, and jean Piaget by Kieran Egan

• John Dewey & The Decline of American Education: How the patron saint of schools has corrupted teaching and learning by Henry T. Edmondson III

• Trust in Schools: A Core Resource for Improvement by Anthony S. Bryk and Barbara Schneider

• What Great Teachers Do Differently: 14 Things That Matter Most by Todd Whitaker

AND

• Dumbing Us Down by John Gatto Taylor

A clean sweep.



New York state tests coming right up

In March.

Christopher's class took a sample test (pdf file) this week; only 2 kids scored a 4. Christopher thinks he got a 3. Apparently the teacher told them that any kids scoring a 1 or 2 would be moved down to Phase 2-3.

This is the Highly Accelerated, Algebra-in-the-6th-grade, Death March to Algebra-in-the-Eighth Grade Phase 4 extravaganza I've been banging on about. Only two of 19 children can score a 4 on the sample test and apparently there are enough kids in danger of scoring 1s and 2s that the teacher is talking about it in class.

So here's the scoop.

Christopher is studying algebra in the 6th grade, but he can't do percent. I pulled the Sample Test, which turned out to be the test Christopher's class took this week, and asked him about problem number 26:

On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.

Part A

What percent of the total number of cars were in the parking lot on Friday?

Show your work.

Part B

What percent of the total number of cars were in the parking lot on Saturday?

Show your work.

Christopher has no idea how to do this problem, in spite of the fact that he's just 'finished' the chapter on ratio, proportion, and percent in Prentice-Hall. (Says he 'froze up' on the test; expecting another D; etc.)



my vacation and welcome to it

We are on mid-winter vacation this week.

For my vacation, I will be teaching Christopher how to do percent.

I know how I'm going to do it. I'm going to use the Singapore-Saxon bar models and the Saxon-Dolciani percent charts.

I think I'm starting to get a feel for teaching-to-crammery, which is the skill middle school parents need most. If I've got 5 days to teach percent word problems to proto-mastery, I'm going to need bar models & charts (& possibly Saxon's brilliant starter W_P variables to boot).

If that were all I had to do this week, I'd be cool.

It's not.

I'm also going to have to figure out what's on the freaking test.

I read some guy last week complaining that Most Parents don't have the Sense of Responsibility it takes to find out what the state standards are.

Sure, sure; we all know about those Parents who don't have a Sense of Responsibility as defined by the people who write state standards.

How many parents fall in this category?

I'd estimate, conservatively, that perhaps 99% of all parents have zero interest in what the State Standards are.

The reason 99% of all parents have zero interest in what the State Standards are is that their Bayesian priors are telling them the State Standards are likely to be:

a) impossible to find

b) bunk

Given my household's limited common sense-y, my own attitude can be characterized as: 'Damn the Bayesian priors, I want those standards!'

Thus, I have now attempted to a) locate and b) comprehend my state standards.

Which means I am now qualified to tell you that all those irresponsible parents are correct. Spending your Sunday morning tracking down New York state standards (pdf file) is what Carolyn calls a FWOT.





See?



a visit to the mathematical reasoning strand!

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Students:

• apply a variety of reasoning strategies.
• make and evaluate conjectures and arguments using appropriate language.
• make conclusions based on inductive reasoning.
• justify conclusions involving simple and compound (i.e., and/or) statements.

This is evident, for example, when students:

• use trial and error and work backwards to solve a problem.
  
• identify patterns in a number sequence.
• are asked to find numbers that satisfy two conditions, such as
  n > -4 and
  n < 6.

That certainly clarifies things.



source:
New York state standards




the return of common sense-y

So forget about the New York state standards. If I need standards — and I do — I'll use California's.

My job now is to go through every page of the Sample New York state test, pull out the problem genres, and teach them to crammery.

I have one week to do this.

We're going to have to pedal, because we also have to help Christopher with the massive scale drawing exercise Ms. Kahl has sent home for the kids to do over vacation:

The Task: Stop daydreaming and design the bedroom of your dreams!

This project requires you to be creative and draw up the floor plans of your ideal bedroom. Will you have a big screen television, a walk in closet, or even a king sized bed? You will map out the blueprint for your room and show the furniture and items contained in our room from an aerial view in the form of a scaled blueprint.

The blueprints must contain at least two of each of the following geometrical figures:

• square

• rectangle

• triangle

• trapezoid

• paralleleogram

• circle

Oookaaaayyy!

Two trapezoids coming right up!

And two parallelograms!

In a 6th grader's dream bedroom!

Making those real world connections!



my vacation and welcome to it, part 2

Getting Things Done:

• analyze sample state test

• find out if Christopher can do any of the problems on it

• teach to crammery

• re-vamp book proposal, deal with inevitable assorted mishegoss sp?

• help Christopher construct highly complex scale drawing he can't possibly do on his own

question

You are teaching accelerated 6th grade math.

You give your class of 19 students a sample New York state standards test.

Only two children score a 4, 'exceeds state standards.'

Many of the children, who have just taken a test on ratio, proportions and percent, miss the percent question.

For mid-winter vacation you assign:

• daily 20-item problem sets of percent, ratio, and proportion problems ranging from simple calculations to word problem applications

     or

• a complicated scale drawing requiring two trapezoids and two parallelograms

Alright. It's 2:28, and I must go for my 45-minute aerobic walk-run. If I do this 6 days a week until I'm dead I'll be younger next year and, even better, I'll stop screaming at my kids.

So I'm going to do it.

Because I am a responsible parent!

When I get back I'll analyze the test. Then I'll break the news to Christopher that we're going to spend mid-winter break cramming math.

Farewell, Ms. Kahl! We who are about to die salute you!



update, update, update: Verghis speaks!

For the blueprint, why not have a square study desk whose top is decorated with (a) 2 trapezoids, (b) 2 parallellograms, (c)....

This should (1) satisfy Ms. Kahl's requirements and (b) blend nicely with the surrealism that pervades the math curriculum.

Don't you think?

Yes! I do think!








resources for grade 6

• Academic content standards for kindergarten through grade twelve, adopted by the California State Board of Education for mathematics

• Mathematics Content Standards

• David Klein's Practice Problems for California Mathematics Standards Grades 1 - 8 (excellent)

^* heaping loads of cr***** probably doesn't distinguish my job from most other people's jobs, I realize



pre-algebra is bunk
death march to algebra
NYU ed textbooks; NY math test
state test impending doom

cram school
teaching to crammery in middle school
the kind of kids who can be taught to crammery
free teach to crammery clip art

Glencoe Top Secret Test Prep
Amsco protects its 'customers

teachtocrammery


-- CatherineJohnson - 19 Feb 2006

---

AdviceFromATopHighSchoolStudent 21 Feb 2006 - 00:59 CatherineJohnson



Ed struck gold today.

He's interviewing students from Westchester County who are applying to Princeton.

Today he interviewed two amazing students, both of whom are headed for math-related careers.

Both students have Math Brain parents, and both are Chinese-heritage immigrants, which I think is OK to say, given articles like this one. ($) They went to school abroad during their early years.

One of them gave Ed an amazing piece of advice.

He said his dad had complained all the way throughout his school years here in the U.S. that math was not being taught conceptually.

He countered this by having his son derive every formula he used.

The boy said this had helped tremendously, that he now has a great deal of conceptual understanding of math. (He's in BC calculus.)

I think that's brilliant.

My challenge, now, is figuring out how to teach math in the tiny pockets of time we have that aren't devoted to school.

Grade school was easy. I taught my own separate curriculum. Saxon Math: every lesson, every problem in every problem set.

We had the time, and we did it.

There's no time now. Christopher goes to school all day, then has homework to do at night, and his brain is consumed by thoughts of girls and lunchroom rivalries with his friends and he's rebellious, resistant, and emotional. (Apparently, middle school means mood swings, something I didn't know going in.)

Carolyn and I started writing this blooki nearly a year ago saying reactive teaching was a bad thing.

Now I have to figure out how to do reactive teaching that works.

This may be the way to go.



update: an example from Saxon

Susan asked about what deriving a formula means.

I'm not certain I know, but I think I can give an example from pre-algebra.

Saxon 8/7 teaches the 'formula' for finding the area of a trapezoid thusly:

To me — and let me know if I'm wrong — that's 'deriving a formula,' or close to. The student has to know that a trapezoid can be divided into two triangles, and that you can add the areas of the two triangles together to get the area of the trapezoid.

In contrast, Prentice-Hall teaches the formula this way:

To us this is the same thing, but to an 11-year old just starting out it's not.

Saxon gives kids a lot of practice with the un-simplified version before anyone moves on to the standard, simplified expression.


advice from a top high school student
rote knowledge in Everyday Math



-- CatherineJohnson - 19 Feb 2006

---

WhyDontSchoolsTeachDimensionalAnalysis 23 Feb 2006 - 15:11 CatherineJohnson



Does anyone know?

Can't remember if I've mentioned that last summer Ed and I spent some time with his cousin, who began life as a Ph.D. researcher in chemistry and is now a chemistry teacher at Evanston High School.

About five seconds after we'd started talking he told me the Big Problem with his students was that — ALL TOGETHER NOW — THEY CAN'T DO FRACTIONS.

He also said, more specifically, that they don't understand ratio and proportion.

His solution is to teach them unit multipliers.

Which brings me to my question: why don't middle school textbooks teach dimensional analysis?

If unit multipliers are so easy that a chemistry teacher can teach them to incoming students and still have enough time left over to teach chemistry, that's a strong recommendation.

I just taught Christopher unit multipliers (Lesson 50 in Saxon 8/7) for the second time. He's obviously forgotten our first go-round, which is to be expected.

I taught them again today, because he had just missed this question on his GLENCOE MATHEMATICS Grade 6 Mastering the Intermediate Level Mathematics: Test Diagnose - Prescribe - Practice Workbook:

Esther was traveling down the highway at the rate of 75 miles per hour. How far would she travel in 3 hours?

Show your work.

Christopher showed his work.

He divided 75 by 3 and got an answer of 25.

This is one of the consequences of never, ever assigning word problems....the kids fail to develop the habit of asking themselves whether the answer they just got makes a lick of sense.

Still, even if he had spent some time this year developing good habits, questions like these are confusing for kids.

I've always been able to figure questions like this easily, but I've discovered that there are certain questions that confuse me....like Christopher, I can't tell which number I'm supposed to be dividing into which. I wish I could remember the problems (the next time I see one, I'll write it down). In any case, I'm sympathetic.

So I pulled out Lesson 50.

Christopher was ticked off. He'd already done his KUMON pages, one page of Megawords, corrections to his other pages in Megawords, and two pages in the Glencoe test practice book. He was in no mood to do a 'lengthy' Saxon lesson on unit multipliers.

I told him I'd truncate the lesson.

Then I asked him if he knew what 'truncate' means. (No.)



unit multipliers, short and sweet

I can really see the Big Deal with choral response.

It's way faster, and it does tend to 'pull' a resistant kid's attention, or at least it did today, with Christopher.


1

I started by reminding him that any number other than zero, divided by itself, equals 1:

Me: What is 2 divided by 2?

Chris: 1

Me: What is 3 divided by 3?

Chris: 1

Me: What is 1,000,231 divided by 1,000,231?

Chris 1


2

Then I reminded him that anything multiplied by 1 remains the same number.

More choral response:

Me: What is 2/3 times 3/3?

Chris: 2/3

Me: What is 1/6 times 5/5?

Chris: 1/6

Me: What is 100 times 100/100?

Chris: 100.


3

Next up: 12" divided by 1' is also 1.

He was kind of taken with that idea (and I bet he had a glimmer of memory that he'd seen this before....) In any case, he instantly got the idea that 1 foot divided by 12 inches is 1.

I wrote all of these down on paper, so he could see them while he was giving his answer.

Me: What is 12" divided by 1'?

Chris: 1

Me: What is 36" divided by 3'?

Chris: 1

Me: What is 24" divided by 2'?

Chris: 1

Me: What is 1.5' divided by 18"?

Chris: 1.


4

Then we came to the idea that you can divide the unit by the unit, without dividing the number of units.

Naturally this led to the question of whether you could divide body parts by body parts, especially super-private body parts.

I said, yes you could, just so long as you were using those body parts as a unit of measurement.

Hysterical laughing, etc.

Then I pointed out that:

a) multiplying a number by 3'/1 yard is the same thing as multipying a number by 3/3

and

b) 3'/1 yd is the same value as 1 yd/3'

At this point I had him tell me 'reverse unit multipliers,' as Saxon does.

Me: How do you write a unit multiplier for feet and yards?

Chris: 3'/1 yd

Me: And?

Chris: 1 yd/3'

Me: How to you write a unit multiplier for feet and inches?

Chris: 1'/12"

Me: And?

Chris: 12"/1'

and so on


5

At this point the lesson became purely procedural, but that's the best I can do under the circumstances. I'll try to fill in conceptual understanding.....at some point.

The beauty of unit multipliers for a student just learning unit conversions is that you never have to think about Do I need to multiply or divide?, which is where Christopher went wrong on the practice test question.

With unit multipliers you're always multiplying; it's just that some kinds of multiplication, i.e. multiplication by a fraction, are actually division.

This was the final 'script':

I started with 'Twelve inches equals how many feet?''

[ed.: oops, I left out a step. I also had him tell me, several times, where you would put the units so as to cancel out the 'unwanted' unit - in the numerator or the denominator? He got every one right.]






tomorrow & the next day

I don't think he'll be able to set up a unit multiplier and do a unit conversion start to finish tomorrow, though I'll check to see if he can, just out of curiosity.

We'll use this same script (or a new, improved version — whatever occurs to me on the spot) and we'll do maybe 5 problems tomorrow, including the problem he missed on the practice test.

I'll stress tomorrow that using unit multipliers protects you against choosing the wrong operation.

I didn't stress that today, and I should have.

I'm also going to show him how to use two unit multipliers in a row, and how to use unit multipliers to find out how many square inches there are in one square foot.

I don't know whether I'll have him practice those two uses tomorrow, but I want him to see them because he'll realize how much easier his life is going to be once he's mastered unit multipliers.



update

I'll show Christopher this problem from Math Forum:

I'm also going to tell him Caroline's line about the guy who realized that a fraction is a division problem you don't have to do.

update: Google Master reminded me of this example of a dimensional analysis from Elements of Physics, edited by Alpheus W. Smith and John N. Cooper, McGraw-Hill 1979. ISBN 0070586349.



a section of Donna Young's lesson

This is cool: note: you may have to go to her homepage & search for the lesson on unit multipliers)

udpate: article on unit conversions

Haven't read a word of this, but thought I'd post it: Unit Conversions by Ben Logan (pdf file)

Abstract

Conversion between different units of measurement is one of the first concepts covered at the start of a course in chemistry or physics. Unfortunately, unit conversions are also one of the most confusing concepts to many students. Because unit conversions are used throughout the sciences, it is crucial to understand them from the start. Hopefully, I can help clear up some of the confusion surrounding this topic. Please email me with questions, comments, or corrections.

dimensional dominoes - announcing Dan's dimensional dominoes
Dan has added new worksheets
Dan K's "dimensional dominoes" (PowerPoint worksheets)
dimensional analysis at Math Forum (includes other links at Math Forum)
Dr. Ian talks about fractions & units
dimensional analysis from Elements of Physics, edited by Alpheus W. Smith and John N. Cooper, McGraw-Hill 1979. ISBN 0070586349
Donna Young's online lesson in unit multipliers (you may need to start at her homepage and search)
a way to teach dimensional analysis
why & how to use dimensional analysis
rough script for teaching dimensional analysis
another triumph for dimensional analysis
dimensional dominoes emergency
report from the unit conversion wars



-- CatherineJohnson - 20 Feb 2006

---

RaysArithmetic 22 Feb 2006 - 23:35 CatherineJohnson



I've just discovered a series of arithmetic textbooks from the 1800s while cruising geometry workbooks at christianbooks.com. (fyi, Charles put me on to christianbooks, which has the apparently-out-of-print Saxon Physics for a good price. I'm still mulling that one.)

According to the publisher, Ray's Arithmetic was the most popular arithmetic series in the 1800s, selling more than 120,000,000 copies.

Does anyone know anything about these books? Have you used them? Seen them? Read them?

The books have glowing reviews at Amazon. My ADD TO BOOKBAG finger is starting to twitch.

The 8-volume set is $100, but you can buy individual titles as well.

Christianbooks has posted 14 pages of Ray's New Practical Arithmetic online.


titles
Ray's New Primary Arithmetic
Ray's New Intellectual Arithmetic
Ray's New Practical Arithmetic
Key to Ray's New Arithmetics (Primary, Intellectual)
Ray's New Test Examples in Arithmetic
Ray's New Higher Arithmetic
Key to Ray's New Higher Arithmetic
Ray's New Arithmetics-Parent Teacher Guide








uh-oh

I'm going to get myself in serious trouble.





Fortunately, the listing appears to be closed.

I've sent an email to the seller just to make sure.




sources:
Amazon
Biblical Worldview Learning Center
Farm Country General Store
Homeschoolingbooks.com
Mott Media

-- CatherineJohnson - 21 Feb 2006

---

TheNightlyHomeworkBattle 27 Feb 2006 - 19:24 CarolynJohnston


Is anyone else finding that evening life with their middle schooler has become a desperate, pitched battle to get them to do their homework?

I've had friends with older kids go through this. I have one friend who was talking about cleaning out his child's bedroom of all distractors, including the bed, so that there was nothing left but him, his desk, his book and his pencil. He suspected that even with such sensory deprivation, his child would be unable to settle down and get his homework done.

It's been 5 years since then, and the same kid is now a senior in high school doing very well and accepted to the (engineering) college of his choice. But 5 years ago, that kid was having as much trouble with his homework as could be imagined. Now he and his friends have study groups at his house, and sit around and speak French to each other. I cling to his example; perhaps there is hope for us as well.

Another one of Ben's friends in 6th grade also has fits and rages when it's time to do homework. His mother has to take him down in a tackle to get him to do his homework, every night. He never wins the fight, never never never; she knows her behavioral theory; it doesn't matter. I suppose the fight simply delays the onset of homework; that's what's reinforcing about it.

Another friend with a slightly older child (8th grade) doesn't fight with him to get him to do his homework, and he doesn't do it. His grades aren't up to snuff. She asks why he can't simply take responsibility for himself and do what he's supposed to do, when he knows perfectly well what it is; I tell her I don't know why, but he can't -- no executive function, that's just how it is -- so she's just going to have to ride him. He'd much rather argue than work, so it won't be fun for her, I'm afraid.

It wasn't the same in elementary school. Yes, Ben fought to avoid having to do homework, but he's suddenly become much more vociferous and strong-willed and rude about it. The difference is exponential; Ben this year is the T-Rex of homework avoiders.

I can't help but note that all of my data points are boys. Are girls, too, fighting at this middle school age to avoid having to do homework? Please tell me they are. I know I'm not alone in fighting the nightly fight, but I'd hate to think that the whole country is full of angry boys every night, and of girls getting down to work with sharpened pencils, their highlighters, and a good attitude.

Not that I wish ill on those of you with girls, but I just couldn't take it.

-- CarolynJohnston - 23 Feb 2006

---

FreeTeachToCrammeryClipArt 27 Feb 2006 - 19:35 CatherineJohnson



from the School Discovery Zone








if you prefer black and white:





cram school
teaching to crammery in middle school
the kind of kids who can be taught to crammery
free teach to crammery clip art

teachtocrammery

-- CatherineJohnson - 23 Feb 2006

---

DimensionalAnalysisWordProblemsAndAnswers 26 Feb 2006 - 18:11 CatherineJohnson



I spent some time yesterday cruising the internet looking for dimensional analysis problems for Christopher.

They're hard to come by.

Here's a pretty good selection for kids in the 4th to maybe 8th grade range. (Actually, you could use these problems with any beginner.)

I've included everything inside this post, but I've also created separate pages that ought to be easy to print out, using the 'printable' tab at the top of the screen. (I think these two pages are editable by everyone, so you ought to be able to add your own problems, take problems away, increase or decrease the space between items, etc.

For future reference, all of these pages can be found in math lessons and in the Book-Style Index.


dimensional analysis word problems to print
answers to all 14 problems
answers to Gisele Glosser's problems only



10 problems by Gisele Glosser

1 kilometer = 0.6 miles
1 mile = 1.6 km
1 fathom = 6 feet
1 meter = 3.3 feet
1 kilogram = 2.2 pounds
1 mile = 5280 ft
C = 5/9 • (F – 32)
1 m = 100 cm



1. A dolphin dives to 24 feet. How many fathoms is this below the surface of the water?

2. The deepest part of the ocean is the Marianas Trench; its depth is 11.03 km. How many feet is that?

3. The largest whale measured 33.27 meters in length. How many feet is this?

4. The average temperature of the oceans is 3.9° C. What is this in Fahrenheit?

5. The highest tides on planet Earth occur near Wolfville, in Nova Scotia’s Minas Basin. The water level at high tide can be as much as 16 meters higher than at low tide! How many feet is this?

6. Sunlight only reaches 30 to 120 meters under the waves. Convert this to feet.

7. A blue whale can weight up to 280, 000 pounds. That’s larger than the largest dinosaur. How many kilograms is that? (Round your answer to the nearest whole kg.)

8. Previous studies suggest that the expected global warming from the greenhouse effect could raise sea level approximately 100 centimeters in the next century or two. What is this in feet?

9. If all the ice in glaciers and ice sheets melted, the sea level would rise by about 80 meters, or how many feet?

10. The longest river is the Nile River, in Egypt, Africa. It is 4,160 miles long and flows northward into the Mediterranean Sea. How long is it in km?

copyright © 2001 Gisele Glosser (from Math Goodies - can’t find URL, but Gisel Glosser seems to have worksheets posted at schoolhousetech)



2 problems by Donna Young

1. Convert 640 ounces into pints.

2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?



2 problems from Chemistry 192

1. How many seconds are there in 1.2 weeks?

2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?




Carolyn's real-life problem

Carolyn & Bernie are going to buy a new car, which they will drive 13,000 miles a year.
They've narrowed their choices down to a Honda Civic or a Dodge Caravan.
The Honda gets 35 miles per gallon.
The Caravan gets 25 miles per gallon.
If gas is $4 per gallon, how much money will they save on gasoline each year driving the Civic?




problem from Lesley Stevens

An example of the kind of math my job requires:

2.2 pounds = 1 kilogram
1 gram = 1000 milograms
1 liter = 1000 milliliters

You need to administer an IV drug to a dog.

Part 1:

The dosage is 20mg per kg of body weight. The drug is in a solution of 5g per 1 Liter. The dog weighs 66lbs. How many mL of solution do you need?

Part 2:

IV drugs can be administered using a drip set which delivers a set quanity of liquid at an adjustable rate.

You need to administer the drug over a period of 4 hours. Your drip set delivers 1mL of liquid per 8 drips. At what rate (in drips per minute) do you need to set your drip set?




problem #3 from Saxon 8/7 Lesson 96

The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?







answer keys

answers to Gisele Glosser's problems:

answers to Donna Young's problems:

1.Convert 640 ounces into pints.
640 oz/1 x 1 pt/16 oz
40 pts

2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?
1000 pounds/1 x 20 shillings/1 pound
20,000



answers to Chemistry 192 problems:

1. How many seconds are there in 1.2 weeks?

1 week = 7 days
1 day = 24 hours
1 hour = 60 min
1 min = 60 seconds
1.2 weeks x 7 days/1 week x 24 hrs/1 day x 60 min/1 hr x 60 s/1 min = 7.3 x 105 seconds

2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?
Given: 37 grams
Want: lbs
Know: 453.59 g = 1 lb

37 g x 1 lb/453.59 g = 8.2 x 10-2 lb

Chem 192 problems:
Chemistry 192 Worksheets
Chemistry 192 worksheet
Chemistry 192 answer key




problem #3 from Saxon 8/7 Lesson 96

The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?
2000 miles x 1 gal/25 miles x 1 tank/16 gal
5 tanks



dimensional analysis word problems & answers
dimensional analysis word problems to print
answers to all 14 problems
dimensional analysis word problems answer key only for Gisele Glosser's problems



-- CatherineJohnson - 23 Feb 2006

---

HenryDavidThoreau 02 Mar 2006 - 21:41 CatherineJohnson



What does this mean? (I don't understand the line about 'steering within the fewest points of the wind.)

He is the best sailor who can steer within fewest points of the wind, and exact a motive power out of the greatest obstacles.

- Henry David Thoreau

-- CatherineJohnson - 28 Feb 2006

---

RatioProblemFromTheBbc 01 Mar 2006 - 01:27 CatherineJohnson




What is ratio?

Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another. For example:

• Use 1 measure screen wash to 10 measures water
  
• Use 1 shovel of cement to 3 shovels of sand
  
• Use 3 parts blue paint to 1 part white
  

Ratio is the number of parts to a mix. The paint mix is 4 parts, with 3 parts blue and 1 part white.

The order in which a ratio is stated is important. For example, the ratio of screenwash to water is 1:10. This means for every 1 measure of screenwash there are 10 measures of water.

Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all.



3 parts blue paint to 1 part white paint = is ¾ blue paint to ¼ white paint.

If the mix is in the right proportions, we can say that it is in the correct ratio.






"BBC Skillwise enables adults to improve reading, writing and number skills."



This mission - improving the basic skills of adults - probably means Skillwise is going to be a good resource for math problems real people use in the real world: the kinds of problems you can show a child - or a Washington Post columnist - who's wondering out loud whether he'll ever 'use math' once he's out of school.







more real-world math

from the Delta College Teaching/Learning Center:



Ratio and Proportion in Nursing Math

Proportion is often used to calculate a dosage. Suppose a drug comes in tablets of 150mg. The dosage ordered is 375mg. How many tablets are needed? Here is the problem:


                


To Solve for x, we have to cross-multiply:

                    
                             

                

                            x = 2.5 tablets


I don't know about you, but I would like any nursing staff taking care of me & mine to know this stuff cold.


Ratio And Proportion in Nursing Math: Sample Problems & Answers

more Nursing Math



-- CatherineJohnson - 28 Feb 2006

---

CoolDimensionalAnalysisProblemFromSaxon87 01 Mar 2006 - 17:15 CatherineJohnson




The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?
(source: Saxon 8/7 Lesson 96 page 660 #3)







printable version


keywords: dimensional analysis unit multipliers

cool dimensional analysis problem Saxon 8/7 L96 #3
printable dimensional analysis problem Saxon 8/7 Lesson 96 #3
printable solution to Saxon 8/7 Lesson 96 dimensional analysis #3



-- CatherineJohnson - 28 Feb 2006

---

GraphPaperForOurTeachers 09 Mar 2006 - 17:22 CatherineJohnson



I found a terrific cache of graph paper online this weekend at a site called Mathematics Help Central — perfect for homework or for taking notes in class.

Mathematics Central is a lot of fun:

Are you stumped on a math problem? Help is on the way! Mathematics is a challenging subject that mystifies many. Imagine the problem as a complicated puzzle that you must solve. All the pieces must fit in order for you to realize your success. This web site is devoted to helping you through your math worries! Take a look around! There's plenty of lecture notes, helpful links, personally developed graph paper, and a little section about why I love math. Enjoy!

She's posted her lecture notes.


From her 'About Me' section:

I have not always loved math. In fact, math does not come easily for me. I have to work hard for it! I suppose that's why I find it so challenging.

I am a college student enrolled full time at a southern university pursuing a major in mathematics. I am also a divorced mother of two beautiful little girls. In February 1998, (Friday the 13th of all days), my husband of five years and I were separated. At the time, my oldest daughter was almost four years old, and I was six months pregnant. I was hurt, devastated, and miserable. The divorce was painful. My self-confidence was nowhere to be found. I returned home to live with my parents because I was a stay-at-home mom who had devoted most of my time to loving my family, and simply didn't have a way to make it on my own.

My parents encouraged me to go to college. I was excited about the idea, yet a little intimidated also. It had been years since I graduated, and I just wasn't sure if I could do it by myself with two small children. My parents assured me that they would help me in whatever ways they could, even though both are disabled and are experiencing increasing health problems to date. With much thought, a little preparation, and a lot of guts, I enrolled for classes during the spring semester at our local community college.

My father, and many others I had talked to, encouraged me to go into an engineering or computer related field with a concentration in mathematics. I had never had any trouble keeping my checkbook balanced--that is when I had money in it! My first class in college was Intermediate College Algebra. I was excited and ready to go. I thought to myself, "This should be pretty easy. Probably mostly review from high school."

Boy, was I wrong! When my professor began reviewing pre-requisite material, I began to panic! I didn't remember anything! (And my teacher was so tough!) I looked for help anywhere I could find it, and I even had to ask my 15 year old nephew for help with fractions and equations.

USA Today mentioned her in a story, too.



the graphs

There are 9 different forms, each in color or black and white.


Here's a terrific homework form for kids learning functions:

"Three graphs per page with plenty of room to work problems, also."


There's space for equations & calculations, and an already-made chart for the 'input' and 'output' numbers. I love it.

(He obviously took a screen shot before he'd finished; the actual sheet doesn't have the funky mis-matched lines on the graphs.)

Here's another:




"Eight graphs per page. This graph paper is best when you have a lot of graphs to make. The graphs are
small without numbers."



This one might be great for hand-outs —





"Large x-y Co-ordinate Graph Paper. This graph paper is a must for any student doing extensive
graphing. This graph is perfect for graphing class notes quickly. The x and y axis and the rectangular
co-ordinates are already drawn to speed up the homework and study process! The minimum and
maximum x and y values are blank so that you can scale the graph to fit your needs."



Graph paper for college geometry:




This one is an original!!! This graph paper was designed for College Geometry where proofs are
involved. You can fit two proofs to a page. The "Given" and "To Prove" are labeled beside the
Statements/Reasons tables, and there is room to draw your given geometric figure. This was a
HUGE time-saver for me. The headings and color scheme are the same as Form 5A. The paper is
probably suitable for for other types of mathematics proofs, but it was not designed for that purpose.



Graph Paper Printer Program

He's also got a 'Graph Paper Printer Program' available for download.

I tried to download it, but didn't know how to work it. Apparently you're supposed to 'paste' it into your word processing program?

I have no idea how one would do that, sad to say.






'graph paper' for word problems?

I'm thinking about creating some kind of how-to-solve-word-problems template for Christopher.

He has essentially zero idea how to tackle even a simple word problem, and the state test is on March 14 - 15.



polar coordinate graph paper (pdf file)


-- CatherineJohnson - 06 Mar 2006

---

HowDoYouTeachChildrenToSolveWordProblems 03 Apr 2006 - 03:15 CatherineJohnson



I could use some advice.

The New York State test is coming up on March 14 - 15.

The kids aren't doing well on the sample tests they've taken. Only 2 out of 19 in Christopher's class got a 4 - 'exceeds state standards' - on the one they did last week. Two 4s in an 'accelerated' math class. [update: turns out that's 2 out of all 3 Phase 4 classes, which is close to 60 kids. Two of sixty children in the Irvington Middle School accelerated math class exceed state standard on a practice test.]

It's a joke.

Christopher got a 3 on the sample test, and of course I'm determined that he earn a 4 on the real one; don't ask me why. Same reason people climb Mount Everest, probably. [update 4-23-2006: no, that's not why. Christopher's 4's on NY state tests to date are at odds with the grades he receives in his classes at Irvington Middle School. Part of our new data warehousing initiative involves comparing grades in school to scores on state tests.]

Mount Everest aside, this is a golden opportunity for Christopher finally to learn something about solving word problems. I've mentioned several times that they've done essentially no word problems this year; I'm thinking they must not have done many in 5th grade, either, though I don't recall.

Saxon 6/5, I do recall, does not stress word problems. Or, rather, Saxon teaches word problems very, very carefully, slowly, and deliberately. Kids learn different genres of problems, such as 'problems with equal groups' and practice one-step versions of those problems to mastery. I don't think they do two-step problems until Saxon 7/6 or maybe even 8/7 (though I could be wrong).

This always used to bother me about Saxon. Singapore Math has two-part problems starting in 3rd grade or possibly even earlier. However, now that I'm almost done with Saxon 8/7 myself, I can see the point.

Back when I wrote my dissertation (on 1950s film comedy, no less) I talked about the 'narrational presence' in movies, by which I meant the implied director or author hovering over the proceedings. The narrational presence in a Saxon book is a kind and intelligent person who really, really wants you to learn math - and doesn't expect your parents to hire a tutor or send you to cram school to see to it that you do.

So Saxon builds word problem solving skills slowly, incrementally, and logically. After awhile you're doing two-step and three-step word problems, you're doing them easily, and you're doing them without your parents ever having spent $300 to attend a 30-hour weekend seminar on how to understand changes in math instruction.

John Saxon must have had broad shoulders, because he sure carries the load.

Unfortunately that's not what we need here.

We need teach-to-crammery problem-solving strategies, and we need them today.

We need teach-to-crammery problelm-solving strategies today because the state test has an open-ended question section that's a killer. It's wall-to-wall story problems, none of which Christopher has ever seen or done. He got 20 out of 25 multiple choice questions right on the sample test. That's not great, but that it will improve easily with practice.

He got 13 out of 24 open questions right. Awful.

The smartest child in the class missed 5 of the open questions. This is a kid who, from where I sit, is unstoppable. And she's scoring 5 wrong out of 24.



'make a chart'

I spent this weekend teaching Christopher the fantastically helpful charts that are in Saxon, Dolciani, and Brown and Dolciani (Brown's book being a terrific basic algebra text, btw. In the past, inexpensive teacher's editions for Brown have been easy to find.)

How I wish I'd known about 'word problem charts' when I was a kid. They're incredible.

And how I wonder why Prentice Hall doesn't have them.

I'll post a couple of examples, but in the meantime, here's the simplest one:




I find this beautiful.

• It's simple, clean, and instructive. Every time Christopher fills out a Dolciani/Saxon/Brown-type chart he rehearses and 'sees' again the relationships among these numbers.

• Once a value has been entered in its correct place on the chart, the student doesn't have to hold it in memory. Nor does he have to re-read the problem to re-find whichever number he's forgotten while remembering whichever number he's (currently) remembering. When you're just learning to solve word problems, you're constantly forgetting one number while remembering some other number. People always say that the 'big problem' with word problems is they're hard to read, but I'm starting to think the big problem is they're impossible to remember. Which may amount to the same thing, of course.
  These charts take such an enormous burden off of working memory that I wonder whether Temple might have been able to learn algebra if someone had taught her to construct them.)

• Finally, the fraction bar is already there, implicitly and almost explicitly, in the lines of the chart. When I pointed this out to Christopher he said, 'Oh, yeah' in his happy 'I get it' voice.

more charts
















update

Here are the Prentice-Hall triangle charts.

Horrid.



your advice?

So here's my question.

Last night, watching Christopher read word problems, I could see that he had no clue.

He wasn't even pulling out the numbers, especially; his approach seemed completely haphazard. He seems just to guess positions and operations.

The minute I showed him the charts, he started knowing what he was after & being able to find it in the problem.

He needs a strategy.

At the moment, I'm telling him to circle each 'math fact' and underline the question. I also suggested using yellow highlighter to highlight the math facts and blue to highlight the question. He likes that idea, but I'm not sure it's practical for the state test, which is timed.

But I'm wondering whether I also ought to make up some kind of 'teaching template' he would have to fill in for each problem he does.

Something like this:


question: _________________

what I know: _______________

what I know _______________

what I know _______________

what I need to find out (if needed) _____________

what I need to find out (if needed) _____________


I thought of this because I saw somebody on a website somewhere do something similar. Now, of course, I have no idea what or where that website was.

Any suggestions?


I gather Mildred and Tim Johnson's book, How to Solve Word Problems in Algebra, is the best of the lot, but I probably don't have time to pick up a copy before next week.




how do you teach your child word problems?
mini problems (important)

teachtocrammery



-- CatherineJohnson - 06 Mar 2006

---

MegawordsMissionAccomplished 08 Oct 2006 - 22:18 CatherineJohnson



I was going through old posts on spelling, and I found this one, which I wrote on May 1, 2005:

Christopher and I finally finished Megawords 1 today.

Megawords 1 is the 4th grade book, and I've been saying for months now that my goal in life is to finish the 4th grade book before Christopher gets out of 5th grade.

My new goal is to finish the 5th grade book (Megawords 2, in case you were wondering) before Christopher gets into 6th grade.

I would like to be doing the 6th grade book in the 6th grade.

I don't feel that's asking too much.

wow

That makes me feel good.

We're midway through 6th grade and we've got 22 pages left to do in Megawords 3 (22 out of 67 total) plus 2 tests.

We'll manage to start the 7th grade book before this school year ends. (That's my new goal: finish the 7th grade book before 7th grade.)

cool



speaking of goals

One thing I like about the state tests — this probably puts me in a tiny minority — is the pressure they put on Christopher.

His competitive nature kicks in, and even though he'd like to blow me off, and tries to blow me off, he can't quite bring himself to do it.

This gives me a one-week Golden Opportunity to get ratio & proportion problems pretty solidly drilled into him.



Which reminds me....I need a vocabulary for the stages of learning & mastery.

Christopher is what we used to call a 'quick study.' He memorizes quickly, and remembers well.

My sense is that's what's getting him through his math class. He doesn't have anywhere near the conceptual understanding he needs, and I'm guessing he doesn't have the same 'pattern recognition' skills the A students in the class must have.




sidebar

There are a number of kids in Christopher's math class who are doing great. They're getting straight As, and they seem to be getting straight As without a lot of effort. One of those kids has had ZERO help from his parents this year. Straight As. (And he doesn't even like math! His mom told me so.)

I'm pretty sure there are several other kids who aren't getting much help from their parents, either (though there are plenty who are).

How are these kids doing it?

I'm INTENSELY curious about this.

possibilities:

• they've started with a better base than Christopher, who continues to have his 'lost year' of math (4th grade, when his teacher was poor & he failed at least a third of the coursework)

• the straight-A kids innately understand math better.....or 'see it' quicker.....or something. The only problem with this hypothesis is that it's not clear that these are 'gifted' kids. I know at least two of them aren't; their mom has told me explicitly that they absolutely aren't gifted. 'They work hard,' she said. Probably one or two of the easy-A kids do have special talents in math, but not all of them do. (Also: WHAT IS GIFTEDNESS IN MATH?? I'd love to know.)

• better attention — Christopher has said consistently, throughout the year, that Ms. Kahl's explanations are clear. I have no reason not to trust him on this, and now that he's going in for extra help he comes home having understood what Ms. Kahl told him one-on-one (I think). He's also told Ed that his class is rowdy and ill-behaved, and that it's hard to pay attention. I take all of this with a grain of salt; i.e. I wouldn't use this report to assume that Ms. Kahl has trouble keeping order. If I walked into her class I might very well perceive the atmosphere to be sufficiently calm and focused. However, I do think this report is true for Christopher. I think he's probably distracted by the other kids in class — and I assume the straight-A kids probably aren't.
  
  Plus we have the whole weird visual processing issue, which I don't understand at all (Christopher had vision therapy for awhile & wore prism lenses, which made a huge improvement in his soccer playing), so it's possible he's having trouble taking in what the teacher says, what she writes on the board, AND blocking out distractions at the same time. As I understand it, if your brain has to use a lot of energy compensating for deficits you don't have as much energy left over to filter and suppress distractions...something has to be sacrificed.

• better pattern recognition?? I don't necessarily know what I mean by this. I'm thinking about my own experience learning to read and spell. I 'taught myself to read' and I just naturally knew how to spell. How did this happen? I assume I picked up on patterns. I learned to read through being read-to by my mom. She says that one day, when she was reading MADELINE to me for the umpteenth time (I think it was Madeleine), I told her I could read. She said I couldn't, so I read the page to her correctly. She assumed I'd just memorized the words by heart, so she started turning pages and pointing to individual words. I could read them all correctly, taken out of sequence. I think this must have happened the summer after Kindergarten. (We weren't taught to read in Kindergarten; reading was taught in 1st grade.) I went into 1st grade able to read every book we were going to use that year.
  
  I'm assuming the straight-A kids must be doing the same thing with math. They're picking up on patterns. I also assume Christopher isn't picking up on these patterns; he has to have the patterns pointed out and explicitly taught.

That's all I've come up with so far.

I'm fascinated by this, because I know quite a few of these kids, and there's no obvious difference in basic intelligence between Christopher & them. (Nor is there any obvious difference in intelligence between Christopher and his friend J. who was his partner-in-flunking back in 4th grade & is now further & further behind Christopher in math. His friend J. is a very bright boy. And unless some kind of heavy-duty intervention happens, he will not be able to take any math at all in college. Period. He just got a C on a test on order of operations, because he was out of school sick for a week. This is the kind of thing that makes me crazy: what happens now? They just move on and assume he'll pick up order of operations somewhere along the way?)

As to pattern recognition in math, as I've been relearning math I've realized that some of my own math knowledge, sparse as it is, came from pattern recognition.

The only example I can think of is what Saxon calls algebraic addition — defining subtraction as addition of the opposite.

At some point I figured out, entirely on my own, that you had to 'keep the addition or subtraction sign with the number.'

By that I meant that if you had an equation like:

5 - 3 + 10 - 16 - 7 - 6 = x

you could rearrange it any way you wanted to as long as you kept the operation sign 'attached':

(-3) + (-16) + (-6) + (+5) + (+6) = x

I didn't understand this as 'algebraic addition'; I didn't think of myself as having turned the operator into a positive or negative sign.

I needed this idea because I'd been taught that there was no commutative property of subtraction, and I needed a way to make simplifying expressions easier.

I'm going to have to start paying attention as I go along, to see whether there were other rules I picked up on & formulated on my own. What's amazing, frankly, is the number of rules & obvious shortcuts I didn't pick up on! I've spent my entire life calculating price by figuring out the tax and adding it on; it never crossed my mind that, if tax is 5%, I could take 1.05 times the price and be done with it. sigh

I wonder whether the straight-A-with-ease kids are good at perceiving math rules without being taught.



getting better

Christopher, since Christmas, is seeming more like the A kids than he did.

He's still doing poorly on tests. He's had two B-minuses so far, with the class average at 90. (How on earth?)

However, a B-minus is a great improvement over a D, which was his last test grade before Christmas.

And these two B-minuses are funky. He got the first one on the Weird Figure test, which obviously threw him off. He knew all the formulas going in, and still knows them; he can use them pretty easily. He got tangled up on the test per se.

The second B-minus was on the 14-item word problem ratio & proportion test where he took most of the class to do the first 3 problems, then panicked & started to cry. He still finished every item and pulled out an 80. So there, too, when you strip away the 'extras' (panicking, crying, writing too big for the space provided, not being able to read your own handwriting) he's not bad.

The big change we see, suddenly, is that he's coming home able to do his homework without any help at all.

That is a HUGE change. Throughout the entire fall he could do nothing he was assigned. He didn't even know where to start. I retaught every class lesson start to finish; then I talked him through the assigned problems.

Now he comes home knowing what to do.

How did this happen?



back on topic

So I was saying.....I need a vocabulary to describe stages of learning and mastery.

I need it, because it would help me gauge where Christopher is on different topics.

On many of the pre-algebra topics they're covering, Christopher is now somewhere in between a 'novice' and an 'expert.' He has some kind of toehold.....if I ask him to do a proportion problem he'll look blank, but he'll rapidly get on track after an initial hint from me or after he's frowned at the page and thought it through for a couple of seconds.

That's why I like having this week of test prep. You might think a week doesn't allow you to do much, but I suspect that when a student has the degree of 'starter knowledge' Christopher seems to have you can accomplish a great deal in 7 days. I don't understand this — am I seeing that we've moved into the Practice-practice-practice phase? Maybe that's it. He has 'initial' mastery; what he needs to do now is solidify the concept, as a teacher said on Amazon.

We'll see.



summer plan

In any case, the good news is that I've struck an agreement with Christopher about summer math.

I was pushing for Saxon Algebra 1/2, which is Saxon's pre-algebra book. There are 137 lessons - something like that - so it's a lot to get through, and he needs to get through it. He starts algebra in the middle of next year.

The teacher on Amazon, who teaches accelerated students, was having her kids do two lessons a day, and just one problem set.

Christopher says he'll do two lessons a day and half of one problem set, which would be 15 problems.

I think that's fine. I'd prefer he do 30 problems, but what he really needs is the conceptual understanding Saxon is so good at providing.

As to problems & problem practice, I'll have him do bar models EVERY SINGLE DAY - bar models along with the corresponding equation. I'll either have him work through Challenging Word Problems 3 ($7.80 plus shipping; 129 pages) or he can do bar models for the Saxon problems.

My goal for the end of summer is automaticity and comprehension.

I want this kid to have a clue why he's doing the things he's doing.







-- CatherineJohnson - 07 Mar 2006

---

MiniProblems 15 Jul 2006 - 16:33 CatherineJohnson



I've been complaining for months about the lack of word problems in Christopher's math class.

The kids memorize one procedure/rule/formula a day, do a few calculations, and march on. As a direct result, IMO, their knowledge really is rote as opposed to procedural. At least, Christopher's is. And I've had enough math talks with other kids in the class to know some of them are in the same boat.

Today I had a eureka moment reading a Comment left by Kathy Iggy:

The old math books I found (the same ones I used in grade school) have lots of what they call "mini problems" used to illustrate how a recently taught concept would be presented in a word problem. Megan likes these because of their brevity and she doesn't have to struggle with comprehension that much.

For example:

20 yards of ribbon. 1/4 used for dress. How much ribbon used?

That's IT!

mini problems


That's the concept, and the phrase, I've been looking for.




mini problems:word problems :: basic skills:higher order skills .

That's from Ken, and he's exactly right.

[update 4/23/2006: no! he's not right! Actually, he's write about using mini problems to teach word problems; I'm talking about mini problems to teach math - to teach the fundamental concept in a lesson. Awhile back I realized that word problems are the 'real manipulatives.' Now I know what I mean by that.

All concepts should be taught — illustrated — with mini problems. All concepts, every last one.

PRIMARY MATHEMATICS does this; SAXON MATH does it; KUMON does it. I'll post examples.

I've come to feel that the first word problems illustrating a new concept should be so simple children can do them in their heads.

For example, the very first ratio word problem a child does should be something like this:


Christopher bought one pencil for one dollar.
How many pencils can he buy for two dollars?


The question should be written this way, too: on two separate lines, so the child sees instantly that the first sentence is the set-up, and the second sentence is the question. Richard Brown's revision of Mary Dolciani's BASIC ALGEBRA, a book I like very much, does this for many of its word problems. I'll post some of those, too, as I get to it.

mini problems are applications

The problem with word problems is that, in the U.S., they're always hard.

Word problems are so hard people have apparently come to think that if a word problem isn't hard it isn't really a word problem.

I'm wondering if we ought to ditch the phrase 'word problem' (ditto for 'story problem') and adopt the word 'application.'

A better idea: we should think about the point of word problems.

Some word problems are written and assigned to give students practice.

Many word problems are written and assigned to assess whether students have developed flexible knowledge.

I'm talking about a third purpose, which is instruction. I'm talking about word problems designed to teach.


instructional word problems


A word problem is an application. A super-simple, starter word problem explains and demonstrates a mathematical concept by showing students how the concept is applied.

As a matter of fact, an instructional word problem shouldn't even be a 'problem.' It should just be a question, and the answer should be obvious.

A simple, instructional mini-problem should not test the child, should not challenge the child, and certainly should not trick the child.

It should teach.


examples to come


be sure to see Google Master's comment



how do you teach your child word problems?
mini problems (important)
arithmetic to algebra & mini-problems

-- CatherineJohnson - 07 Mar 2006

---

MathJournalDayTwo 30 Jun 2006 - 16:49 CatherineJohnson



OK, state tests start one week from tomorrow, and the kids wrote in their Math Journals again today.

They wrote in their Math Journals yesterday, too. The teacher put an inspirational quote about what to do when you crash into a wall up on the board, and they were supposed to write about how the quote related to the state test. (NOTE: Christopher cannot pronounce inspirational.)

Today's quote was something about 'not thinking about what you've lost.'

Excuse me while I hunt down a Google image for banging my head against the wall.

[pause]

OK, that was quick.




No math homework tonight!

No Top Secret Glencoe Diagnose - Prescribe - Practice workbook!

No math of any kind!

So I've spent my entire evening pulling worksheets out of the 3-inch DuraTech worksheet binder I assembled awhile back and combining them with fill-in-the-gap worksheets I tracked down on the web today and coaxing-coercing Christopher to apply himself and do some math.

news flash: Christopher does not appear to know how to read a coordinate plane.

More specifically, he does not appear to know that a coordinate plane is made up of two number lines; nor does he seem to understand that you never, ever, under any circumstances have positive numbers to the left of the zero, or below the zero in the case of the Y axis.

THEY ALWAYS PUT THE NUMBERS ON!!!!!

HOW WAS I SUPPOSED TO KNOW THAT WAS A NEGATIVE NUMBER!!!!

THEY DIDN'T PUT ANY NUMBERS ON!!!!

etc.

diagnose - prescribe - practice!



winner worksheets

Two fantastic resources:

• Glencoe Pre-algebra Parent and Student Study Guide
  "The Glencoe Parent and Student Study Guide is designed to help you support, monitor, and improve your child's math performance. These worksheets are written so that you do not have to be a mathematician to help your child."
  The entire guide is available free online.
  SUPERB

• Mathtastic worksheets by Susan D. Phillips
  50 worksheets, mostly pre-algebra with some algebra, all available free online
  EXCELLENT

The other two sources I'm relying on are Kelley Wingate Pre-Algebra and Instructional Fair Pre-Algebra. Both are quite good, though I've gotten more use out of Instructional Fair for some reason. I'll probably spring for most of the Instructional Fair workbooks as I go along. The Lakeshore stores carry them, and you can order them online from Frankschaffer.com, though they're somewhat difficult to track down on the site.



Instructional Fair



Kelley Wingate




This is interesting. A Math Journal with a bunch of math inside. No sayings about "not thinking about what you've lost" and such.

update

Is this a DuraTech 3" binder?

I think not.


-- CatherineJohnson - 08 Mar 2006

---

DontStudyForTheTest 30 Jun 2006 - 16:44 CatherineJohnson



Christopher is upstairs screaming and crying — I have also heard the f-word — because I've missed my train to the city and thus will be home tonight & able to make him STUDY FOR THE STATE TEST.

This is occasion for screaming, crying, and f-wording because he is the ONLY child in the ENTIRE SCHOOL who is being FORCED to STUDY FOR THE STATE TEST.

That, I believe.

There's no reason a parent should do what I'm doing unless he or she wants to. [update 6-16-06: wrong] Even if he or she did want to, I'm not sure most parents could, on short notice, put together a STUDY FOR THE STATE TEST PROGRAM.

The reason I can do it is that I've spent the past 4 months of my life a) figuring out what 'pre-algebra' is, and b) assembling a superb collection of 'pre-algebra' worksheets, if I do say so myself.

(Most of them are linked on the Our Favorite Math Supplements for Kids page on the sidebar.)^*

From there it was a reasonably short hop to figuring out the state test.

My point: I'm possibly the only parent in all of Irvington — apart from the 6th grade parent who actually is a math teacher in real life — who's in a position to do what I'm doing. You can be a genius at math, you can work in a math-related profession; that doesn't mean you're going to know what's in 'pre-algebra' or what's going to be covered in a brand-new, never-before-administered, annual 6th grade state assessment.



do you see steam coming out of my ears?

The reason I missed my train is that I had to take Christopher & his friend M. to tennis.

In the car they both went nuts over the fact that Christopher is being FORCED TO STUDY FOR THE STATE TEST. They were horrid.

Both boys say, and I believe them, that virtually every single teacher they have — they named names — has told them they shouldn't study for the state test because they don't know what will be on it.

I'm furious.

I'm so furious I'm going to be writing a non-furious email to the principal when I calm down. [update 6-16-06: nope, didn't do it]

The message being given to Christopher, which directly contradicts the message we are giving him at home, is:

• we don't know what's on the test; it's random; it's capricious; it's pointless

• the only reason to study for a test is to get a good grade

• there is no intrinsic value in study & learning
  

let's start with 'we don't know what's going to be on the test'

4 problems:

• Number one, it is false. The state has content standards; the schools know what they are.

• Number two, unless you're taking an open-book test no one ever knows what's going to be on the test.

• Number three, all of the teachers have done extensive test prep all year long. The kids take one 'sample test' after another; Ms. Kahl's class has done nothing but take sample tests and do practice test problems for the past two weeks. If you shouldn't study for the test, you certainly shouldn't spend taxpayer money on Top Secret Glencoe Diagnose - Prescribe - Practice test prep workbooks.

• Number four, politics. Why do we have NCLB? We have NCLB because the schools are not doing their jobs. We have NCLB because black and Hispanic children graduate from high school functioning at an 8th grade level compared to white kids, whose level is already low compared to the rest of the world. If you want to talk to the kids about The State Test, tell them the truth.

'the only reason to study for a test is to get a good grade'

Appalling.

Is the content being tested on the state test worth knowing or not?

If it's worth knowing, it's worth studying.



'there is no intrinsic value in study and learning'

Ditto.



paying the school to make my job harder

Ed and I are bookish people. Two Ph.D.s, 5 published books between us, etc.

We believe in study and learning. We are the 'lifelong learners' it is the mission of IUFSD to create (SEE: 4th paragraph from the bottom).

At home we are trying to teach Christopher that hard work is good, going above and beyond what's called for is good, learning is good.

Why are we studying for the state test when nobody else is studying for the state test?

Because we can.

Because we have an opportunity.

Because we believe 6th grade mathematics is important and we want Christopher to master it.

That's what we tell Christopher.

Then he goes to school and the grownups there tell him not to study for the test because he doesn't know what will be on it.

And after that we have screaming, we have the F-word, we have eye-rolling and hectoring even from Christopher's friends.




vignette

"People think you're crazy, Mom. Do you know that?"^*

Won't be the first time.







update from Carolyn

This is the truth:

I think what you're seeing here echoes a general sentiment among teachers (here at least) that the CSAPs (the CO state equivalent) are capricious if not malevolent, and that they have no clear control over the test's outcome for kids, either as individual or in groups. I think they feel the whole exercise is doomed to failure.

and from Doug!

Yeah. Of course it's always the same schools that get the good scores and the same schools that get the bad scores. (Bar a few schools getting better or worse each year.)

Perhaps the tests are delivered in a Chevrolet Caprice?

It took me a couple of minutes to get that one —


^* I've got the two most important resources at this particular link, but do a search on the entire page if you're looking for material; I'm afraid some of the stuff may be scattered around in various categories.

^*'crazy' meaning: crazy math-tutoring mom, crazy math-test-studying mom, etc. In the same vein as homework Nazi



don't study for the test
news from nowhere (placement in accelerated science)
don't study for the test part 2



-- CatherineJohnson - 08 Mar 2006

---

OnStudyingForTheStateTest 11 Mar 2006 - 23:10 CatherineJohnson



This is thrilling.

I noticed today that on February 19 Christopher couldn't do this problem from the Glencoe test prep book:


On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.

Part A
What percent of the total number of cars were in the parking lot on Friday?
Show your work.

Part B
What percent of the total number of cars were in the parking lot on Saturday?
Show your work.


Tonight he did it no sweat.

Thanks to Saxon Math.


-- CatherineJohnson - 09 Mar 2006

---

AmscoTeacherEdition 14 Mar 2006 - 06:34 CatherineJohnson



Go to Amsco School Publications & click on Homeschooling.






I am not a customer.

I am a taxpayer and potential test-cheat.

I can pay for a copy of the Teacher's Manual, or the Top Secret Glencoe Diagnose - Prescribe - Practice workbook, when my school places the order.

I can't actually own it.


So....if anyone knows where I can get a copy of the Teacher's Manual for INTEGRATED MATH COURSE I (3RD ED) by Edward P. Keenan & Isidore Dressler, let me know.

Teacher's Manual available (R 638 T) $12.00
ISBN: 87720-230-3



Amsco protects its 'customers'
Glencoe Top Secret Test Prep



-- CatherineJohnson - 09 Mar 2006

---

StickingPointsInAreaAndPerimeter 09 Mar 2006 - 23:07 CatherineJohnson



I've finally found an image to explain one of the toughest concepts for kids:





Christopher has a dreadful time with figures like these, and so did my neighbor's son last year (no report on how he's faring this year).

Christopher simply can't 'see' that if all the angles are right angles, the right side equals:

8 ft + 5 ft

Nor can he see that the short horizontal line segment between the 8 & the 5 equals:

30 ft - 22 ft

I would like to have a few worksheets of figures like these.



taking a measure without starting at 0

Here's another category of problem that's incredibly hard for kids to do:




Doug, if you're around, and you feel like taking on another project, this is something I'll wager every grade schooler on the planet could use.

Christopher would be in much better shape today if he'd been given a bunch of 'simple' measurement problems in which the left side of the object being measured is placed somewhere other than 0 on the ruler.

For the life of me, I don't know why kids aren't bringing home such assignments as homework.

Some of you may remember that, last year, Christopher eked out a '4' on the TONYSS ('Test of New York State Standards,' a test schools in NY state can purchase from a private company to use in 'off' years). His score was one point above the cut-off.

The scale he flubbed was measurement!

I was shocked.

I'd been working around the clock with him (at an age when he was still willing to work with his mom) — and he flunks measurement! (Apparently, this was true of kids all over the state.)

Then we heard from teachers explaining that measurment is a difficult concept and skill to learn. Meanwhile the Singapore series takes measurement as one of its core subjects. They place huge emphasis on that topic.

Live and learn.

Now I see why measurement is a) difficult and b) incredibly valuable.

Think how much knowledge and skill goes into figuring out a problem like the line measurement above.

1
You can figure out the measure of the line either by adding or subtracting fractions.

2
The fact that you can figure it out by adding or subtracting reinforces the concept that addition and subtraction are inverse operations.

3
You can also figure out what the measurement is by counting-up using fractions instead of whole numbers. 'Counting by fractions' is an incredibly valuable activity. You almost can't not see that 'fractions are numbers' when you count by fractions. Saxon Math has numerous Mental Math tasks requiring students to count up (and, I think, back down) by fractions.

1/5, 2/5, 3/5, 4/5, 1, 1 1/5, 1 2/5, 1 3/5, 1 4/5, 2

btw, Schoolhouse Tech has a very nice sheet of fraction number lines available for download. (pdf file)







update from Doug

Doug recommends drawing simple perimeter problems on quadrille paper, like this one from Enchanted Learning (I think you have to be a member to download the sheet):








I'm going to print out the sheet and see if Christopher readily transfers from the quadrille problems to problems written on blank paper.



from last year

I just found a number of comments about kids and measurement that I'd forgotten:


measurement advice from Carl L:

My first year teaching high school freshman (I just finished my 3rd year at a urban neighborhood school) I was completely shocked that none, and I mean none, of the kids could measure using an inches ruler.

How can they get out of middle school, or even grade school, not knowing how to measure? I still have no clue. I doubt its the constructivists fault due to their fondess for hands-on, manipulatives, and project, which all lend themselves to measurement.

What I have observed:

• Metric OK, Inches Not -- While the kids can't (or won't) measure in inches, many (but not all) can measure using a centimeter ruler. Fractions rear their ugly head again.

• Estimation, Schmestimation -- The kids do not know when it is, or is not, appropriate to estimate. The kids have trouble estimating measurements between the lines of the ruler. But the kids are very willing to make bad estimates to avoid having to figure out what the little lines mean. 2 5/16 inevitably becomes 2 1/2.

• What is a protractor? -- The kids REALLY don't know how to use a protractor (except as a frisbee). Most don't even know that its purpose is to measure angles.

A side note related, I believe, to measurement. Each year I do a lesson where we compare the kids height in inches to their shoe size. The majority of the kids do not know how tall they are, let alone how to convert the height in inches.

So by all means get a ruler, protractor, some measuring cups and spoons, and a kitchen scale (or even better a pan balance) and start measuring everything around the house!

Barry's reaction:

Interesting observation and good advice. I just purchased the Saxon Math 76 book for 6th grade, and I notice that many of the problems have a scale on the page (in inches, sometimes divided into 8ths, 16ths, etc depending on the problem), with a line above it and students are asked to give the length of the line. I thought it strange to have such measurement practice but now I don't.

(Obviously that's part of our problem around here. We skipped Saxon 7/6 and went directly from 6/5 to 8/7.

from Interested Teacher:

Learning to read/measure from an 'inch' ruler has to be incremental. Younger students can't look at a ruler and automatically discern what all of those marks mean. They have to be taught to find the 'half' mark and measure using the 'half' marks. Then add the 'fourth' marks, (Don't be surprised that students don't automatically know that the 'half' mark also becomes a 'fourth' mark.) Then have students measure using the 'fouth' and half' marks. And so on, going into 'eighth' marks, etc. Practice between each incremental step.

Practice is necessary so students develop the skill of disregarding the smaller (16ths and 32nds) marks. For some students, with visual discrimination problems, this is horribly difficult.

Saxon 6/5 covers through 'fourths' and I add a little 'eighths' for more advanced students.

I was looking through Passport to Mathematics,Book 1, a text that I am previewing for personal reasons, and I see lots and lots of metric work, but little with feet and inches. On pg. 32, students measure to the nearest inch, and nothing else that I can see until pg. 318. With no review of 'half' and 'fourth' inches, it jumps to 'eights' -- there is one problem.

-- CatherineJohnson - 09 Mar 2006

---

AreaAndPerimeterWorksheetsFromSmartestTractor 13 Mar 2006 - 04:13 CatherineJohnson



Wow!

Smartest Tractor comes through again!

Here are four area and perimeter sheets from schoolhouse teach:

shape 1

shape 2

shape 3

shape 4

THANK YOU!!!

I just tried Christopher on the page I printed out from Enchanted Learning. He couldn't do it at all. I can't tell if he totally doesn't get the concept, or what.

The graph lines seemed to get him even more confused....he kept counting interior lines....

So at the moment, I'm stumped.

This is reminding me of the Betty Edwards drawing boot camp, where you just have to keep at it.

Learning to draw, all drawing instructors universally say, is learning to see.

So you just have to keep trying to see the object you're drawing in the unnatural way you need to see it to draw it.

That may be all that's involved with Christopher.


-- CatherineJohnson - 09 Mar 2006

---

DefensiveTeaching 13 Mar 2006 - 23:37 CatherineJohnson



Ms. K rarely assigns word problems.

What problems she has assigned have been, frequently, far above the kids' skill level. (examples here: scroll down for the entire list)

The parents do these problems at home, then the kids turn them in. This is an open secret. My favorite Extended Response moment happened last year, before Christopher had moved to Phase 4. One weekend parents all over the soccer grounds were grabbing each other & asking whether anyone knew how to do the latest Extended Response. These were all highly educated Westchester parents with important jobs requiring advanced training.

And they're running around the soccer games accosting people about the latest Challenge Problem their kids have to hand in.

This year there's one student in one of the Phase 4 classes who, last semester, was getting 60s & 70s on his tests and had straight '10s' — the highest score possible — on the Extended Response problems.

NOTE to IMS Math Department:

Look for a pattern!

Cs and Ds on tests, A+ on Extended Response problems — what does this suggest?





The Extended Response problems are assigned because, in the beginning, the Phase 4 students were supposed to be mathematically gifted, and Irvington's pedagogical philosophy where the mathematically gifted are concerned can be summed up in two words: Math Olympiads.



gifted and talented according to Math Olympiads

The MATH OLYMPIADS approach to educating the gifted and talented, as far as I can determine, is the following:

• The mathematically gifted child needs, above all, to be challenged.

• The best way to challenge the mathematically gifted child is to give him super-hard problems he's never been taught how to do & send him off to grapple with them on his own.

I have the Challenge Philosophy in writing. The Assistant Superintendent for Curriculum said, in a letter to me, that Phase 4 kids 'need to be challenged' — although he agreed that kids shouldn't be given problems so challenging their parents would have to do them.

He may be right about kids who really are GATE in math, although I can't imagine GATE kids don't need instruction.

And my leaning where GATE kids are concerned is towards acceleration over enrichment.

I may be wrong about GATE kids.

But I'm right about the high achievers.

Kids who do well in math because they're high-achieving don't need Math Olympiad problems.

In fact, I'll go for the Strong Form here:

Kids who do well in math because they're high-achieving are harmed when they spend time on Math Olympiad 'challenge problems' instead of word problems pitched to their level and embodying the concepts they are currently trying to master.

Ms. K assigns Challenge problems, not Instructional problems.

As a result, virtually all of the word problems Christopher has done this year fall under the heading of lost instructional time.

What Christopher needs are brilliant instructional word problems of the kind provided by Action Math.





has Math Olympiads become a national curriculum?

I always saw the Extended Response problems in the accelerated class as an 'add-on.' The mathematically talented kids were taught math like everyone else, only they had to do Extended Response problems, too.

Now I'm wondering whether in fact the 'challenge' approach is simply another manifestation of constructivist math.

Instead of being taught how to do word problems, kids are handed a problem and told to figure it out on their own.

Here's what I see in Christopher's class:

number one: The kids have been given virtually no 'normal' word problems — normal meaning do the odd problems for homework-type problems — all year.

number two: They've been given 9 Extended Response problems, only 1 or 2 of which they could plausibly solve on their own.

number three: To my knowledge, they've been given little-or-no direct instruction in the kinds of word problems that will appear on the state test.

number four: This week, when Ms. K. finally did assign a page of word problems for homework, she gave them no instruction whatsoever on how to do them.

number five: Having read all of the sample problems for the state test, I would be stunned if any problems like the ones Ms. K. assigned this week will appear on the state test next week.

number five: My guess is she didn't demonstrate how to do the problems in class the next day, either, unless the students asked her to. (I'll ask Christopher.) I don't see how she could have. There were 5 problems in all, each requiring a different approach the kids have not been taught, and they spent at least 10 minutes writing in their math journals. That doesn't leave a lot of time for demonstrating and explaining five different word problems in one class period.

update: As I suspected, Ms. K went over 'the problems kids had trouble with,' which means that it was up to the kids to a) know they needed help and b) say so in front of a class filled with peers who, at lunchtime, are going to be calling them 'fat,' 'gay,' and/or 'stupid.' The only problem Christopher remembers her going over in class was 'the runner problem.' (This is two days ago, we're talking.) He has no memory, none whatsoever, of what she actually said about how to do the runner problem.

I'm sure the runner problem came up because no one in the class could do it, so there was no shame in admitting defeat.

Almost certainly most of the kids solved problems 8, 11, & 12 through guess-and-check, and that was that. It's unlikely that any of the 11-year olds Christopher knows would say, "I got the right answer, but I'm wondering whether there's a more elegant and efficient way to go approach this problem."

I'm not privy to Ms. K's thinking, but I know exactly what the effect of her approach to word problems has been on Christopher (and I know he's not the only one):

a) properties, rules, and procedures are learned by rote

and

b) all word problems, including simple, beginning problems in algebra, become Challenge Problems

I'm guessing that this approach is the result of the constructivist pedagogy Ms. K, who is very young, would have been taught in ed school — whether she's aware of it or not.

She teaches the 'basics' in class, the kids memorize what she's put on the board, then the kids discover how to apply the basics to word problems on their own.

In fact, it's probably worse than that, since Ms. K. told a friend of mine that she teaches the concepts the day after the kids have done homework on those concepts. My friend said Ms. K told her this in a 'DUH!' tone, as if it should just be obvious a teacher wouldn't teach a new concept before assigning homework on the concept.

I'm wondering whether this is an ed school truism at this point.

Do ed schools teach future math teachers to have the students discover everything first, including rules, properties, and procedures, and then "go over it" later after the kids have discovered whatever they're going to discover?

I don't know.





this is where bar models come in

Here is 1 of the 5 problems Christopher's class was assigned for Wednesday night:





None of the kids has been given any instruction whatsoever in how to set up such a problem algebraically.

Nor have they been given any instruction in the Official Prentice-Hall Problem Solving Strategies:





Wednesday afternoon I was working on these problems with Christopher and his friend M.

Needless to say, neither boy Looked for a Pattern, Guessed and Tested, Simplified the Problem, Made an Organized List, Worked Backwards, Accounted for All Possibilities, Made a Table, Wrote an Equation, Solved by Graphing, Drew a Diagram, Made a Model, Solved Another Way, or Simulated the Problem.

No.

Instead, both boys, working independently, subtracted 280 from 2870 and then stopped. They knew they weren't done, but they didn't know what to do next. They didn't know why they'd subtracted 280 from 2870, either.

I pointed out to M. that one runner went 280 m further than the other. Unfortunately I can't remember what he did with this information. I do know that he ended up with answers that were 280 m different, but added up to a whopping big batch of meters, far more than the original 2870. Then he started getting upset, and insisting his answer was right.

I decided it was bar model time.

In hindsight, this was the wrong decision where M. was concerned. Both of the kids do know how to translate English words into an equation, and M. might have been able to think the problem through using x to stand for one runner's distance.

He was flat-out unwilling even to look at a bar model. 'I don't understand anything about this problem,' he said, and that was that. He was done. My mistake.

Christopher was game. He knew he was getting nowhere doing what he was doing, and he'd had enough experience with bar models to take it on faith that a bar model would work.

Which reminds me: I must stress to Christopher that the point of the bar model isn't to solve the problem, but to show you which operations you need to do in what sequence. Bar models are a way of setting up the problem.

He didn't know exactly where to start, though he did know he should draw two bars, one for each runner.

When I started talking him through he caught on quickly and he was able to label everything correctly and quickly on his own, without prompting.

Here's what he drew (this is my version):





Seeing the problem laid out this way, Christopher again subtracted the 280 from the 2870. Then he got stuck again, in the same place he'd been stuck before.

We've got work to do.

However, when I started walking him through it, asking what we had left now that we'd subtracted the 280, he was able to say that we had the two other segments left, and he was able to say, with prompting, that these two segments were equal.

The instant he said they were equal he realized he needed to divide the difference by 2.


2870 - 280 = 2590

2590 ÷ 2 = 1295


At that point I asked him where the 1295 belonged on the bar model, and he knew.

Then he knew that Runner 1's distance was 1295 + 280 meters while Runner 2's distance was 1295 meters.



So I'm thinking....

a) is this happening in other school districts? are math teachers taking a discovery approach to word problems?

and —

b) the best defense is a good offense


If I had little ones I'd be teaching them bar models just so they have a way to tackle all the discovery word problems they're not going to be taught how to do in the years to come.

My mom used to always tell us to Drive Defensively.

Same thing here.

Teach Defensively.





extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

-- CatherineJohnson - 10 Mar 2006

---

MsKTeachesDimensionalAnalysis 19 Mar 2006 - 06:46 CatherineJohnson



This is hilarious.

Christopher came home today and said that in math they 'did measurement.'

I asked him if they did any measurements not starting from the 0 end of the ruler, and he said scornfully, 'We didn't do rulers. We did cups.'

Then he said, as an afterthought, 'Oh, Mommy! She taught us those unit multipliers!'

I love it!

I guess after nobody could convert 48 ounces to quarts she had the same thought I did:

UNIT MULTIPLIERS!

NOW!

BEFORE IT'S TOO LATE!

Naturally I'm feeling smug that my child was the only student in the class who'd heard of the things & knew how to use them.

update 7-16-2006: Smug is one thing; mastery is another. Christopher knew what unit multipliers were & how to use them, but he wasn't anywhere near mastery. We're starting unit multipliers again today. I'd like him to reach mastery/automaticity by fall, which I think should be possible. If not, this summer's unit multipliers will put him in good shape for the unit multiplier lessons he'll have in Saxon Algebra 1/2, which he'll be working his way through this summer and next school year.

update 9-14-2006: Christopher worked his way through 12 lessons of Algebra 1/2 and numerous pages of Vocabulary Workshop this summer. And that was about it. New target date: mastery of unit multipliers before college.


dimensional analysis word problems and answers
another cool dimensional analysis problem Saxon 8/7
Dr. Ian at Math Forum on dimensional analysis

Dan K's dimensional dominoes
Dan's dimensional analysis page

a nice dimensional analysis problem for printing

Carolyn on dimensional analysis & when to teach it
Carolyn teaches dimensional analysis
rough script for dimensional analysis lesson at home (needs revising)

another triumph for dimensional analysis

the sad life of a teen who failed to learn dimensional analysis

-- CatherineJohnson - 10 Mar 2006

---

GlencoeListsGrade6NewYorkStandards 12 Mar 2006 - 00:02 CatherineJohnson



In a fit of civic-mindedness I've decided to type up Glencoe's list of NY State standards to be assessed in Tuesday's test.

I'm coming to love Glencoe. I've mentioned their Parent and Student Study Guide, which they've made available to everyone free online, as well as Glencoe's Diagnose - Prescribe - Practice test prep booklet, which has been terrifically helpful. IMO it would have been helpful whether we'd had a state test coming up or not.

A couple of weeks ago my friend Kris said she wished she had a list — a simple list — of the procedures & concepts her son is learning this year.

That way she could keep track of what he knows and doesn't know, and quickly give him a few more problems to do when she sees he's weak on something.

I think every parent needs a List, and I imagine most teachers either need such a list or already have one.

Glencoe's list of 'Strands and Performance Indicators,' at the front of the booklet, is just the ticket. I spent quite a bit of time searching the NY Department of Education website looking for a list of Grade 6 skills and concepts that made sense — a list that specified math that could actually be done on a test.

What I wasn't looking for were standards like 'Understand that some ways of representing a problem are more efficient than others,' or 'Act out or model with manipulatives activities involving mathematical content from literature.'

If it's there on the NY website, and I have to assume it is, I didn't find it. [update: found it ]

Then the Glencoe test prep book came home and I had what I needed. Glencoe lays it all out in 4 pages.

Below are the 'Post-March' Grade 5 'Strands and Performance Indicators' that are tested in 6th grade.

When I type up the rest of the Strands and Performance Indicators I'll post them on a side page with a link here and elsewhere.



New York State Mathematics
Content Strands, Grade 5, Post-March Indicators

These indicators from Grade 5 are assessed on the Grade 6 Test.

STRAND ALGEBRA
Variables and Expressions
5.A.2 Translate simple verbal expressions into algebraic expressions
5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations
Equations and Inequalities
5.A.4 Solve simple one-step equations using basic whole-number facts
5.A.5 Solve and explain simple one-step equations using inverse operations involving whole numbers

STRAND GEOMETRY
Coordinate Geometry
5.G.12 Identify and plot points in the first quadrant
5.G.13 Plot points to form basic geometric shapes (identify and classify)
5.G.14 Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes)

STRAND STATISTICS AND PROBABILITY
Probability
5.S.5 List the possible outcomes for a single-event experiment
5.S.6 Record experiment results using fractions/ratios
5.S.7 Create a sample space and determine the probability of a single event, given a simple experiment (e.g., rolling a number cube)


source:





another Glencoe Parent and Student Study Guide

Searching for the URL for the Pre-Algebra Parent and Student Study Guide, I found this Glencoe guide to their book MATHEMATICS: APPLICATIONS AND CONNECTIONS COURSE 2.

I haven't looked at it yet.


Pre-Algebra, Parent and Student Study Guide Workbook at Amazon





-- CatherineJohnson - 11 Mar 2006

---

MorePreAlgebraResources 23 Mar 2006 - 18:20 CatherineJohnson



I now have a HUGE collection of pre-algebra worksheets and 'extra example' sheets. Huge. I don't even know where I got half of them (though recently I realized I'm accumulating so many I ought to try and keep a record....)

I'm trying to get all the various links pulled together on the pre-algebra section of Our favorite math supplements for kids, which is on the homepage sidebar.

My latest finds:

• A set of sheets called More Examples, to accompany McDougal Littell's Pre-Algebra, at Class Zone.

• A very nice set of free worksheets, in pdf file, created by Xcel Math Center, a tutoring center in Minneapolis. (I think Smartest Tractor may have told me about these sheets.) This page also includes an online worksheet generator for the basic math facts.
  

And don't forget two other terrific resources:

• Glencoe Parent and Student Study Guide: "designed to help you support, monitor, and improve your child's math performance. These worksheets are written so that you do not have to be a mathematician to help your child." The entire guide is posted online. Wonderful.

• Mathtastic worksheets (42 worksheets and answers in pdf file)
  

Last but not least, I've found two workbooks helpful:

• Instructional Fair Pre-Algebra by Frank Schaffer, my favorite of these two. (IF workbooks can be hard to track down on the web; no idea where to get the best price.)

• Kelley Wingate Pre-Algbra

-- CatherineJohnson - 23 Mar 2006

---

TheThreeSimpleBuildingBlocksOfSuccess 27 Mar 2006 - 21:13 CatherineJohnson



A friend just asked for this passage, and since I've typed it up for her, I'm posting it here, too:

In the past few years, a great many educators have become confused. They have become so fascinated with the content of social studies, physics, foreign languages, and the like, that they have forgotten how simple a good education really is.

A good education—a bedrock education—an education upon which your child will either succeed or fail—consists of just three simple skills.

• The ability to read.
  
• The ability to express thoughts in words.
• The ability to solve mathematical problems.

source:
How to Double Your Child's Grades in School
by Eugene M. Schwartz
first published in 1964

I would like schools to add foreign language to the earliest grades, but apart from that, I'm with Schwartz.

It's interesting that, when he comes to math, he calls the critical skill "the ability to solve mathematical problems."

I agree there, too.

-- CatherineJohnson - 26 Mar 2006

---

EmailToThePrincipal 08 Oct 2006 - 22:40 CatherineJohnson




back story here

Ed just talked to the principal on the telephone.

He was aggressive and unresponsive. The principal, I mean. Not Ed.

So.




Hi Scott —

I’m sending a detailed memo covering our experience with Ms. K’s class this year.

But I’d like to respond to one point immediately.

You observed that Ms. K does not know whether Christopher can do the calculations involved in constructing a scale drawing.

Scott, I agree.

Ms K does not know whether her students have learned the material she’s covered in class.

This is true for all of her students, including those who did record their mental math. We know of one child in the class who has earned grades of C and D on his tests, while scoring an unbroken string of As on the Extended Response problems he takes home to do.

What has that child learned about pre-algebra?

Can Ms. K tell you?

Punishing a child for failing to write down mental math is not teaching; nor is it information. Punitive grading is entirely negative. It demoralizes the child, angers the parents, and erodes trust.

We have two core problems with Ms. K’s teaching, one concerning her ability to inspire, motivate and lead her students to success in mathematics, the other concerning her ability to assess performance. It’s the latter that concerns me here.

Ms. K does not perform systematic, ongoing formative assessment.

She covers material, gives tests, and assigns grades.

And there her responsibility ends.

This year Ed and I have been fully responsible for seeing to it that Christopher actually learns the math Ms. K has ‘covered.’

This wasn’t the case at Dows Lane; nor was it the case with all but one of Christopher’s teachers at Main Street School. That teacher was not asked to return.

I would hope everyone involved in Ms. K’s tenure case would ask himself this question:

Suppose Christopher—or any other student in the class—does not know how to construct a scale drawing?

What happens now?

Ms. K’s answer is: Nothing. Once she’s recorded a grade, she’s done.

If Ms. K wanted to know whether Christopher can construct a scale drawing, she would have him do a simple scale drawing in her presence. She should do that with the entire class, because none of the kids I know was able to handle this assignment on his own. By rights, Ms. K ought to be finding out whether any of her students can do a simple scale drawing independently, without parent guidance.

Instead, it’s up to us to make sure Christopher has mastered this skill.

I will do so this summer when I reteach pre-algebra using Saxon Algebra 1/2.

If I’m going to do Ms. K's job, I want a refund. Ms. K, after two years of work, is going to be awarded lifetime employment, lifetime benefits, and a generous retirement, all funded by taxpayers like me.

Scott, I need to earn a living. I have two children with severe handicaps who will require lifetime care; I must fund my own retirement.

I need to be able to rely on our very well paid teachers to teach my son.

Instead I’m pulling worksheets, buying and studying textbooks, reteaching math lessons, preparing Christopher for the state test (Ms. K told the kids not to study because they ‘don’t know what’s going to be on the test’),^* and helping Christopher’s friends in the class to boot.

This isn’t right.

Catherine Johnson

^* Topics covered on the New York State tests are listed here: http://www.emsc.nysed.gov/ciai/mst/mathstandards/g6.html. These topics are also listed in the Glencoe Test Prep book Ms. Kahl sent home sporadically in the run-up to the test.





I am KICKING myself for not homeschooling.

Actually, it's not even at that level.

I'm kicking myself for not having a clue.

I'm kicking myself for not having the slightest idea what was wrong with our public schools.

I'm kicking myself for not even suspecting that, when it comes to public schools, money ≠ quality.




Christopher won't be doing any more 4-hour projects for Ms. K.

That's over.

My only concern now is: is he learning pre-algebra to mastery?

Everything else is noise.




extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

keywords: performance indicators New York state tests New York state standards


-- CatherineJohnson - 27 Mar 2006

---

SteveOnMemorization 31 Mar 2006 - 15:16 CatherineJohnson



start with Carolyn

Carolyn's laundry list of Science Stuff To Commit To Memory has sparked a superb display of Google Mastery.

(Hey! Google to mastery!)

First, here's Carolyn's List.

To which I say: blech

(I know some of you think this is a good list for a survey course, and you could certainly be right. My science education, in grade school, was nonexistent. I still say blech, but I say it advisedly.....um, maybe I should look up 'advisedly' before I say I'm saying blech advisedly....)

[pause]

hmm


advisedly

• With careful consideration; deliberately.

• with intention; in an intentional manner; "he used that word intentionally"; "I did this by choice"
  

OK, maybe I'm saying blech provisionally.




move to Ken

I'm partially remembering a quote that stated that your typical biology text introduces more new words per page than your typical foreign language. Worse still is the fact that unlike the foreign language the definitions of the new terms are complicated and also unknown to the student. I can't remember the source of this though.

I was having the exact same memory, which I attributed to Engelmann, which caused me to while away the minutes Googling Engelmann, science texts, and vocabulary.

That was fun.



on to Google Master

I found a reference to that quote.

Yager (1983) reviewed 25 of the most commonly used science texts in K-12 classrooms and found that more new science words were introduced in those texts than foreign language words introduced in foreign language texts. Scruggs (1988) found the same pattern in junior high science texts, which introduced as many as 2500 technical terms and unfamiliar words.

question: Has Google Master ever not tracked down obscure and arcane data points nobody but us gives a fig about?

I think not.

Anyway, this passage tells you what e're up against with Christopher's ersatz physics book.

That thing is the mother lode of technical terms and unfamiliar words.



finally getting to Steve

Memorization is fine if there is a framework. I have been looking for (and not found) a book(s?) that breaks science into the different disciplines: chemistry, physics, biology, zoology, etc. and discusses the breakdown, major ideas, and theories of each.

I'm having one of those This Is Why We Have Constructivists moments, dealing with the science curriculum.

Obviously I'm in favor of memorization.....and yet I find the constant memorization Christopher is called upon to do pointless, meaningless, and all in all just a big fat freaking FWOT.

Steve's right, but what does this mean in practice?

What does it mean to 'have a framework'?

How do you get a framework?!

How do you help your child acquire a framework?

These are huge questions, I realize, so I'll try to whittle it down. More specifically my question is: when you're trying to help your child learn something from an incomprehensible science text on a subject you yourself know nothing about, what should you do?

What are your options?

Is there a 'Saxon Math' for 6th grade physics?

Anything else?



update — Ken found it!

A related issue in high school curricula is the "textbook," which is probably a misnomer. For many subjects, the "textbook" is not designed to teach the student in a progressive and systematic way. It is a reference book, with the earlier chapters written with no concern about the fact that kids have not yet read the later chapters. The average high-school text in biology, for example, introduces about three times the number of new, unfamiliar words that would be recommended for the first year of learning a foreign language. What makes this figure even more astonishing is that the concepts behind these words are new (unlike the foreign language that presents new words for familiar ideas).

The War Against the Schools' Academic Child Abuse. S Engelmann, p. 155.

I was just saying in the Comments thread....this is really something you have to see to believe. Ed had been complaining about the science book, and until I actually sat down and 'studied' 10 pages in the thing, I didn't know what he was talking about.

-- CatherineJohnson - 29 Mar 2006

---

LindaOnK12 10 Apr 2006 - 17:29 CatherineJohnson



from Linda P

I've never commented before, but I have a suggestion for the homeschooling option: the k-12 curriculum at k12. I homeschooled my daughter last year using it. She had an abysmal experience prior to that, and was behind in reading and math. After a year of that curriculum (albeit, taught poorly by me) she was on grade level - she is in 5th grade now. It is based on the core knowledge curriculum, but it goes beyond that. Being at home didn't suit her, so she is now enrolled at a local core knowledge charter school, is doing great (happy as a clam and feels good about herself academically - she used to call herself stupid), was advanced mid-year from 5th grade language arts to 6th grade l.a., and her teacher mentioned the possibility of also advancing her mid-year to 6th grade math (not sure I want to do that - she will have missed 5-6 months of 6th grade math content at this point).

Anyway, this is a long winded way of saying that k-12 might be worth looking in to. If you want to know more about my experience, you can email me. Or, ask Carolyn - she knows my daughter.

I'm SO glad to get this.

Quite awhile back I'd read a glowing reference to this group at eduwonk, I believe, and then I'd forgotten all about it.

Boy....this could be something that would make a move into homeschooling doable on relatively short notice. I'm going to have Ed look it over. He already admires the Core curriculum. I think if he felt like there was a 'Known Quantity' out there, an already developed and field-tested curriculum (no crass comparisons, pls.), he'd feel the whole concept is less radical.

Plus the fact that Linda — a real live existing person — did homeschool for a limited period of time is helpful.

Thank you!





science book recommendations from Verghis and Charles

Before I lose track of these titles, I'm posting them here, where I can find them again:

Verghis: Integrated Science, Books 1 & 2, by J. M. LeBel. Recommended by John Hubisz, and I took a look at Book 1.

Charles: Science books I like are the Concepts and Challenges in physical science, earth science and life science published by Globe Fearon. They focus wonderfully on concepts in bite-sized form and are all substance.

and a math group from Google Master

Catherine, do you follow the k12.ed.math newsgroup? It's moderated, and gets a lot of "how do I do this homework problem?" answers, but the moderators and denizens provide quite good answers and have lots of references.

Thanks!





update: more from Verghis

You might also look at Calvert, extremely impressive. In addition to their school, they also sell their stuff for homeschooling.

For an example of their English stuff, see the examples in "The War Against Grammar" by David Mulroy.


keywords:
middle school science textbooks
middleschoolscience


Linda P on K12
eduwonk op-ed in TIMES on virtual charter schools
Change Agent Me

keywords: marketing


-- CatherineJohnson - 29 Mar 2006

---

SingaporeMathRecommendation 24 Apr 2006 - 23:03 CatherineJohnson




A friend asked me for the Singapore math placement test, and I'm posting my email. If any of you have advice to add, please do!

The placement tests are simple to use. Just print one out and give it to your child. You shouldn't skip this step, because Singapore students are advanced compared to U.S. kids. When Christopher took the test at the end of 4th grade he placed into the beginning of second semester 3rd grade, 1 1/2 years behind where he was in SRA Math.

The only books you really need to get are whichever textbook your kids place into, along with the corresponding workbook. Americans typically use the PRIMARY MATHEMATICS U.S. Edition, and the books are cheap, around $8 apiece.

I would also buy whichever CHALLENGING WORD PROBLEMS book is appropriate, because Singapore Math is a ‘problem-solving’ curriculum, and the CHALLENGING WORD PROBLEMS books are gold.

Apart from that, you could add some extras, but you don’t need to. My Singapore Math kids LOVED Brain Maths the last time I taught the course.


for parents

The Singapore Math website sells teacher manuals, but you don’t need them (the one I bought is good, but I found it confusing to read & use).

If you want to purchase a book explaining Singapore Math to parents, these are the 3 I like:

Elementary Mathematics for Teachers by Thomas H. Parker and Scott J. Baldridge

The Essential Parents’ Guide to Primary Maths

Problem Solving the Systematic Way (books 1 & 2)

Although these are terrific books, I have yet to read or work the problems in even one of them, although I've made my way through the first few chapters of Parker and Baldridge. Of the 3, PARENTS' GUIDE would be my first choice if I wanted something short; Parker & Baldrige would be my choice for a thorough treatment of Singapore Math.

So:

• have your child take PLACEMENT TEST
• purchase PRIMARY MATHEMATICS US EDITION textbook & corresponding workbook
• probably purchase CHALLENGING WORD PROBLEMS
• consider purchasing BRAIN MATHS
• consider purchasing ELEMENTARY MATHEMATICS FOR TEACHERS
• consider purchasing ESSENTIAL PARENTS' GUIDE TO PRIMARY MATHS
• optional, if you’re interested: PROBLEM SOLVING THE SYSTEMATIC WAY
• skip the teacher’s manual

advice on Singapore Math 6-2005
Singapore Math book recommendations in a nutshell

-- CatherineJohnson - 24 Apr 2006

---

HelicopterParentsAtTheAft 08 Sep 2006 - 21:01 CatherineJohnson



This interesting.

But there’s one component to the development of literacy that we dare not mention. It doesn’t show up in any policy discussions, nor do we talk about it (publicly, at least) as being a part of any of the solutions mentioned above. It is The Solution Whose Name We Dare Not Speak.

Parents. There, I’ve said it.

Research has clearly shown that parental involvement - parents seen reading in the home, parents reading to their children, parents ensuring that children have an array of reading materials available to them - is one of the most critical indicators of success in helping a child learn how to read.

And the education community treats this as an unmentionable secret.

Sure, we address it to an extent at the local level: schools send home tip sheets, bring parents in to sign reading compacts, and do their best to keep parents apprised of kids’ progress through updates and report cards. But we’re asking too late – so many of the building blocks of literacy happen before a child ever walks into a formal school – and I think we’re probably beating around the bush, hinting and cajoling without ever laying things out in black and white. [ed: yes! let's lay it out in black and white! nice imagery there!]

My jaw would drop – DROP – if I ever saw a public figure call us on this.

AFT reaction

As I recall from my short-but-memorable teaching days, parental involvement is a bit of a double-edged sword. Sure, it's great to have parents who make sure their children do their homework and who are willing to pitch in when necessary in the classroom or on field trips. But let's be honest--some parents are, well, kind of a pain in the butt. They call and call--I guess now they email and email--and their concerns are often, "Why isn't my child getting an A in your class?" regardless of whether the student deserves an A.

I agree. It's great to have parents who make sure their children do their homework and are willing to pitch in when necessary.

And it's excellent to have parents who "make sure" their children actually learn the material covered in class. Especially parents who make sure their kids actually learn the material and do so without getting any big ideas about how maybe that ought to be the school's job.

Unfortunately for my own district, that ship has sailed.

Or, rather, that ship has sailed for me.

Having delved into the research on teaching and learning, I've become the Emailing kind of parent, the parent who wants to know why my child hasn't learned enough in class to score a 90 on a test, 90 being defined as mastery by behaviorists.

When I'm not emailing our teachers, administrators, and board members, I'm spreading the Gospel of formative assessment, direct instruction, and teaching to mastery.

I have yet to meet a parent who thinks formative assessment is a bad idea.

And I have yet to meet a parent who already knew that our schools use spiralling curricula.





differentiated instruction & metacognition

Yesterday I skimmed a bit of Carol Tomlinson's book, Differentiation in Practice: A Resource Guide for Differentiating Curriculum, Grades K-5. According to Steve Carol Tomlinson is the diva of differentiated instruction.

A few minutes with her book helped me understand the pre-tests Ms. K has been giving for a couple of months now.

I was thrilled the first time Christopher came home and told me Ms. K had given a pre-test.

I thought, yes! Formative assessment!

Wrong.

Ms. K gives pre-tests, but she does not give post-tests. Actually, she does give post-tests; she gives lots and lots of post-tests. But her post-tests are all summative in nature. The point is to assign a letter grade.

These days Ms. K gives a pre-test, covers the unit at a rate of one new topic a day, then gives a chapter quiz or test a week or so later. A few kids get As; some kids get Bs; there seem always to be Cs, Ds, and Fs. The grades are recorded and data warehoused (or will be data-warehoused soon), the tests sent home to parents to sign. The Emailing parents launch doomed offensives questioning the grading, the content covered on the test, the unclear directions, whatever.

Then it's on to the next pre-test and the next unit.

As it turns out, this is the Differentiated Instruction way. Pre-tests to discover children's prior knowledge,.....and c'est tout.

This came up in my conversation with the Math Chair.

Her position was that Ms. K is now doing formative assessment because she is giving pre-tests.

It really is stunning, the way the-child-is-responsible-for-his-own-learning meme shakes off all challenges. Tomlinson's book is filled with references to children being given "the opportunity" to take responsibility for their own learning via Differentiated Instruction. The teacher will give a pre-test and start her lesson where the children are, but the teacher will not give a post-test to discover whether or not his/her teaching has actually changed the contents of the child's mind.

Inputs, not outputs.

Inputs not outputs is the unshakeable foundation of American public education.





I'm going to hope that my own district commits itself to performing actual formative assessment, or assessment for learning.

At present, all of the public statements coming from the administration speak of 'using data' to 'adjust our curriculum/teaching.'

That's good as far as it goes, but I haven't seen a single reference to the possibility that an individual teacher will be called upon to adjust his/her teaching in real time, so that the students who are providing all this data for the warehouse, do in fact learn the material the teacher has covered.

Everything is top-down.

The District will Adjust Instruction.

So far, my experience is bad. The Math Chair's response to the fact that I'm reteaching math at night is to say Christopher should be moved down to the slower math class.

That's the exact opposite of Adjusting instruction.

So we'll see.


helicopter parents, part 1
helicopter parents, part 2
helicopter parents, part 3
helicopter parents at the AFT
news from nowhere, part 6 (AP students)
helicopter parents of the word, unite
helicopter parents of the world, unite part 2a (t-shirts)
MiddleWeb says hovering is good

differentiated instruction
strategic plan for differentiated instruction
teacher's role in differentiated instruction
differentiated instruction in middle school
differentiated instruction & the pre-test
differentiated instruction in Steve's town
follow-up on DI in his town from Steve

flexible achievement grouping & accelerating average children
acceleration for average & slow learners
Tom Loveless on tracking research
flexible achievement grouping in Dan's school

Wayne Wickelgren on math talent & when to supplement
Wickelgren on math talent



-- CatherineJohnson - 05 May 2006

---

LoneRangerTutorsReading 06 May 2006 - 01:00 CatherineJohnson

I think whole language causes many children to become utterly confused about reading and appear to have a disability. Then the problem compounds itself as the child begins to feel stupid and then stops trying. I think many children are suffering from poor instruction not dyslexia. I believe that becuase once these students experience systematic explicit instruction they are cured. The young teachers here also were taught as children with whole language and do not have any background with phonics. Colleges of Education also favor balanced literacy. These teachers are mystified when a child cannot learn to read using balanced literacy and speak with reverence of the savior, "Linda Mood-Bell" This phonetic approach is saved for Special Ed kids in 4th or 5th grade, when all else has failed. "All else" includes Reading recovery which is whole language applied one-to-one. It's infuriating to me because I believe it is educational malpractice and waiting until 4th or 5th grade is too long as the damage has been done. I had another little guy in 3rd grade and his Mom came to me in tears. She reported that the school said her son would never learn to read. I realized immediately that the little boy was brilliant. He knew many things about the world and his vocabulary was incredible. He couldn't read at all. We started with Phonics Pathways, a white board and my magnetic letters and worked on consonants combined with short vowels.. sa, se, si, so ,su etc. In 3 half hour lessons he was starting to read the BOB books. This was due to the explicit program I used, not me. It is not rocket science to teach someone to read, but it sure is rewarding. Too bad our school system can't seem to get it right.

Thomas Zeffiro, of Georgetown, told me a few years back that the Linda Mood-Bell folks are fantastic.

He said (paraphrasing), "If you wanted your child to become a superb basketball player you'd get the best coach you could find. The Linda Mood-Bell people are the best reading coaches out there. They're light on their feet."

I loved the image of reading tutors being light on their feet.

He meant that they were completely focused on the student and on what the student was learning.

If what they were doing wasn't working, they shifted at once.

Which brings me back to my Columbia U. story....a friend of ours told us that there was a legendary professor at Columbia Medical School who taught all the Big Medical Brains in the city.

His motto, which he drilled into his students, was: If what you're doing isn't working, try something else.





Zeffiro's study

I'm sure this is the one he was telling me about way back when:

In this study, Eden, Zeffiro and their colleagues studied 20 adults with a lifelong history of dyslexia. They divided the adults into two groups of 10 and conducted baseline brain scans on both groups. One group then participated in an intensive eight-week interventional program designed to improve reading skills, while the other group received no intervention at all. At the end of the eight-week period, brain scans showed that the group that had taken part in the reading program showed measurable improvements in reading and related changes in neural activity. The brain scans of the control group showed no differences.

"It was quite exciting to be able to see such clear confirmation of our hypothesis in the fMRI scans," Eden said. "This is a great step towards better understanding the neural mechanisms involved in reading and learning."

I'm just about positive the program he's talking about here is Linda Mood-Bell. IIRC - and I do - he said the improvements were staggering. These were lifetime dyslexics. I have a memory of him saying some of these folks were almost illiterate (that could be wrong).

I spent a long time talking to him, because I was desperate to teach Jimmy and Andrew to read. He was serving on NAAR's Scientific Advisory Board that year. Fantastic guy.





visual processing & dyslexia

Zeffiro also told me, when I repeated the standard line about dyslexica being a problem with phonological processing, that this wasn't as true as people thought. There are visual components, too:

Addressing a long-standing controversy concerning the causes of reading disability, a series of research studies done by a team at the Georgetown Center for the Study of Learning indicate that the areas of the brain used for reading are the same areas used for other visual tasks, and that these areas may not work properly in the brains of people with dyslexia. However, the researchers also found that an intensive, phonologically based reading intervention program could not only improve reading skills in dyslexics, but could also effect changes in brain activity that can be measured using functional magnetic resonance imaging (fMRI) technology.

more from Lone Ranger

I know two teachers who have jumped off the balanced literacy bandwagon.

Teacher 1 : For the first seven years of her teaching career, she taught k-2 grades. She preached balanced literacy. We would get into heated debates over this topic. She went on to get her master's and is now a Reading Specialist. She has ditched balanced literacy for phonics instruction. She has used the same workbooks (Explode the Code), borrowed many from my homeschooling library (including Phonics Pathways) to remediate the kids that are in the "pull out" programs at her school.

Teacher 2: Taught 1-3 grades for many years. She too bought into the balanced literacy approach. She decided to homeschool her own three children when they were in 2,3 and 4 grades for health reasons. She realized that her oldest (4th grade) hated to read and was struggling. Retaught her oldest to read using phonics. She has said that she could never go back to teaching using "balanced literacy" as she has seen first hand the results. If she returns to teaching, it will most likely be as a reading specialist where she can use phonics.

The whole thing is horrifying to me.

The whole language versus phonics "debate" was resolved years ago, when the NICHD came out with its findings.

Now it's been unresolved.

Now Reid Lyon is an affiliate of George Bush and the White House push to require schools to use research-based curricula is "improper" and "scandalous."

A National Institutes of Health–created commission of Ph.D.’s came down squarely on the side of phonics in a 2000 report, influencing the Bush administration to crack down—some say improperly, perhaps even scandalously—on non-phonics programs.

This really is something.

The NIH says phonics is supported by research & whole language is not, and NEW YORK MAGAZINE translates this into a possibly improper and even scandalous "crack down" on schools.

These are people who make their living writing stuff for other people to read.


-- CatherineJohnson - 05 May 2006

---

QuizSite 06 May 2006 - 19:15 CatherineJohnson




terrific quizz site - includes a link to Selected Answers to Questions at Math Forum

-- CatherineJohnson - 06 May 2006

---

HomeschoolMomSaysParentsAreResponsibleAfterAll 15 May 2006 - 12:02 CatherineJohnson



music to my ears . . .

With regard to the April 25 letter "Defeated budgets ruin opportunities," I laughed at the writer's statement that those who voted against the school budget "failed (her) children."

Parents are responsible for their children's education. With more and more families relying on two incomes to support a household, the public school districts have become a glorified day care system. If you are the type of parent who feels that educating your child is the burden of the taxpayers and local school district, you are the one who is failing your children.

The writer states that she wants her children to "have every opportunity." Then, give it to them. You can start by erasing the notion that taxpayers should foot the bill for extracurricular activities. Dip into your own pocket and support your offspring's endeavors.

With New Jersey's test scores dropping lower each year and incidents of violence in our schools on the rise, budgets that ask for new turf on football fields, additional sports teams and other nonessentials are irresponsible and asinine. If the money were going toward the basics — reading, science, history and mathematics — perhaps more people would consider voting "yes." But don't expect responsible parents and taxpayers to allow their pockets to be tapped once again to support noneducational agendas.

I am the parent of two children. I pulled them out of public school last year and began home-schooling this year because I realize as the parent, these children are my responsibility to educate. I taught them for less than $2,000 this year. That figure includes books, manipulatives, bowling, tae kwon do, music lessons and field trips to places like Philadelphia and Plymouth Rock. Compare what my children have done this year to what other children were offered at an average cost that exceeds $10,000 per pupil.

Unfortunately, I still pay the school portion of my property taxes. But don't expect me to vote "yes" when there is such a discrepancy in spending, overhead and test scores.

Lucille Kentner

via: This Week in Education

I do think it's the state's responsibility to educate children, but seeing as how the state isn't doing it, I'm happy to read letters from mom's who are educating their kids on an annual budget of $2000.

That's probably about what I'm paying to afterschool one child. That and the $18,000 in property taxes.

Of course, that's not counting opportunity costs.


-- CatherineJohnson - 09 May 2006

---

HelicopterParentsOfTheWorldUnite 09 May 2006 - 21:36 CatherineJohnson







source:
BSA Troop 113




Douglas MacArthur had a helicopter mother...

...according to Wikipedia.

Wikipedia seems to think that's a bad thing. We may need to enlighten them.




lost comments

sigh

TWiki ate the Comments left on Friday, one of which was a great anecdote about a principal asking whether parents had anything better to do than hover over their kids and monitor the school's performance.

The mom involved said No.

Unfortunately, I no longer have the original, so that's the jist.


helicopter parents, part 1
helicopter parents, part 2
helicopter parents, part 3
helicopter parents at the AFT
news from nowhere, part 6 (AP students)
helicopter parents of the word, unite
helicopter parents of the world, unite part 2a (t-shirts)
MiddleWeb says hovering is good



-- CatherineJohnson - 09 May 2006

---

HelicopterParentsOfTheWorldUnitePart2a 14 May 2006 - 13:24 CatherineJohnson




Rewriting lost posts for posterity....

t-shirt order from cafepress —

from:
Helicopter Mom





from:
Autism Rocks





helicopter parents, part 1
helicopter parents, part 2
helicopter parents, part 3
helicopter parents at the AFT
news from nowhere, part 6 (AP students)
helicopter parents of the word, unite
helicopter parents of the world, unite part 2a (t-shirts)
MiddleWeb says hovering is good

-- CatherineJohnson - 14 May 2006

---

OnlineGrammarResourcesAndSingaporeGrammar 15 May 2006 - 13:11 CatherineJohnson



Parent Pundit has a question:

I have concluded that the schools don't even attempt to teach grammar anymore so that it will be mastered for the long term. They describe grammar, they give out worksheets ABOUT grammar, but they don't give ANY worksheets so the students can actually practice grammar. In other words, let's figure out how to do grammar in a conceptual manner and, voila, every kid will be able to create sentences in the "correct" manner.

HELP!

I found www.aleks.com to fix the problems with math, but I'm looking for a program like this to help with grammar. I could get out my old Katharine Gibbs Handbook of Business English, but it doesn't come with any worksheets. Furthermore, the hierarchical model of aleks combined with the ability to have instant feedback just works! And if you get the concept by getting it correct five times, Aleks moves you onto the next concept so no one is doing mindless rote because it moves as quickly as the individual moves.

Anyone have any ideas?

I've just recently become frustrated over the same issue.

Christopher's English teacher has made headway teaching him how to identify the grammatical parts of sentences, which is great (and will be important when he finally takes a real Spanish class, as opposed to the ersatz course he's taking now).

But he's had precious little practice actually writing grammatical sentences.

I'm using Don Killgallon's book this summer (Killgallon's website), but I may also use the resources a Commenter left:

• grammar workbooks from Singapore Math

• Speak Better English Czech site with terrific online exercises & immediate answers (Speak Better English homepage)

• English Language Study Zone (more online exercises with immediate feedback)
  sample page from Study Zone

sentence combining worksheet

• sentence combining worksheet
  

• tons of grammar worksheets & answers
  (some of these may require student to produce a sentence; I don't know)

• online list of sentences to be combined in various ways (w/feedback) - college freshmen

• 10 online sentence combining exercises w/feedback
  These are hard & fun. (It's hard coming up with the combination the website prefers.) I'm going to see if Christopher can do them.

If any of you finds other sentence combining and/or sentence composing worksheets online, let me know. (Not sure whether edhelper has these — I'll check.)


online grammar resources and Singapore grammar book
successive sentence combining exercise
kid-friendly explanation of sentence combining & online exercises

keywords: sentencecombining grammarpractice

-- CatherineJohnson - 14 May 2006

---

AnotherParentDoingTheSchoolsJob 18 May 2006 - 19:09 CatherineJohnson



Becky C is sounding about as frayed as I sound these days ....

As you might guess, we have had quite a few writing assignments sent home to our family this year from the public school. I have been working really hard to teach my boys to write. I have been feeling bitter about this.

Differentiated Instruction does not happen in real life. It is about as scarce as Direct Instruction.



"[I've conducted] a grand experiment in pre-teaching... if even one gullible parent of a 4th grader directly instructs her child how to write a summary paragraph by holding the child accountable for the quality of their paragraph, which is to say that the paragraph contains the right amount of important details... why, that's one more child who magically shows up in 6th grade already knowing how to write, and one less child that will need direct instruction in writing in 6th grade. Magical!

I've just HAD IT with writing assignments that are ASSIGNED to the student but are not GRADED constructively by the teacher as a means of instruction.

HAD IT HAD IT HAD IT



"Speaking of cargo cults, ...

... teachers assign a ten-year-old to write a summary paragraph on The Lousiana Purchase. The ten-year-old is to pull the right amount of important details about that happy event from a two-page single spaced essay given out in class.

To a ten-year-old, every sentence of that essay seems as compelling and important as every other sentence BECAUSE TEN-YEAR-OLDS HAVE NO LIFE EXPERIENCE LET ALONE KNOWLEDGE OF WORLD HISTORY TO JUDGE what they can leave out of their summary and WHAT MUST NOT BE LEFT OUT.

It's this weird inversion of developmental expectations.

It's like they envision my child comfortably attired in a wool cardigan, sitting at home in a shabby leather wingback chair, thick black reading glasses perched low on his nose and hair thinning slightly on top of his head, and he puffs away thoughtfully on his pipe while he writes down the right amount of important details from the essay on a yellow legal pad with his leaking fountain pen.

Teachers think that if you CALL a child a writer, if adults SEE him as a writer, if we CELEBRATE and PUBLISH his writing, that good writing will follow like cargo planes landing on a South Pacific island.

But, NO IT DOESN'T.



And these same teachers think that trying to teach mathematical algorithms too early will result in conceptual damage because children aren't developmentally ready.

And if I complain that they are assigning summary paragraphs before they have taught my ten-year-old how to draw the right amount of important details from a larger piece of writing, they reassure me that all children are different, and my child may not be developmentally ready, and that I really shouldn't be doing his work for him.

I'm NOT DOING HIS WORK FOR HIM. I'm not letting it go, either. I'm trying to teach him how to write a summary paragraph so that he won't get used to school assignments as NOT SERIOUS.

Teachers have the earnest thing down pat, but teachers are not serious.

Whew. Thanks for letting me get that off my chest. Now I'll go have some breakfast.

I find that a good breakfast — or a life-extending glass of red wine over lunch (today's surprise treat!) — is always helpful.

-- CatherineJohnson - 18 May 2006

---

GreatestHitsTeachYourChildToTouchType 20 May 2006 - 23:29 CatherineJohnson





how to teach touch typing - advice from a pro




Of course, I'll probably be too busy teaching math, spelling, vocabulary, grammar, and writing to teach touch typing, too.

UPDATE 11-27-06: good call. Last summer I was too busy teaching math, spelling, vocabulary, grammar and writing to teach touch typing, too.

I still am.

-- CatherineJohnson - 20 May 2006

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ParentSupportMeansParentReteaching 27 May 2006 - 15:22 CatherineJohnson



Great observation from D-Ed Reckoning:

D-Ed Reckoning's tip of the day to parents with kids learning how to read: if your child is confronted with a word she doesn't know how to read and her reading teacher tells her to first look at context clues to guess the word's meaning instead of directing her "sound it out," make no mistake about it, your child is being mistaught how to read. If you're lucky, your child will be one of the ones who finds reading effortless. If, however, your child finds reading difficult, parental support isn't needed. Parental reteaching is needed and needed fast, because the teacher isn't doing her job. And, the longer the child is mistaught, the more difficult the inevitable reteaching will be.

Ken has pulled numerous studies showing that poor learning leads to emotional and behavioral problems in children — problems that can be remediated by improving children's learning, not blaming the child's parents.

It's also worth reading Climb Every Mountain by Laura Logerfo in the new issue of Education Next, a study of the positive relationship between a first grade teacher's personal sense of responsibility and his or her students' learning.

The 4 findings that stood out for me:

• "...teachers who believe that children should know basic reading skills before reaching 1st grade are less likely to hold themselves accountable for student learning..."
  

• first grade teachers who "[endorsed] ... daily homework for 1st graders" felt less responsible for student learning.

• "Teachers in Catholic schools scored 0.28 standard deviations higher on the responsibility index than their public-school counterparts did."

• "...the less financially well-off a teacher’s students are, the less responsibility she takes for their learning (a decrease of 0.18 standard deviations in responsibility for each standard deviation decrease in family income)."
  

These are first grade teachers we're talking about. Their students are 6 years old. When a low-income 6-year old comes to school, he or she has an excellent chance of being placed with a teacher who is already skeptical of his or her ability to learn.

I'm sure this is one reason why Catholic schools do better teaching low-income children than public schools.


keywords: Catholicschools teacherresponsibility


-- CatherineJohnson - 27 May 2006

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VideoMathCurriculaAndSupplements 23 Jun 2006 - 17:39 CarolynJohnston


Dive Into Math

A friend who is looking for a math curriculum for her son for next year (I think he is entering 5th or 6th grade) is investigating video curricula and supplements. She sent me a link to the Dive Into Math curriculum. She's looking for any information anyone might have about it.

Dive Into Math consists of CDs that are designed to supplement the regular Saxon Math curriculum. The lecturer's name is Dr. David Shormann, and he is not shy about telling you that he is a serious Christian. From the Dive Into Math website:

Dr. Shormann's Christian testimony is included on each CD, and several math lessons begin with an encouraging Bible verse. Many DIVE science lessons end with information about famous scientists who were Christians or comments about how a Christian worldview can be achieved through studying science. Dr. Shormann believes that God created the earth in 6, 24 hour days, because the Bible tells him so!

I would find a steady diet of Bible verses in math class a bit tough to take, myself. However, we definitely both like Saxon math. His comments about Saxon's treatment of algebra and geometry are new to me; I guess I haven't thought that far ahead in the K-12 math curriculum yet. I do recollect from my own high school years that we did stop learning algebra for a year, in tenth grade, in order to learn geometry.

We chose to follow Saxon curriculum because we believe it is the best curriculum to prepare a student for college entrance exams and college level math. Saxon problem sets and tests contain a variety of problems, which is good preparation for taking tests like the PSAT, SAT and ACT. We believe the review system implemented by Saxon is very beneficial and greatly increases student retention of the material, which will help any student learn math better. Saxon also integrates geometry with algebra (similar to curriculums found in Europe and Asia), which ensures that the student will never have to stop learning algebra to learn geometry. Some people have heard that Saxon does not have enough geometry. This was true of the older editions, but the new editions have more than enough geometry. To learn more about Saxon Publishers and the legacy of John Saxon, go to www.saxonpub.com.

Contrary to some of the speculative claims currently being made about Saxon Mathematics, we still think it is the best math curriculum available. To find out why, click here to read more.

Teaching Textbooks

My buddy also asked about another curriculum, Teaching Textbooks. She's checked into this video curriculum a bit; she feels it would work well for her son, but it's a series for older kids; they've just added a 7th grade offering, and that's as low as they go. A peek at the table of contents shows a course that is similar in many ways to Saxon 8/7 (Catherine, would you agree with this?), but moves much more slowly in some places and much faster in others. I like the pacing of Saxon, so I wonder about the pacing of this course. Has anyone looked over this curriculum?

And does anyone -- particularly any homeschoolers -- have any other video curricula or supplements that they would recommend?

-- CarolynJohnston - 31 May 2006

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MathTricks 31 May 2006 - 23:43 CatherineJohnson




Came across Math Tricks while looking for Math Teach and Math Learn. This is my favorite so far:

From: Bob Stanarrow <Straitfromtheheart@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001030718:38:50
Subject: How to remember how many feet in a mile

   I figured out a way to remember how many feet are in a mile.

Just say to yourself 5 tomatoes. Really there are 5,280 feet in a
mile, so you can remember that by saying 5 tomatoes.

  5    to   mat  oes
( 5 ) ( 2 )( 8 )( 0 )

-- CatherineJohnson - 31 May 2006

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AGoodYear 10 Jun 2006 - 17:36 CatherineJohnson




We’re ending the year on a high.

Jimmy has his Marra Award; Andrew is defeating digital timers at school. Better yet, Andrew and I have hit the +1 worksheets in KUMON. He's zooming.

Then there's Christopher. Christopher is fantastic. He’s happy, he's confident, he's in the best shape we've seen, I think. We’re glimpsing the person we hope he’ll be when he’s 16 or 17.

Two weeks ago he came home with a 92 on a science test I hadn’t even known he was taking. His science teacher is very good, but still. A couple of months ago he wasn’t getting As on science tests without help from Ed or me.

Christopher studied for this test on his own. “I quizzed myself,” he said.

He invented a study method, which I think he may have based on rap: “I chanted the answers out loud to myself,” he said. That part, I do remember. I heard him downstairs one night loudly reciting material from a textbook.

What he said next may have been the best part: “I don’t know if it works.”

That was a moment, the beginning of skepticism and humility.

In edu-terms, it was the beginning of metacognition, but I don’t want an edu-term just now.

He’d invented his own special way of studying, and he’d gotten a 92 on the test, and even though he'd done well he knew he'd have to try his method out a few times more before deciding it worked. He knew that he didn't know!

Little kids, when they’re happy, think everything they do is great.

If they’re not happy they think they “stink.” “I stink at science” – a classic Christopherism.

When I was in grad school, one of my professors, who was a fairly well-known avant garde filmmaker, said that the beginning of maturity came when you stopped thinking you were a genius, but also stopped thinking you were nothing. He was talking about age 30, as I recall, but kids must make a similar discovery somewhere in the middle years, too.

We’ve spent the whole year battling Christopher over whether he did or did not know whatever it was he was supposed to be able to do on a test. He would insist he knew the material, we would insist he didn’t, he would insist he did, and invariably the dispute would end in tears and yelling. You hurt my feelings!

6th grade is not easy.

On Mother’s Day, Christopher suddenly looked at me and said, “Thank you for all the extra work you give me, that helps me succeed.”

6th grade isn’t easy, but this has been a good year.


-- CatherineJohnson - 02 Jun 2006

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CommonSenseInEngland 08 Jun 2006 - 18:18 CatherineJohnson



In the midst of a terrific post at math-teach, Vlorbik (who, I'm discovering belatedly, has created VLORBLOG 2.0) links to this article in the TELEGRAPH:

Back to basics as maths problems multiply

Modern methods of teaching maths which have mystified parents and confused many pupils are to be abandoned six years after the Government forced them on primary schools.

The same unit at the Department for Education which devised the strategy now wants teachers to go back to the "standard written method" it abolished.

The decision has prompted a backlash from some primary teachers and maths advisers who say children are better able to understand the concept of arithmetic when they break sums down into a series of units.

They say the "back to basics" approach heralds a return to the "dark ages" of adding up, subtracting, multiplying and dividing in vertical rows without understanding what they are doing.

But evidence has shown that many pupils are arriving at secondary school unable to do long division and multiplication and reliant on columns of workings out which take longer and are more prone to errors along the way.

The proposed change, put out to consultation yesterday, has already won support from many teachers on the website of The Times Educational Supplement, who say it is better for pupils to master one, simple, standard method than struggle with many. [ed.: I'm not surprised - I also haven't been able to track this down.]

[snip]

The decision to return to the old methods will come as a relief to many parents.

Christine Turno says she dreads the twice-weekly homework with her nine-year-old daughter.

"She goes ballistic," she said. "We have massive rows because she says I'm doing it wrong and she has to do it the way the school says. But she can't understand what they want and it's a complete mystery to me."

A 20-minute homework session turns into an hour.

Mrs Turno, of west London, said: "The teachers say it is the new way and if the answer is wrong it doesn't matter as long as she is using the right method. It's quite bizarre."

I've learned from The War Against Grammar that Britain also restored formal instruction in grammar in 1998.

So we'll see.





All this stuff is going away:








British education URLs

• Department for Education and Skills
  UK Department of Ed
  

• QCA
  "non-departmental public body, sponsored by the Department for Education and Skills (DfES)...
  maintains and develops the national curriculum and associated assessments, tests and examinations"
  

• Ofsted
  "inspectorate for children and learners in England"
  

-- CatherineJohnson - 07 Jun 2006

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NewYorkSun 11 Jun 2006 - 01:10 CatherineJohnson



I finally broke down and subscribed to the New York Sun, scandalizing Ed, who thinks 3 newspapers a day are enough.^*

I'm glad I did it. The Sun makes me feel as if I've picked up and moved to another city. In The Sun, New York is a town filled with charming & obscure neighborhood chapels and International Centers of Photography staging exhibits of mysteries like Unknown Weegee, Weegee apparently having been a photographer who followed cops around in the 1940s and took pictures of dead bodies. It seems that Weegee was an unpleasant character:

Weegee was a pest," Helen Gee wrote in 1997. "Popping off flashguns in customers' faces ... handing out greasy name cards, rubber-stamped with his logo, Weegee the famous."

Gee, the proprietor of Limelight, the first New York gallery devoted exclusively to photography, admired Weegee's tabloid photojournalism from the 1930s and '40s, but she had little use for him as an individual. (Among other things, he asked to photograph her daughter naked.) By the late 1950s, Weegee's fame was fading, and he had become something of a pathetic character. When Gee finally offered to give him a show at Limelight, he wanted to put up pictures taken with a trick lens, instead of his famous crime shots. "These broads with five tits will be a sensation," he insisted. "Nobody's done anything like it."

That sounds good to me.

On another morning I find one Lawrence Otis Graham ($?), a black man who went to Princeton and supported himself handsomely while there by writing books:

"Some kids worked in the dining halls or the library - my job was writing books," he said.

The first of his 14 books was about a 10-point plan that Mr. Graham devised for high school students to gain acceptance at a college of their choice. It was an instant success, not the least due to its serialization in Good Housekeeping magazine.

"I wrote a book a year while in college," he said. "By the time I entered Harvard Law School, I was making a tremendous amount of money."

Mr. Graham also became an entrepreneur while at Harvard. Teaming up with a friend, he launched a newsletter about marketing to young people, especially in affluent black communities. The newsletter, which sold for a subscription price of $500 annually, made its publishers a tidy fortune.

It was at Harvard that Mr. Graham met Pamela Thomas. Like him, she hailed from a prosperous African-American family. Like him, she was ambitious - obtaining an M.B.A. from Harvard in addition to a law degree.

They married not long afterward. The Grahams have three children, Gordon, 7, and twins Lindsey and Harrison, 4.

Pamela Thomas-Graham is group president of Liz Claiborne Incorporated. Earlier, she was president and chief executive officer at CNBC. Before that, at 32, she was the first black woman to become a partner at the fabled consulting firm McKinsey & Company.

Ms. Thomas-Graham writes mysteries whose locales are Ivy League schools.

"There might be a hint of the overachiever in both of us," her husband said. "But we were brought up to succeed - and to make our contribution to contemporary American society."

I think Lucy Calkins should spend more time reading the Sun, and less time reading the Times.

Lawrence Graham has a new book coming out: The Senator and the Socialite: The True Story of America's First Black Dynasty.






The Sun also seems to run sayings on the op-ed page nearly every day. Now that is an excellent idea.

From today's paper:


Nothing will ever be attempted if all possible objections must first be overcome.
- Samuel Johnson

My thoughts exactly.

And here's Emile Zola on Edouard Manet:


In beginning a picture, he could never say how it would come out.




On Tuesday I woke up to find this dress on the front page:



designer: Oscar de la Renta

I want this dress. I'm never going to have it, but I want it.

Since I'm not going to have it, I think getting to look at it on the front page of my newspaper is a good thing.



Here's Weegee:




Weegee
source:
The Gibbes Museum of Art

source:
bezembinder




Summer
source:
coldbacon



Naked City
Weegee chronology
Weegee's profile & photos
Weegee: Paparazzi or Social Documentarian?
Fragment.nl "Writing is a trip"
coldbacon index of Weegee pics





^* Grammar query: 3 newspapers are? or 3 newspapers is? Now that I've read David Mulroy's The War Against Grammar, I intend to find out.



-- CatherineJohnson - 09 Jun 2006

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HowToSucceedInMiddleSchoolWithoutReallyTrying 29 Jun 2006 - 16:34 CatherineJohnson



I think our household stumbled onto a plan for managing middle school this year.

Christopher continues to be in almost bizarrely good shape. He brought home another couple of As this week — a 92 and a 98 — both in English. One of the tests had essay questions on which he lost just one point.

This is the teacher who had been giving him grades of C on his writing.

It’s not just the sudden appearance of high grades that’s so good to see. It’s the attitude. Christopher today is the kid we’ve been trying to grow. He’s serious, friendly, cheerful, and above all non-cool.

Ed is funny on the subject of cool. We were talking about Christopher not being cool one night, and Ed said, “You never want a boy to be cool.”

I suspect you don’t want a girl to be cool, either.

Of course, he’s young yet, so I shouldn’t count my chickens. Coolness may yet emerge. For the moment, though, Christopher has no sardonic humor (middle-school quippiness, yes; sardonic humor, no), his hair is short, and his pants aren’t hanging off his bottom. I’ll take it.

I have an idea how this happened – and I think this may be a workable approach for other kids in other schools.





Toru Kumon was right

Christopher’s afterschooling is pretty minimalist at this point. At least 5 days a week he does:

• Megawords, 1 page
• Vocabulary Workshop Level A, 1 page
• KUMON Math, 1 to 2 pages
  

Christopher does this work on his own. He takes his materials down to the basement and works alongside his dad, who has set up a desk for him there.

I’m going to add grammar (sentence diagramming in particular), writing, and possibly some extra work in Spanish to the mix. But when I do I’ll follow the same formula. One page a day in each subject, assigned from the same book each day, which lives in the same place on his desk upstairs. A book he can manage on his own.

When I first went to KUMON, part of the pitch was that KUMON's daily worksheets turn children into “self-learners.”

The American website seems to have dropped that language now, but you can still find it on other sites:

Self learning and Self motivation

Kumon students study independently at both Kumon Centers and at home. The role of instructors within the Kumon Method is focused almost entirely on the development of a student's ability to learn on their own. Kumon refers to the ability to set goals and solve unfamiliar and challenging tasks independently as "self-learning" ability. Instructors foster this "self-learning" ability in students by using worksheets that allow students to learn at one's own pace, moving forward when they are ready. The students' enthusiasm for learning is aroused in this process, as the goals they set are their own goals. In addition, this process awakens a desire in the students to take on new challenges.

Instructors ensure that students can, without any hindrances, experience over and over a sense of accomplishment, thereby boosting confidence in their own abilities. Problem solving abilities are enhanced, and independent methods of solving problems are encouraged.

When I read this passage last fall, I didn’t get it.

It made sense that KUMON would increase a student’s self-confidence, but I didn’t see why “succeeding” at worksheets would produce a “self-learner.” When you talk about self-learning you're talking about executive function, and I didn’t see how filling out 5 math worksheets a day had anything to do with frontal lobe development.

Now I think Toru Kumon was right, though I still don’t quite understand it. “Drill and kill” doesn’t just lead to procedural mastery and confidence. Somehow drill and kill also helps develop independence, motivation, and a responsible nature.

Is it the same principle that’s at work in military training?

It’s probably fair to say that military training is literally “drill and kill.” I don't know anything about the military, but as far as I can tell the result of military training is a young man who can follow commands or give them, and keep his wits about him in the midst of battle. All good things.

I don't know how it works, but I do think "the KUMON principle" has proved itself around here.

I also think that, in terms of Christopher's grades, the psychology of this year's "hands-off" afterschooling has been more important than the actual content Christopher learned. His afterschool books have little to do with his present school work. He's still in Level D - 4th grade - in KUMON Math, and vocabulary and spelling will pay off in the long run, not the near term.





who's in charge

I've mentioned more than once that, before Christopher entered middle school, I had decided I needed to "own" math.

I figured Phase 4 was going to be brutal, and I needed to "own" math to limit the damage.

Then it turned out we needed to own more than math; we needed to own the whole academic enterprise. Christopher has had at least 2 — maybe 3 — good teachers this year in his core subjects, but the school is a dark place.

Yesterday a friend of mine captured the unspoken school motto in 5 words: Do this or you're f*****.

That's it. That's what our kids are up against.

Label your graph, or 50% off.

Show your work the way I want it showed, not the way you thought I wanted it showed, or 20 points off.

Use complete sentences on the science test or points off. (That's coming up next year.)

Have your mom sign your test tonight or it's points off-off-off!

I think Tracy once used the expression gale of negativity.

That's what it's been.

Setting up an "afterschooling household" strips power and authority from the school in a good way. The message to a 6th grade child is: your job is to learn stuff.

Doesn't matter what grade you got.

Doesn't matter if the other kids think you're dumb. (Christopher says the other kids think he's dumb.)

Doesn't matter that you spent 4 hours on your scale drawing and Ms. K. deducted 20 points because you showed your work the wrong way and you still don't know what the right way was.

Go get your books and learn something.

Remember when Mr. Liu said that the Asian way is to be persistent and patient?

I didn't set out trying to create our own Personal KUMON. It evolved.

But I think we ended up teaching persistence and patience. I hope so.



NEXT: LEMONS & LEMONADE, WINDS OF WAR, AND REACTIVE TEACHING REDUX


-- CatherineJohnson - 10 Jun 2006

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SummerPlans2006 22 Oct 2006 - 21:34 CarolynJohnston


School ended on Thursday, and I can already see Ben calming down and relaxing. This has been a tough year for him. I've read Catherine's description of Irvington Middle, and I can't complain that Ben's school is anything like that; that's a whole different order of awful. But I think middle school, even at its best, is pretty awful. Give em another couple years in elementary, that's what I think.

High points of the year:

• Science class -- he had a great teacher who taught a very content-heavy class (yes, I'm a content freak). As a result of this class, we can talk about why people in airplanes (with which he is fascinated) feel pushed back in their seats when the airplane takes off, even when it's level. We can talk about Bernoulli's principle, and how it makes planes fly. I can talk about what causes mirages with him. It's wonderful. It's what school is about. Ben really dug that class, too. Great science teachers are rare as hen's teeth, too, so we lucked out.

• Math -- good old Saxon. Ben worked hard and learned alot. He was sad not to be in the regular class, though -- next year, we'll try again (I hear this teacher is more heavy on the Prentice-Hall and less heavy on the Connected Math than the 6th grade teacher).

A coda on this story -- the other day in the local coffee house, I heard a bunch of moms talking about the math class Ben was originally in, and how they can't help their kids with the math, and how the teacher tells them that's because it's different math that they learned. Snicker.

• Reading -- Ben's reading skyrocketed this year, independently of everything else that was going on. He read all the Harry Potters up through half of Harry Potter 5 (which got to be rough going because it's dark and depressing). Last year, I couldn't have imagined it. However, he's slowed down since doing all that Harry Potter, since he hasn't liked anything else as much (JK Rowling really has a golden touch). Any recommendation as to where to go from Harry Potter?

• Personal growth -- Ben's official record doesn't show it, but Ben definitely went through some heavy changes this year. He is much more socially aware than he used to be, and this brings pain with it, of course. But much better to have him become more socially aware than not. Pain comes with the territory for all these kids.

Low points of the year:

• Reading and writing class: pretty much a waste of a year, since he did no true research writing assignments, short or long. It was a special ed class with a lot of in-class support for all the kids, and they wanted to keep Ben there, and after pushing the math issue I decided not to fight to have him moved. He's regressed as a result, but we'll work on it over the summer. Maybe we'll reinstate the Kumon reading I tried to start with him last winter.

• Social studies: not so much good or bad as neutral. They covered the same stuff he covered last year. This kid is an expert on South America now.

Last but not least, something for the special ed parents. Ben had a set of (what we all thought were) reasonable goals on his IEP in October. Such as: Ben will express in words what is bothering him, 70% of the time without adult prompts (this is a very typically stated IEP goal). Another one: Ben will organize his own folders and keep track of his belongings (HA. Double HA).

I got the last installment of his quarterly IEP report the other day, and all 8 or so goals have been listed as being "in progress" every single quarter. Not a single goal has been achieved, and I don't know why not because I have no real information about it. As far as I can tell, noone was taking the document seriously. I am tempted to call an IEP meeting for this summer and ask for an explanation and a change in course, but my first impulse is usually wrong. Any ideas from the experts on how to make next year a better year for him?

Summer plans, 2006, really this time

So now it's the summer, and he has a little time and mental space for doing some learning and catch-up. Here are my plans:

• Get him reading for pleasure again (this means finding good books that he likes. Anyone have any ideas? He really loved Harry Potter).
• Have him do his vocabulary a little every day (this is pretty easy with the Sadlier-Oxfords).
• Finish Saxon 8/7 (he got up to lesson 90 in school, so there are 30 lessons to go. This is definitely a reasonable goal).
• Have Laura work with him on his writing (Laura is our brilliant and genial therapist, who's been pulling Ben along reluctantly* for 9 years now).

I'm not going to pursue getting him touch typing this summer, much as I'd like to. I know darn well that I probably won't achieve all the stuff I've already set out to do, so why make it worse than it has to be?

Please share your summer plans for your kids with us, if you have any.

One more thought

I was at a barbecue tonight, and someone mentioned a recommended practice from a book on adolescent-rearing. The practice is that when you tuck your child in, you play a sort of a game: you each tell each other things that you like about them. Ben and I did it tonight, and it was lovely. It went something like this:

Me: I like it that you're so nice that you could say you felt sorry for [Adult family friend in bad position], and tell me why. (It really was amazing).

Ben: I like it that you snuggle me, and take me out for dinner.

Me: I like the way you love maps and are interested in where things are, and can tell me which way is the right way to go.

Ben: I like it that you're smart and you can teach me math (!!!!).

Me: I like it that you're so nice you let those toddlers chase you and play with you at the party today.

Ben: I like it that you do computers and make maps for your work. (!!!!!)

And so forth. I think it's an every night thing, and I think it's okay (I think it's necessary!) to repeat themes, but with new examples from their day. It's basically a codified positive interaction, and I thought it worked very well for us, which means it would probably work very well for practically anyone.

* reluctantly refers to Ben, not to Laura!

-- CarolynJohnston - 11 Jun 2006

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MeetTheParents 10 Nov 2006 - 22:43 CatherineJohnson




From today's Wall Street Journal — why is the tutoring industry exploding in the U.S.?

It's the parents!

Back in the 1980s, when Japanese financiers gobbled up U.S. companies like so many Pacmen, Americans became unnerved. Japanese society seemed scarily focused: The discipline in schools was so brutal that a tardy child might be crushed to death by the doors slamming shut precisely on time. We heard about juku, cram schools where Japanese children went each afternoon after regular classes for three hours more of academic drilling; Saturdays, too.

Americans joked about how we'd all be carrying yen in our wallets someday, but we could comfort ourselves -- and people did -- by saying that at least our children were individuals. American childhood was to be enjoyed, not grimly marched through with joyless eyes fixed on getting into the Ivy League.

Ah, but will you look at us now? We're building a juku system of our own. Millions of American children no longer have the time to kick a ball around after school because they're already late for an appointment with the math tutor or a "study skills" lesson or cognitive skills training or Spanish immersion or "reading comprehension support" or academic enrichment of one sort of another.

[snip]

...tutors have long been a fixture of both ends of the bell curve. Struggling children got help to keep afloat at grade level; super-bright children might see tutors to challenge them further. What's happening now is different. Tutoring has become near ubiquitous among the panicky classes: middle- and upper-middle-income families where there are ample brains and money.

Today it's not uncommon for six-year-olds to receive private lessons in how to overcome "executive function issues," for if they can't handle the paperwork in first grade, heaven help them in the cutthroat bureaucracy of third. Middle-schoolers see tutors to boost their math and reading skills, and thus help them get into the right high school; high-schoolers sign up for private SAT prep.

source:
Educational Supplements
by Meghan Cox Gurdon

question

If someone were to tell you his child was enrolled in a school where six-year olds can't handle the paperwork in first grade, would your first thought be, "Wow. Tutoring has become near ubiquitous among the panicky classes"?

Or would it be something more along the lines of, "Wow. John Gatto Taylor was right"?


there's more

"In 1989 I would mumble, 'I'm a tutor,' and hang my head a little, because it seemed a marginal job," says David Kahn, who runs a tutoring company in Manhattan. "People used to think it meant I was poor, and now they think it means I'm rich."

There is no real mystery about why tutoring has become such a growth industry. It can be traced in part to the proliferation of standardized tests. At Kaplan, the biggest corporate tutor, the number of students in its test prep and after-school programs has more than doubled since 1998. According to the research firm Eduventures, schools spent $879 million on corporate tutoring and test prep in the 2004/2005 academic year -- 25.2% more than the year before. Uncle Sam is giving tutoring a boost too. Under No Child Left Behind, the federal government pays for the tutoring of any kid in a failing school. (This market in tutoring for low-income students barely existed six years ago.) In all, Americans spend more than $4 billion a year on tutoring.

The propelling force behind this revenue stream is, of course, [ed.: "of course"?] modern parents: a whole generation of anxious, competitive, aspirational parents who agonize about whether their children are doing well enough, or missing out on anything, or, God forbid, falling behind in some crucial way.

So David Kahn has either got to be married to someone at the WSJ, or he's tutoring all their kids. He doesn't have a tutoring company, as far as I can tell, and the journal has run a full-length op-ed that he wrote and is now quoting him in a follow-up.


it gets worse

It is a truth universally acknowledged among teachers and tutors that modern parents want their children to do exceptionally well. They demand A's, not B's. They expect stratospheric SAT scores. Anecdote suggests, however, that they seldom want to spend any time in pursuit of these goals themselves.

Anecdote suggests, does it?

Well that settles it!

[A] whole generation of anxious, competitive, aspirational [and lazy] parents who agonize about whether their children are doing well enough, or missing out on anything, or, God forbid, falling behind in some crucial way is the problem!


it's all bad

Mr. Rossiter's experience hints at a darker trend of which mass tutoring is only a symptom: the spread of a high-grade, get-ahead academic ethos that is decoupled from an actual, mind-broadening education. On NPR recently, a reporter asked 87-year-old Hazel Haley, who just retired after 67 years of teaching English in a Florida high school, how today's teenagers differed from the ones she taught generations ago. She gave this dispiriting response: "Today's young people [think], 'I'll learn it for the test, I'll do well on the test, and then I will flush it.'"

Mr. Kahn, the Manhattan tutor, notices the same thing. He sees a distressing number of children who are "completely burnt out and won't accomplish anything in college because they were driven through high school the way an associate is driven through a law firm."

"For many kids," Mr. Kahn says, "getting into college is such an ordeal that once they're there, they just kick back." Shades of juku again: In Japan, cram schools focus on getting into university, not necessarily getting much out of it. It's a shame that we're importing that frame of mind.

Ah.

Further Googling reveals that Mr. Kahn is "a former teacher in New York City who has been tutoring middle and high school students in math and English for 15 years."

That explains a lot.

Parents love and idealize teachers; at least we start out loving and idealizing teachers. Teachers, as a group, do not return the sentiment.

Exhibit A: Mr. Kahn. This is a man who makes a tidy living tutoring other people's children; his employers are parents. Yet here he is piping up with the parent-bashers.

Personally, I would like to hire a tutor for Christopher. I would like to hire Mitchell Dobbs, the legendary writing teacher now retired from our middle school. So far, no luck. His mother is ill; when we spoke he was going back to Kentucky to care for her.

I would like to hire Mitchell Dobbs because Christopher's school is not going to teach him how to write, and that's making me feel anxious, competitive, and aspirational. The very thought that Christopher, going into 7th grade, has not been taught to write and will not be taught to write next year, either, is causing me to agonize about whether my child is doing well enough, or missing out on anything, or, God forbid, falling behind in some crucial way.

So, yes, I would like to hire Mitchell Dobbs.

I will not be requiring the services of Mr. Kahn, however. Nor will I be ordering any of his books (assuming that Princeton Review David Kahn and WSJ David Kahn are the same person, of course):

High School Math III Review
Cracking the Regents
Cracking the AP Calculus AB and BC Exams, 2006-2007

I take it back

"It's hard to teach your own child," says David Kahn, M.S., a former teacher in New York City who has been tutoring middle and high school students in math and English for 15 years. "A kid will listen to a tutor when he won't listen to a parent, or maybe even a teacher. A tutor can be an impartial referee — someone to motivate and guide, without judgment and without any emotional baggage."

Now that is a sensible, friendly, non-parent-bashing observation.

Which puts me back in the market for one or two or three of his books. Check out this Amazon review:

This book saved my skin. I found out two days before classes started that I had to take a math placement test in order to get into calculus. I had taken trig 7 years ago and forgotten it all, but this book explained everything so well, it re-taught me all my trig in two days and I aced the test! The explanations are so simple and clear, you only have to memorize three things--you'll understand everything else well enough that you can just draw a triangle and figure it out! This book summarizes everything you need to know clearly and concisely, and it gives lots of examples and problems to work. If I saw the authors right now, I'd give them a big old smooch!

New theory: David Kahn is probably a superb tutor who's being endlessly quoted in the WSJ because the gazillion anxious, competitive, aspirational [and lazy] parents who've hired him to get their kids through math (and English) think he's a genius.

I hope Mitchell Dobbs comes back soon.

When he does, I hope he'll be willing to take a new client.




I wonder what Meghan Cox Gurdon thinks about helicopter parents?





meet the parents (big-time tutoring)
debunking the debunkers (Rothstein; What Money Can't Buy)

gradedeflation

-- CatherineJohnson - 17 Jun 2006

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UnderstandingMath 18 Jun 2006 - 14:33 CatherineJohnson



from Peter Alford's website (scroll down)—

You understand a piece of mathematics if you can do all of the following:

• Explain mathematical concepts and facts in terms of simpler concepts and facts.

• Easily make logical connections between different facts and concepts.

• Recognize the connection when you encounter something new (inside or outside of mathematics) that's close to the mathematics you understand.

• Identify the principles in the given piece of mathematics that make everything work. (i.e., you can see past the clutter.)

Wonderful.

In terms of math and the math wars, I especially admire the first principle: you understand mathematics when you can explain mathematical concepts and facts in terms of simpler concepts and facts.

The NSF-funded curricula seem to have been trying for this idea. But they bungled it.

A person who understands something can explain it in different terms. But those terms don't have to be words - and, in the case of math, probably shouldn't be words, or at least not solely words. Alford's formulation is more sophisticated. Being able to explain something means being able to explain it in simpler concepts and facts.

I'm think I'm going to post these principles over Christopher's desk. They're universal. I've been using them for years, without having tried to sort them out or write them down. Alford has made them explicit for me. When I'm writing a book or an article, I know I'm succeeding when I can do these four things.

Seeing past the clutter — that's the big Kahuna.

Temple calls it "finding the basic principle."





Saxon Math

Saxon Math probably does a superb job of using these principles to teach math.

This year I learned from Saxon Math, for the first time in my life, that when we find areas we are always multiplying "two perpendicular dimensions." (Saxon 8/7 Lesson 82 Area of a Circle)

Of course, I sort-of knew that.....but I'd never made the connection between finding the area of a square and finding the area of a circle. (Have I mentioned my education in mathematics left a lot to be desired?)

That one observation, in Saxon 8/7, permanently changed my perception of area & volume, permanently increased my comprehension of area and volume, and permanently improved my ability either to remember area and volume formulas or to derive them when I don't remember them.

Saxon used seven sentences, illustrated by geometric figures, to make that observation. This passage embodies all four of Alford's principles:

We can find the areas of some polygons by multiplying two perpendicular dimensions.

• We find the area of a rectangle by multiplying the length by the width.
  
  A = lw  [illustration of square]
  
  

• We find the area of a parallelogram by multiplying the base by the height.
  
  A = bh  [illustration of parallogram]
  
  

• We find the area of a triangle by multiplying the base by the height (which gives us the area of a parallelogram) and then dividing by 2.
  
  A = bh/2 or A = 1/2bh  [illustration of triangle]
  
  

To find the area of a circle, we again beegin by multiplying two perpendicular dimensions. We multiply the radius by the radius. This gives us the area of a square built on the radius.  [illustration of circle]

-- CatherineJohnson - 18 Jun 2006

---

LegosForVolumeAndArea 03 Jul 2006 - 19:32 CatherineJohnson







After Ed did his final teaching-to-crammery unit on volume formulas, "teach conceptual understanding of volume formula" popped onto my to-do list.

I don't know whether I acquired much comprehension of volume formulas when I was in school. I don't think I did. Since I've been reteaching myself math I've spent quite a bit of time staring at array models trying to grok the fact that 3 x 4 really is 3 "of" 4 and vice versa.

I love array models.






source:
joannegoodwin 2nd grade class



Saxon 8/7 has a number of fantastically effective lessons in which students have to figure out how many 1-inch square sugar cubes will fit into a square or rectangular box. I haven't checked Prentice - Hall (I may never be able to look at that book again) but I'm guessing Christopher didn't spend a lot of time thinking about how many small cubes can fit into a larger cube or prism.

So I was gearing up to search through Saxon 8/7, find all the lessons with sugar cubes, figure out a schedule, harrass Christopher to sit down with me and go over them, etc. when it struck me that a cottage-cheese size six-dollar plastic container of tiny Legos would do the job.

I bought two little white bases plates, each measuring 8 x 2cm and a bunch of white & see-thru red squares. Christopher likes to build Legos &mdsah; at least he's back to liking them at the moment — so he can spend some time building Lego rectangular prisms & cubes and I won't have to spend hours tracking Lessons in Saxon 8-7 and then tracking Christopher to get him to come do them.

I also found the coolest little Lego thingie for fooling around with area & circumference of circles! It's a Lego square with a Lego circle on top, that turns. don't know what it's supposed to be. I'll see if I can find a picture.

[pause]

I have no idea what I bought. It's minute — diameter is 3 cm — and we won't spend much time with it.

But it's all I need for some hands-on distributed practice.


I'll also have him take a look at this webpage for Houghton Mifflin Math:


The volume of a rectangular prism can be found by counting the number of cubic units or by using a formula. The formula for finding the volume of a rectangular prism is V = l w h.




The volume of this rectangular prism is 30 cubic meters.

Another way to measure a solid figure is to find the surface area. Surface area is the sum of the areas of all the faces of the solid figure. Since opposite faces of rectangles or cubes have the same area, you can also multiply each area by 2 and then find the sum of the areas of the faces.





The surface area of this rectangular prism is 52 yd2.

Perimeter, area, volume, and surface area are measurements of geometric figures. Perimeter and area are measurements of plane figures and surface area and volume are measurements of solid figures.


This one's nice, too:

To find the area of a complex figure, separate it into simpler figures, find the areas, and then add the areas together.





And these two:


Figures with the same perimeters can have different areas.





Figures with the same area can have different perimeters.





teachtocrammery



-- CatherineJohnson - 19 Jun 2006

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BlowUpTheEdSchools 23 Jun 2006 - 15:59 CatherineJohnson



Eduwonk links to Mike Piscal again today. You should read and memorize all 3 of his posts, but at the moment I'm interested in this one:

Why can’t a future teacher get a bachelor’s degree in a field he/she loves, take an additional 7 or 8 classes on teaching while still an undergraduate, and graduate with a credential? The most elite private schools – Exeter and Andover and Choate, for example – hire teachers with that kind of preparation. So do the country’s network of successful charter schools. Why can’t public schools do the same?

In the words of Deep Throat: follow the money. A recent article in Education Week (March 16, 2005) sums it up: “Critics have long accused universities of using education schools as cash cows, generating more in tuition from a steady stream of students than the institutions actually spend to educate them. With the expansion of off-campus programs in educational administration taught mostly by part-time professors, the report warns, the problem is getting worse.”

A college graduate who wants to teach in public school must attend school fulltime for one or two additional years (in some cases for as much as $20,000 a year), or she can go directly to work at a public school and take classes at night and on weekends for the next 3 to 5 years, also at her own expense. The time sacrifice is enormous. In the words of one Education Professor: "the opportunity costs of forcing half of the California Teaching workforce into "continuing their educations" in the name of credential seeking or renewal (AKA life-long learning) while attempting to teach a full day in the classroom, means that typically three days a week many of our teachers are not grading papers or preparing tomorrow's lessons. It means they are stuck in freeway traffic on their way to the next required credential college course, or they are at home writing the paper due tomorrow for that course. We don't train airline pilots WHILE they are flying commercial flights! Teachers are a different matter because, I guess, kids don't crash and burn."

[snip]

At my school, a teacher needs only a scholar’s zeal for the subject s/he studied in college, and a burning desire to lead the next generation. We’ll take it from there – from lesson planning to classroom management, from discipline to communicating with parents, she will learn from master teachers who are eager to lead and encourage the younger faculty. That’s how it works at Exeter – where tuition is thirty-eight thousand dollars a year – and that’s how it works in my school – where tuition is free.

Here in NY state, we're down to the wire (it seems) on the question of whether the cap on charter schools will or will not be raised.

The politics are astounding.

Nick Spano, our state senator & a Republican, presented Irvington with money for white boards or smart boards or something along those lines a couple of months ago. Then he delivered a blistering attack on vouchers, charter schools, and George Pataki.

Ed, who has voted for precisely one Republican in his life, came home scandalized.

"Isn't that guy a Republican?" he said. "He's attacking charter schools! He's attacking George Pataki!"

Ed's capacity to continue to be amazed is exceeded only by my own.



On the plus side, it's nice to know public school teachers are far better trained than the faculty at Exeter and Andover.





update: Joe Williams on NY charter school law

You can email Governor Pataki here after you read Wiliams' post, if you like.



blow up the ed schools part 1

View Park Preparatory Accelerated Charter Schools
Inner City Education Foundation



-- CatherineJohnson - 21 Jun 2006

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ParentsAtKipp 24 Jun 2006 - 15:29 CatherineJohnson

KIPP, I think, makes parents better by giving them something to do, and yet does not put so heavy a burden on them that they might collapse under the strain. In the KIPP system, students who do not complete their homework in time for class the next day are in as big trouble as I would be if I did not send my stories to my editors before The Post was distributed the next morning. The parents don't have to correct or explain the homework. If students have questions, they are told to call their teachers, whose cell phone numbers they have. All the parents have to do is make sure their child had completed the homework, and sign the paper to demonstrate that they have looked at it. If they don't do that, their child is disciplined -- usually made to sit in a corner of the classroom -- and the parents are asked to come to school to discuss it. Their only other important duty is to get their child to school each day, which in most big cities can be done by making sure they catch the right bus.

source:
Assessing the KIPP Schools -- a New Perspective
by Jay Mathews

-- CatherineJohnson - 24 Jun 2006

---

SummerSchool2006 03 Jul 2006 - 19:43 CatherineJohnson




Still getting my act together on the summer program around here.

Andrew's set. He's doing KUMON Math and, as of today, KUMON Reading.

Amazing KUMON moment this week: I took a set of worksheets to school to show Andrew's teacher & aide how well he does with them.

Good thing I did, because they had no idea whether Andrew can or cannot do beginning addition. The answer is that he can, and they're the ones who taught him. They were blown away when they saw him whiz through a sheet of add-ones problems. The problems were sufficiently mixed that it was clear he understood the principle; x + 1 means the next number up from x.

The sheets I'd brought in had problems in the 30s, I think (30 + 1, 32 + 1, etc.). After he did a few of those I skipped ahead to the last sheet in the stack. The final problem was:


1000 + 1 =


Andrew frowned at this and hesitated.

Then he typed "1000" on the AlphaSmart.

I was mortified. I figured this was the moment where his teacher and aide would decide he was just learning by rote.

But I was wrong. They were both watching him intently. I said, "No, 1000 plus 1."

Andrew hadn't stopped frowning at the problem, which I think is part of what had his teachers so interested.

He reached out his hand, and deleted the final zero, then typed in '1.'

1001

They couldn't believe it. The mistake was what convinced them he knew what he was doing. I don't know whether they've seen him self-correct before; they probably have.

But watching him self-correct while doing a brand-new problem no one's ever shown him was the magic.

As impressed as they were, they stilll wanted to know whether Andrew could add ones if you wrote them in a different way, on a different kind of paper. This is the "hyper-specificity" problem that's so frustrating with autistic kids, and that is the center of Animals in Translation. The reason they were so frustrated with his progress in class, apparently, is that his performance is inconsistent – and the inconsistency seems to be related to changing fonts or paper, etc.

I’d never checked to make sure Andrew could do the same problems in different fonts and on different size paper (which I should have).

They gave me a sheet of paper, and I hand-wrote a ones problem.

Andrew answered it instantly.

They were convinced.

They were so convinced that they said they wanted to use KUMON as Andrew’s math curriculum this summer.

We talked about what the problem might be for awhile, and none of us knows. I'm guessing the problem is that the school doesn’t have a math curriculum for Andrew, mainly because there isn’t one, although KUMON may serve.

Clarice ordered Engelmann’s DISTAR program back when she was hired, and she gave it to me to take home. I got to spend two days holding the Presentation Book in my hands (I wish Ken had been there!) It looked like everything it’s cracked up to be, but it didn’t look like something a teacher could do with Andrew. I suppose you could type the script and have Andrew read it....which might be a good idea. I had to return the program the next day, and didn’t have enough time to think it through.

What's happening in class is that Andrew will seem to have mastered an addition fact, but then later on will seem to have lost it.

For the time being, I'm assuming that because they don't have a curriculum any one or all of 3 things has happened:

• they aren't teaching the math facts coherently

• they haven't given him enough distributed practice

• they haven't given him enough massed practice

As to the first, KUMON's worksheets are the ultimate coherent curriculum. The child does many, many worksheets on adding one to a number before moving on to add 2s to a number.

KUMON doesn't stop with the within-ten addition facts, either. Instead it takes the child all the way from 1 + 1 to 1000 + 1 before moving on to + 2. Clarice hasn't done that, I don't think. I think she had him learn all the various addition facts up to 10.

She said Andrew will seem to have mastered 6 + 4 = 10, but then when they ask him 6 + 4 a week later, he doesn't know.

I'm hoping the reason he forgets 6 + 4 is that 6 + 4 doesn't have the meaning it's going to have in KUMON.

I'm also wondering whether "massed practice" — aka drill and kill — may be especially important or even critical for developmentally disabled kids. Everyone in the U.S., constructivists & cognitive scientists alike, seems to have decided that distributed practice is the key to the kingdom. (TRAILBLAZERS & EVERYDAY MATH both claim to give children distributed practice.)

But I've always found I need to do a certain amount of massed practice in the beginning just to remember a concept well enough to be able to do distributed practice. Andrew is tough to deal with; I bet they haven't made him sit in a chair and do the same addition problems over and over again the way KUMON does. I wouldn't have.

In any case, we're moving on to +2 in a couple of days, so at that point I'll start occasionally asking him to do a +1 problem to see if he remembers.

We'll see.

As to KUMON reading, this morning Andrew was aghast at the discovery that in addition to the 5 KUMON math pages he has to do every day he now has 5 KUMON reading pages, too.

heh





summer school for Christopher

First off, I've had my second abject failure in afterschooling books: Sentence Composing for Middle School: A Worktext on Sentence Variety and Maturity by Don Killgallon.

I love this book — I even bought the college level one for me — and it's worthless for Christopher. The first exercises ask you to divide a sentence up at its natural breaks. For instance:

The only way to / keep your health is to eat what / you don't want drink / what you don't like and do what you'd / rather not.
- Mark Twain

The student is supposed to rewrite the sentence putting the slashes where they belong.

Christopher can't do it. He's so far away from being able to do it that he doesn't even really get what he's supposed to be doing. The whole thing makes no sense to him at all.

I thought he'd start to get the hang of it after awhile, but he didn't. He doesn't have an "ear."

Some kids do. My friend Kris's little guy, Charlie, has an ear. I went over one day & he came running up to show me something he'd written. He was missing a comma, and when I pointed it out he stopped in his tracks and talked the sentence to himself under his breath, and he heard where the comma was supposed to go. "Oh yeah!" he said, looking happy.

My other afterschooling flop was Daily Paragraph Editing, which I was using in 5th grade. I pushed Christopher through pages & pages of that book without his performance improving a jot. Finally I talked to his teacher, the brilliant Ms. Duque, and she said forget it. The book wasn't teaching him anything.

I interpret these failures to be more grist for the direct instruction mill. Christopher needs to be directly taught punctuation and grammar. Period. Then he'll have an ear.

I think he will, too. We've finished Megawords Book 3, and his ELA teacher, the other Ms. K, has been giving spelling tests all winter and spring. Ms. Duque taught spelling, too. So he's had a lot of spelling.

Suddenly, Christopher is using spelling rules to spell words he doesn't know, and he's getting them right, too. Boy is that great.

His spelling is so much better, it's amazing. Back in 3rd grade his spelling was A SCANDAL. It was almost psychotically bad, like those jokes about Eastern European languages with no vowels. These days he's starting to have normal not great spelling. In one paragraph of prose he might have two misspelled words, and those words will be misspelled logically.

This is why I'm sure he'll develop an "ear." He's developed whatever the analogous form of implicit knowledge is for spelling; he'll do it for writing, too.





vocabulary, writing, math...

So we're putting Killgallon on the shelf for the time being. Christopher will do Vocabulary Workshop, a book I like more and more as we go along. He does one page a day, which takes 5 minutes max. VW teaches words in 5 exercises:

• definitions — dictionary definition with sample sentences; student writes the word in the blank

• complete the sentence

• synonyms

• antonyms

• choosing the right word (student chooses which of two words on the vocabulary list "satisfactorily completes" a sentence)

• vocabulary in context — prose passage
  

There are 15 units in the book, and you review every three units. 20 words per list; 185 pages in the book. Efficient & effective.


We're big on vocabulary these days. At dinner I make Christian and Christopher learn Greek and Latin roots from English from the Roots Up. So far we've learned photos, graph, tele, metron, tropos, philia, phobos (predictable hilarity with metron, which instantly suggests the neologism metronsexual, philia & phobos), syn, and thesis, although Christian is having a horrible time remembering tropos. For quite a while there he was saying "line" whenever he heard it (too long to explain), so "line" has now become a running gag.

I told Christian to come up with a mnemonic device for tropos, but unfortunately the one he came up with caused him to start thinking tropos means revolving, which come to think of it maybe it does. (Does it?)

If anyone has a suggestion for a mnemonic device that connects tropos to turning, let me know.


I've also got an ancient copy of Word Power Made Easy (a Google Master recommendation, IIRC) next to the dining room table, so we may get to it, too, one of these days.

Then last week Martine went out and bought a dictionary of New York slang, and we all learned the meaning of ace boon coon, a phrase Christian knew and had used. I'm having as much trouble remembering ace boon coon as he is remembering tropos (I can't remember the "ace" part), so we'll see who gets to the finish line first.

Christopher is supposed to take his ALEKS placement test today, so I've got to go figure that out. More later.
















my boon companion



-- CatherineJohnson - 25 Jun 2006

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AlgebraTrick 03 Jul 2006 - 18:22 CatherineJohnson




I love this idea for struggling kids, and maybe for non-struggling kids, too, when they first start writing equations:

Here's a trick I've told me [sic] DE algebra students and some find it helpful.

Make a guess, even a stupid guess and check it. Write down what you did when you were checking it in an equation. Then replace the guessed number with an x. That's the equation. After you have worked a few problems this way see if you can skip the guessing a number part by calling your initial guess x right from the beginning and pretending it is a guessed number that you are checking.

source:
Shelley Walsh
A Universal Method for Solving Word Problems
math-teach

-- CatherineJohnson - 03 Jul 2006

---

DogOfHelicopterMom 21 Nov 2006 - 18:09 CatherineJohnson




t-shirt of helicopter mom

Helicopter Mom

dog of helicopter mom







His name is Surfer.

We got him when he was a puppy at the North Shore Animal League. He'd been brought in from a shelter in Tennessee, and the lady at the pet supply shop next door to North Shore told us he was part shepherd and part coon hound. She turned out to be wrong, though. Once Surfer was grown up, people who know dog breeds said he's part Rottweiler, part pit bull.

Surfer won "Scariest Pet" in the Picture Pet Contest at Main Street School, 2005.

Any questions?



-- CatherineJohnson - 07 Jul 2006

---

HelicopterParentsAtWikipedia 05 Sep 2006 - 19:18 CatherineJohnson




I have just staged my first intervention at Wikipedia.

Guess which section I wrote.

-- CatherineJohnson - 13 Jul 2006

---

CollegeBoardOnHelicopterParents 15 Jul 2006 - 12:00 CatherineJohnson




Is it possible to murder a meme?

This is my question.

I've just emailed the College Board, and I hope you will, too:

I would like to request that you remove your advice to "helicopter parents" from the website.

The expression "helicopter parent" is a pejorative term for parents created by school personnel and popularized by the media. It is a stereotype.

In my own experience with K-12 education, the term is typically used to ward off parent demands for accountability.

I find the term offensive, as does every parent I know. Moreover, parents are now coopting the term by identifying themselves as helicopter parents, wearing helicopter parent t-shirts, and so on.

I assume the college board doesn't use negative stereotypes to characterize students, professors, or college personnel.

It's time to recognize the hostile intent behind the creation of "helicopter parent" and remove it from your webpage.

Thank you.

Send a Message to the College Board

helicopter parents at Wikipedia
official Wikipedia policies
article deletion nominations at Wikipedia

-- CatherineJohnson - 14 Jul 2006

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JohnSaxonPrefaceAlgebra2 20 Jul 2006 - 17:25 CatherineJohnson




Preface to Saxon Algebra 2

This is the second edition of the second book in an integrated three-book series designed to prepare students for calculus. In this book we continue the study of topics from algebra and geometry and begin our study of trigonometry. Mathematics is an abstract study of the behavior and interrelationships of numbers. In Algebra 1, we found that algebra is not difficult—it is just different. Concepts that were confusing when first encountered became familiar concepts after they had been practiced for a period of weeks or months—until finally they were understood. Then further study of the same concepts caused additional understanding as totally unexpected ramifications appeared. And, as we mastered these new abstractions, our understanding of seemingly unrelated concepts became clearer.

Thus mathematics does not consist of unconnected topics that can be filed in separate compartments, studied once, mastered, and then neglected. Mathematics is like a big ball made of pieces of string that have been tied together. Many pieces touch directly, but the other pieces are all an integral part of the ball, and all must be rolled along together if understanding is to be achieved.

A total assimilation of the fundamentals of mathematics is the key that will unlock the doors of higher mathematics and the doors to chemistry, physics, engineering, and other mathematically based disciplines. In addition, it will also unlock the doors to the understanding of psychology, sociology, and other nonmathematical disciplines in which research depends heavily on mathematical statistics. Thus, we see that mathematical ability is necessary in almost any field of endeavor.

Thus, in this book we go back to the beginning –to signed numbers—and then quickly review all of the topics of Algebra 1 and practice these topics as we weave in more advanced concepts. We will also practice the skills that are necessary to apply the concepts. The applicability of some of these skills, such as completing the square, deriving the quadratic formula, simplification of radicals, and complex numbers, might not be apparent at this time, but the benefits of having mastered these skills will become evident as our education continues.

We will continue our study of geometry in this book. Lessons on geometry appear at regular intervals, and one or two geometry problems appear in every homework problem set. We begin our study of trigonometry in Lesson 43 when we introduce the fundamental trigonometric ratios—the sine, cosine, and tangent. We will practice the use of these ratios in every problem set for the rest of the book. The long-term practice of the fundamental concepts of algebra, geometry, and trigonometry will make these concepts familiar concepts and will enable an in-depth understanding of their use in the next book in the series, a pre-calculus book entitled Advanced Mathematics.

Problems have been selected in various skill areas, and these problems will be practiced again and again in the problem sets. It is wise to strive for speed and accuracy when working these review problems. If you feel that you have mastered a type of problem, don’t skip it when it appears again. If you have really mastered the concept, the problem should not be troublesome; you should be able to do the problem quickly and accurately. If you have not mastered the concept, you need the practice that working the problem will provide. You must work every problem in every problem set to get the full benefit of the structure of this book. Master musicians practice fundamental musical skills every day. All experts practice fundamentals as often as possible. To attain and maintain proficiency in mathematics, it is necessary to practice fundamental mathematical skills constantly as new concepts are being investigated. And, as in the last book, you are encouraged to be diligent and to work at developing defense mechanisms whose use will protect you against every humans’ seemingly uncanny ability to invent ways to make mistakes.

One last word. There is no requirement that you like mathematics. I am not especially fond of mathematics—and I wrote the book—but I do love the ability to pass through doors that knowledge of mathematics has unlocked for me. I did not know what was behind the doors when I began. Some things I found there were not appealing while others were fascinating. For example, I enjoyed being an Air Force test pilot. A degree in engineering was a requirement to be admitted to test pilot school. My knowledge of mathematics enabled me to obtain this degree. At the time I began my study of mathematics, I had no idea that I would want to be a test pilot or would ever need to use mathematics in any way.

I thank Tom Brodsky for his help in selecting geometry problems for the problem sets. I thank Joan Coleman and David Pond for supervising the preparation of the manuscript. I thank Margaret Heisserer, Scott Kirby, John Chitwood, Julie Webster, Smith Richardson, Tony Carl, Gary Skidmore, Tim Maltz, Jonathan Maltz, and Kevin McKeown for creating the artwork, typesetting, and proofreading.

I again thank Frank Wang for his valuable help in getting the first edition of this book finalized and publisher Bob Wroth for his help in getting the first edition published.

John Saxon
Norman, Oklahoma



Beautiful.

The third editions of the Saxon books seem to have done away with John Saxon's prefaces; at least, that's the case with the 3rd edition of Algebra 1/2.

Thanks to our ktm Book Fairy, I have a copy of the 2nd edition of Algebra 1/2, so I'll post that preface, too.

The books themselves don't seem to have been changed in other bad direction. If you're interested in buying the 2nd edition, though, Rainbow Resource seems still to have them. So does Seton Books. I'm sure other homeschooling stores do as well.



Wilfried Schmid on procedures and understanding

''I'm a professional mathematician, and I myself very often use mathematical methods that I understand only imprecisely,'' he said. ''It is while I use them that I begin to understand. After a while, the use and the understanding are mutually supporting.''

source:
The New, Flexible Math Meets Parental Rebellion (scroll down)
By ANEMONA HARTOCOLLIS (NYT) 2403 words
Published: April 27, 2000

Carolyn on procedures and understanding

Carolyn has said more than once that she believes in teaching procedures first. Conceptual understanding follows. (I can't find any of her posts on this, so if I've misremembered I'll delete this.)

I was always a little skeptical of this, although my working assumption is that where Carolyn and I disagree, Carolyn is right.

I've now spent enough time working my way through Saxon to see what Saxon, Schmid, and Carolyn are talking about. When you practice a procedure you don't understand over and over and over again, at some point it "naturalizes." It seems right and inevitable. And it makes sense.

John Saxon stresses this idea in book after book. Math isn't hard; it's different. It's unfamiliar.

When you've done so much math that it no longer seems strange, it starts to seem easy — or at least not harder than other subjects.

Of course, the irony is that this naturalizing process leaves me unable to explain procedures to someone for whom math is still strange. It does, however, make me understand why "math brains" tend to say things like, "It just is" when I ask for an explanation!

I'll add that Saxon (and probably Carolyn & Schmid, too) rarely teaches a concept stripped of all meaning or explanation — though he does do so far more often in Algebra 1 than in the earlier books. A student using Algebra 1 must take a lot on faith.

If nothing else, meaning helps memory; it's easier to remember a procedure you understand. (I have references for this observation, but don't want to spend the time to dig them up just now.) I'd be willing to bet that meaning increases student motivation, too. I recall Steve H saying that students always want an explanation if they can get one. (Steve - am I remembering that correctly?) Every one of Saxon's explanations in 6-5 through 7-6 has been pure pleasure to read, and has made me want to learn more math. In contrast, my motivation sometimes flags as I work with Saxon's highly abstract Algebra 1, my motivation sometimes flags.

In short, I think it's probably always good to try to teach some conceptual understanding along with procedure. I also think, after living through Ms. K's Phase 4 math class, that it's essential to include mini word problems — although Saxon does not do so in Algebra 1. But John Saxon can get away with it, because he's a genius math textbook writer. If you're not a genius math text writer, or a genius math teacher, you can't.

Nevertheless, these caveats aside, math is first and foremost something people do. Barry says that constructivist math ends up teaching math appreciation, not math, and I agree.

Teach procedures supported by meaning where possible, and, where not possible, teach the procedure and practice it to mastery. Understanding will follow as "totally unexpected ramifications appear."







John Saxon & John von Neumann on math
preface to Saxon Algebra 2



-- CatherineJohnson - 15 Jul 2006

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JudithKleinfeldOnHomeschooledBoys 22 Jul 2006 - 18:55 CatherineJohnson




Yet-to-be-published research by Judith Kleinfeld:

In separate research that Kleinfeld is also preparing for publication, she has possibly gotten to the root of the problem.

"Here's a fascinating fact," she said. "There is no literacy gap in home-schooled boys and girls."

"Why? In school, teachers emphasize reading literature and talking about character and feelings," she said. "This way of teaching reading does not turn boys on. Boys prefer reading nonfiction, such as history and adventure books. When they are taught at home, parents are more likely to let them follow their interests."

Why Johnny Can't Read: Schools Favor Girls
By Robert Roy Britt
LiveScience

I'm guessing most parents of boys also don't spend huge quantities of time celebrating Women's History Month or holding assemblies devoted to the Columbine killers and how not to become one yourself.

Moreover, your basic homeschooling mom is not concerned that if her boys learn too much academic content they'll grow up to form coteries of experts intent on using their expertise for ill.

Nor is your basic homeschooling mom on a mission from God to prevent the next Holocaust by requiring her children to engage in self-reflection on questions about identity, group membership, and obligations to others.

I could go on.

-- CatherineJohnson - 22 Jul 2006

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VocabularyWorkshopLevelsAndGrades 08 Aug 2006 - 19:27 CatherineJohnson




This summer Christopher has been doing 2 or 3 pages a week from Sadlier Oxford's Vocabulary Workshop, which teaches words in 5 exercises:

• definitions — dictionary definition with sample sentences; student writes the word in the blank

• complete the sentence

• synonyms

• antonyms

• choosing the right word (student chooses which of two words on the vocabulary list "satisfactorily completes" a sentence)

• vocabulary in context — prose passage
  

There are 15 units in the book, with a review very three units. 20 words per list; 185 pages in the book.

Vocabulary Workshop spans grades 2 - 12+ , starting with a series for grades 2 - 5:

Level Purple Grade 2

Level Green Grade 3

Level Orange Grade 4

Level Blue Grade 5


After Level Blue the middle & upper grades series starts in Grade 6 with Level A:

Level A grade 6

Level B grade 7

Level C grade 8

Level D grade 9

Level E grade 10

Level F grade 11

Level G grade 12

Level H (advanced? gifted? SAT prep? not sure, but I'm ordering it)


Levels A - H Teacher's Guide (you don't need this)


online flash cards, Level Blue

online flash cards for several other levels, too

Vocabulary Workshop online high school tests

Vocabulary Workshop online



Wordly Wise series from EPS

word lists & sample lessons from all books in Wordly Wise series



English from the Roots Up (2 volumes)



Vocabulary from Classical Roots
Strategic Vocabulary Instruction through Greek and Latin Roots
by Norma Fifer, Nancy Flowers
Grades 5–11



Carolyn on Vocabulary Workshop
update on Vocabulary Workshop; English from roots up
Vocabulary Workshop levels & grades
afterschooling w/Vocabulary Workshop
vocabulary pre-test
SAT scores for students using Vocabulary Workshop
vocabulary at the dinner table
robust vocabulary instruction (400 words a year)
how much reading a day?
15 new words a day
Engelmann says it's 3 new words a day
Fischgrund on divorce and SAT scores

vocabularyworkshop
greekandlatinroots

-- CatherineJohnson - 25 Jul 2006

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RobustVocabularyInstruction 05 Sep 2006 - 15:57 CatherineJohnson




from the Introduction to Chapter 4 Comprehension of the National Reading Panel report:

The importance of vocabulary in reading achievement has been recognized for more than half a century. As early as 1925, in the National Society for Studies in Education (NSSE) Yearbook, this quotation appears:

Growth in reading power means, therefore, continuous enriching and enlarging of the reading vocabulary and increasing clarity of discrimination in appreciation of word values (Whipple, 1925, p. 76).

Even today, evidence of the importance of vocabulary is usually attributed to Davis (1942), who presented evidence that comprehension comprised two “skills”: word knowledge or vocabulary and reasoning in reading. The Panel reflects this position with the inclusion of the current analysis of research on vocabulary instruction with the other comprehension research analyses. Since Davis’ work, there have been questions regarding the “skills” perspective, but the finding that vocabulary is strongly related to comprehension seems unchallenged.

From Bringing Words to Life: Robust Vocabulary Instruction by Isabel L. Beck, Margaret G. McKeown, and Linda Kucan:

• First-grade children from higher-SES groups knew about twice as many words as lower SES children (Graves, Brunetti, & Slater, 1982; Graves & Slater, 1987).

• High school seniors near the top of their class knew about four times as many words as their lower-performing classmates (Smith, 1941).

• High-knowledge third graders had vocabularies about equal to lowest-performing 12th graders (Smith, 1941).

do children learn vocabulary from context?

The answer is Yes, but —

Conventional wisdom suggests that the major means for developing students' vocabulary should focus on learning words in context. This position is based on three assumptions: First, words are learned from context. Second, school-age youngsters are successfully adding words to their vocabularies. And, third, instruction must focus on learning vocabulary from context because there are just too many words to teach to get the job done through direct instruction.

[snip]


Most of the words children customarily encounter in oral language beyond their earliest years, both at home and in school, are words that they already know. Thus, the source of later vocabulary learning shifts to written contexts—what children read. The problem is that it is not so easy to learn from written context. Written context lacks many of the features of oral language that support learning new word meanings, such as intonation, body language, and shared physical surroundings.

[snip]

Studies estimate that of 100 unfamiliar words met in reading, between 5 and 15 of them will be learned (Nagy, Herman, & Anderson, 1985; Swanborn & de Glopper, 1999).

[snip]

Specific estimates of vocabulary growth vary widely, from 3 (Joos, 1964) to 20 new words a day (Miller, 1978). A figure of 7 words per day is probably the most commonly cited....Although it may be the case that some students are learning as many as 7 new words a day, many others may be learning only 1 or 2, or indeed not any at all.

are there too many words to teach vocabulary directly?

Bringing Words to Life answers this question by pointing out that a mature reader's vocabulary falls into 3 tiers:

• Tier 1: basic words like clock, baby, happy, walk that don't need to be taught

• Tier 2: "words that are of high frequently for mature language users and are found across a variety of domains....coincidence, absurd, industrious, fortunate

• Tier 3: low frequency words that are "often limited to specific domains" e.g.: isotope, lathe, peninsula, refinery
  

Obviously, Tier 2 words are the target of vocabulary instruction:

Nagy and Anderson estimate that good readers [in grades 3 through 9] read approximately 1 million words of text per year. They organized these words into word families, or groups of related words such as introduce, introduction, reintroduce, and introducing, and further estimate that half of the 88,500 word families they calculate to exist in printed school English are so rare that even avid readers may encounter them only once in their lifetime of reading. Using these figures, it seems reasonable to consider word families that would be encountered at least once every 10 years, which Nagy and Anderson calculate to number about 15,000 as comprising Tiers One and Two. These are words that occur once or more in 10 million running words of text. Our best estimate of Tier One, the most familiar words that need no instruction, is 8,000 words families...That leaves about 7,000 word families for Tier Two.

[snip]

Seven thousand words may still seem like quite a large number for instruction to undertake over the course of, say kindergarten through ninth grade. That would amount to an average of 700 words per year.

[snip]

[W]e assert that attention to a substantial portion of those words, say, an average of 400 per year, would make a significant congtribution to an individual's verbal functioning. Aiming for this number of words would allow the depth of instruction needed to affect students' text comprehension ability. We believe this to be the case because about 400 words per year conforms to the rate at which we taught words in our previous research, which resulted in improvements in word knowledge and in comprehension of texts containing the instructed words. (Beck et al., 1982).

quick notes

• The Vocabulary Workshop series teaches 300 words per book.

• I wonder whether teaching Latin & Greek roots increases the number of words students can pick up from context, as Eugene Schwartz and others argue. I'm guessing it probably does, but I don't know.

• Beck's, McKeown's, & Kucan's figures make sense of my own life and times. Kris and I were talking about vocabulary & SAT scores yesterday, and I said, "How did I get a [recentered] 790 coming from the farm?" Kris said, "If you'd lived in an affluent suburb you could have picked up that extra 10 points." It seems obvious to me now that the way I did it was by learning huge numbers of words from context, which I could do because I was a compulsive reader from day one, which meant that I was exposed to zillions of words & then re-exposed to the same zillions of words often enough to learn a lot of them. (One of the words I learned, apparently, was "zillions.") On family vacations I used to walk along reading my book; as I recall, I missed most of Manhattan the one time we visited because I was reading Agatha Christie. Another data point: The Cambridge Handbook of Expertise and Expert Performance, in an article on professional writers, says that professional writers universally describe themselves as "compulsve readers." Converging lines of evidence, that!
  
  
  

Vocabulary Workshop grades & levels
Fischgrund on divorce and SAT scores
how much reading a day?
robust vocabulary instruction (400 words a year)
15 new words a day
Engelmann says it's 3 new words a day

National Reading Panel
NICHD publications on reading
summary of NRP report
International Reading Association on NRP report

vocabularyworkshop robustvocabularyinstruction

-- CatherineJohnson - 26 Jul 2006

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UnitMultiplierProblemFromSaxonAlgebra1 02 Sep 2006 - 17:15 CatherineJohnson




This problem was in one of the lessons in Saxon Algebra 1:



Juanita exercised for one hour.

How many seconds did Juanita exercise?



I love this problem. Don't know why. (Though I do remember, as a child, being tickled by the fact that a short period of time, like one hour, could have a very large number of even shorter periods of time inside of it...)

Anyway, I pulled this one out for Christopher to do.

-- CatherineJohnson - 02 Sep 2006

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TenYearsOfMethUse 20 Sep 2006 - 01:37 CarolynJohnston


A picture is worth a thousand words. This one might be good to show your teenybopper when they're learning about street drugs in health class.

-- CarolynJohnston - 04 Sep 2006

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FardellsNookesAndHides 16 Sep 2006 - 02:32 CatherineJohnson




from the Yahoo Group called Homework Help:

My son and I both came up with different answers to this problem...I am rusty at math but still think that I am right:)

How many fardells are in 8 hides?...
2 fardells = 1 nooke
4 nookes =1 yard
4 yards = 1 hide

This is a medieval Britain story problem. I got 256 fardells as my answer...sure seems like a lot but it's hard to visualize :)

Help!

Start teaching those unit multipliers now!



I'm going to see if Christopher can do this.

[pause]

Nope, he couldn't. He got 32. "I did it in my head."

After he got his wrong answer I started him out with unit multipliers by writing:

8 hides X

on the left side of the paper.

Then I asked him what needed to be in the denominator of the next ratio. (Ratio? Rate? What's the proper term?)

He knew it had to be hides, but he couldn't figure out what would be in the numerator.

sigh

About 5 seconds after that he got with the program, wrote out the series of ratios, and said, "Now what do I do, multiply?"

me: "Haven't you written out a string of multiplications?"

Christopher: "Yes."

me: "Then multiply."

He got 256.

That's one thing about distributed practice. It can't be too distributed. I was thinking that about this at the U.S. Open.

Every year for the past 4 or 5 years we've gone to the U.S. Open.

And every year Ed has to explain the entire scoring system in tennis all over again.

One year between exposures to content is too long.



Next year I plan to remember "All," as in "15 All," and "Deuce," as in .... as in I don't know when people say deuce. I've forgotten. I just know that once you say "deuce" the players have to win by two points. At least, I think that's what I remember.

I'm going to remember "all" because "all" means everyone and "all" is a tie. All have the same score.



OK, so basically what I'm going to remember is "All."

Also, I think I'm going to remember that men play 6 sets.

Or maybe 5.

See what I mean?

One year is too long.

-- CatherineJohnson - 14 Sep 2006

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BoycottEbay 15 Sep 2006 - 15:37 CatherineJohnson




Instructivist has the story.

If you want to email eBay about their decision (I've done so), go here. The site lists emails:

• gfant@ebay.com (manager)

• meg@ebay.com (CEO)

• amyskeets@ebay.com (manager)

And if you want to see Christians and seculars flaming each other about whether we are or are not now living in a socialist country, go here. [correct answer: we are not living in a socialist country. we do, however, in my opinion, have a public education system that could be picked up and transferred wholesale to a socialist country without revision. see, e.g. Al Shanker.]

Of course, saying that our public school system could be picked up and transferred wholesale to a socialist country without revision is an insult to socialist countries.

-- CatherineJohnson - 15 Sep 2006

---

AfterSchoolReportFromLynn 28 Nov 2006 - 16:14 CatherineJohnson




Fantastic news from Lynn Guzelow:

We just got our state CMT scores back -- advanced band in 4th grade math! 107 correct out of 110 problems. Yes, I know they will attribute it to EM, but we'll all know the truth, won't we?

Congratulations, Lynn! To both of you guys!


Lynn's news reminded me that I'd been meaning to post Barry Garelick's comment:

I like Saxon AND Singapore. I like Singapore's presentation of concepts better and their problems are more complex, but I like Saxon's repetitive problems to make sure kids are getting the skills. I will mix Singapore with Saxon in the upcoming year.

Speaking of Singapore, a 6th grader I was tutoring this past year (with Singapore Math) got a perfect score in the Virginia math SOL. She had been getting average scores in math until this year. Nota Bene: The school she's in uses EM. When I started tutoring her, I started at the 4th grade SM book with fractions thinking it would be review. She had had the stuff before, but it was like it was brand new. The wonders of the spiral.

The downside of all this of course is that her perfect score will serve as "evidence" to the Fairfax County Council of Dolts, (aka School Board) that EM is working. You can't win for losing some time. Still, I'm happy for my student.

Which brings me to Linda Moran's recent post (I think instructivist may have left the link):

I'm no longer quick to recommend that parents help with math instruction at home, unless they have a love for understanding-based math and a strong commitment to a possibly steep learning curve. Math teaching isn't easy. The public schools, in taking such extreme about-faces as TERC math, are the first ones to admit this. That's why they're flailing about right now. It will take some time for good math instruction to settle down somewhere in the middle of the two extremes.

Linda Moran, as it turns out, is a certified math teacher who took quite a lot of math in college, which means she knows more about math than I do.

So I'm a little hesitant to disagree.

At the moment, I'm feeling exactly the opposite about parents teaching math after school. It's certainly true that I had and have a strong commitment to a possibly steep learning curve, and a love for understanding-based math, but looking back... teaching Christopher math hasn't been that hard. It's been so not-hard that he is now teaching himself, at age 12.

Caroyn always talks about Saxon providing support for the teacher, and she's right. John Saxon's books can pick a parent up bodily and carry her through. (That's why they're called "Homeschool Editions" no doubt.) When you have two superb curricula like Saxon & Singapore to choose from, I think you're in a strong position to make up for the deficits in a school curriculum.

Or am I wrong about this?

Linda Moran is right about the time & energy I've put into this project; it's been huge. But that's me. I go overboard. I like going overboard! I don't think a parent has to develop a magnificent obsession to teach Singapore or Saxon after school.

Not sure, though.




afterschooling procedural math

I'm also now completely convinced that Carolyn (and John Saxon) are right: teach the procedural knowledge first & attend to the conceptual knowledge as the procedural gels. I'm convinced of this because I've experienced this staged process in my own learning & understanding many times now. Very often I will master a procedure before I understand it.

This isn't an artifact of using Saxon Math. Usually John Saxon gives you the explanation going in, complete with connections to previously learned material, as you begin to learn the procedure. I just don't grasp the explanation at that point. Then, later on, I find that I am grasping it, or starting to.

Conceptual understanding sneaks up on me while I'm doing procedures.

What this tells me is that it's perfectly valid for a parent who does not have a love for understanding-based math to focus on teaching math procedures and leave it at that. There are all kinds of terrific resources for doing this - workbooks mainly - including Glencoe's terrific Parent-Student Study Guides, which are available free online.

I just don't see any reason for a parent who for some reason does not wish to relearn all of the core K-12 math curriculum (difficult as that is to imagine) to conclude that she should therefore leave her childrens' math education up to the school.

I especially don't see any reason to leave things up to the school in the wake of our visit to the edu-attorney, but more on that later.

Glencoe Parent Student Study Guide Pre-Algebra
Glencoe Parent-Student Study Guide Algebra 1

your mother whips you

-- CatherineJohnson - 21 Sep 2006

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YourMotherWhipsYou 27 Sep 2006 - 10:48 CatherineJohnson




As Christopher was zipping through the math problems in his cooperative learning group yesterday, the kid across the way said, "Chris, you're a genius. Your mother makes you do extra work or she whips you."

My reputation is growing apace.




after school reports from Lynn & Barry

-- CatherineJohnson - 22 Sep 2006

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RealWorldMathProblem 09 Oct 2006 - 17:59 CatherineJohnson




After a 2-week plateau, Jimmy is again losing weight. 204.5 this morning.

Christopher is losing, too, and is, according to the CDC, officially "not overweight." (Which, translated, means he's at the 94th percentile for his age. The CDC defines anything from the 85th to the 95th percentiles as "at risk for becoming overweight." This is all pretty silly, seeing as how Christopher's height is at the 90th percentile for his age, but still. Having the CDC officially define him as "not overweight" is good for his motivation. I went through all the various websites and figures the other day, and decided that my goal weight for Christopher is 120. He's got 10 lbs to go.)

UPDATE 10-6-2006 10 pounds may sound like a lot for a child, and of course it is, but visually he's good now. He's "tipped" back across the line that separates "fat" or "chubby" to "normal." So that's good. If he didn't lose any more weight at all, but simply maintained this weight and continued to grow, that would be fine. Also, be sure to read the Comments!

Ed told Christopher his job this weekend is to figure out which one of them has lost more as a percentage of his total body weight to start.

UPDATE 10-8-2006 Jimmy is down to 204 this morning. (5'10" or 5'11")

UPDATE 10-16-2006: Jimmy down to 201; Christopher down to 129.5. I haven't been telling Christopher's weight - just the weight loss - because I didn't want him to be embarrassed in case any of his friends happened to come across the blooki. But now that he's into the 120s, I think it's OK. He is at 90th percentile height and roughly 92-93th percentile weight. None of the kids call him "fat" anymore, which in terms of the social issue of being overweight in middle school tells you all you need to know.

I've lost 5 lbs, but there's no way to "disaggregate" the causes, what with our mad-bad doctor-originated cancer scare over the past few weeks and all. (Haven't posted about it; it's happily resolved; mention it only to say that I can't reach conclusions about Shangri-La based on my own quite dramatic - for me - weight loss.)

I found Jimmy's weight loss chart from the last time I managed to put him on & keep him on a diet back in 2003.

July 25, 2003: 205 lbs
November 15, 2003: 198.5 lbs.
6.5 lbs in 16 weeks. Compared to 15 lbs in 11 weeks this go-round.

By March of '04 he was up to 208.5.

At some point in there (I think it was in '04) we were able to persuade our pediatrician to put him on glucophage, which stabilized the weight gain. He didn't lose, but he stopped gaining.

Then his liver enzymes (iirc) got screwy and that was the end of the glucophage. By this summer he was up to 222.

Taking Risperdal, he's been gaining weight every year, year in, year out, without growing taller. (Eric Hollander managed to get him off the Risperdal, but his new med, Depakote, which he must take for seizures, also produces weight gain.)

When I say he's been gaining every year, I'm talking about a young, strong male, much bigger than I am, who is ravenously hungry, screaming for food, and biting himself until he draws blood.

The diet we managed to do 3 years ago had to be constantly monitored and thought-through; we had to do everything in our power to feed him foods that would take the edge off his unceasing hunger so we could withhold food when his nighttime binge hour arrived and he started screaming and biting himself.

A nightmare.

The nightmare wasn't just that he was screaming, bingeing, and biting himself.

The nightmare was that Ed and I were chained to the refrigerator. To this day we have locks on every cabinet and a bike lock on the fridge. We can only buy side-by-side refrigerators, because those are the only ones you can use a bike cable on.

It would be 10 at night, or 11; we'd be dog-tired; and Jimmy would need to consume a thousand calories of parent-prepared food before the screaming stopped. This after an entire day of manning the kitchen because he was hungry all day long, too.

Dog-tired is wrong.

Bone-tired.

The Shangri-La diet has made all of that go away. All of it. There is no nighttime binge. There's not much daytime noshing, either. We have meals.

We got a little sloppy the last two weeks, and weren't always giving Jimmy his oil. Because you have to give the oil one hour after eating and one hour before eating, you can easily end up without that two-hour window of time, especially when a child has school or weekend programs during the day.

The nighttime binges came back.

I'm a believer.

Meanwhile Ed, who spends a lot of time pooh-poohing whatever my latest idea for self-and-other improvement happens to be, is a huge believer.

He's practically a Shangri-La acolyte.



I weighed myself this morning.

I gained a pound.

I don't think it's a real pound.

Since July I seem to have lost 2 stable, definitely-gone pounds on Shangri-La.

BMI 21.5.

I want a BMI of 20.5.

At most.



another olive oil diet

I went to see Erika yesterday.

We met Erika here in Irvington a couple of weeks after we moved in. She had been the on-call physician for the schools, and had a practice in a little house on Main Street in downtown Irvington.

She was wild. She was the original n-of-1 self-experimenter, and was then writing her book on energy and the mitochondria. She took one look at Ed & packed him off to an acupuncturist to treat his back.

The acupuncture didn't work, but everything else she said made sense and I've been seeing her ever since.

Now I have to trek into Manhattan to get to her office, but it's worth it.

Erika is a female Arnold Schwarzenegger.

I'm not sure how she'd feel about that, but if I had to bet I'd say she'd like it.

She's Austrian, and has the "Arnold" accent, but what's Schwarzeneggerian about her is the inexhaustible energy, the optimism, and the utter indifference to the received views of her betters. A massively publicized NIH study proving once and for all the mortal danger of hormone replacement therapy has no more dampening effect on Erika than a spring drizzle has on a Labrador retriever. She simply goes bounding along evangelizing her precious "bioidenticals."

When I say "bounding along," what I mean is that at the precise moment the NIH death-by-estrogen study hit the papers, Erika decided to stop being an internist and start being a full-time hormone replacement specialist. The mere fact that the entire US media universe is seething with stories of middle-aged women dying of breast cancer because they took estrogen is simply not a factor in Erika's decision-making calculus because, obviously, the study is bunk.

That's Erika.

The other Schwarzeneggerian thing about Erika is that she makes this kind of thing work.

Erika can decide that the NIH and the New York Times are wrong, and she can base a major business decision on the fact that the NIH and the New York Times are wrong, and, for Erika, this turns out to be a good call.

I lost track of Erika for a couple of years when her practice in Hawthorne disappeared. She had by then moved from Irvington to a suite of offices in the Dobbs Ferry Hospital, and then from Dobbs to another suite of offices over in Tarrytown, and after that she set up shop in a huge suite of rooms up in Hawthorne.

But suddenly I couldn't get them on the telephone. The number had been disconnected and nobody had notifed me about a new number some place else.

I felt bad about that. The practice must have failed I figured.

It didn't fail. She'd had some kind of falling out with the folks she was partnered with so she stopped practicing in Hawthorne and started practicing full-time out of the Manhattan office she'd had all along, unbeknownst to me. She is mobbed by patients.

Yesterday I told her the Wall Street Journal had just run an article ($) on a new study showing that hormone replacement therapy is good for the brain (big surprise there) and Erika said, "In 5 years no one will talk about that NIH study any more. Everything will be bioidenticals."

That's Erika.

In 5 years all the bad, wrong ideology will be gone!

Because that's the natural fate of bad, wrong ideology!

I just wish I could train Erika's attention on Lucy Calkins.

Then again, Lucy Calkins is tougher than the NIH.

Or the New York Times.



wasn't I talking about olive oil?

Yes.

I was.

So I sat down on Erika's sofa and said, "I've found a diet that works."

"Tell me."

"It's called the Shangri-La diet."

She started laughing. "You're my funniest patient," she said.

I'm sure that's true.

Then again, Erika is my funniest doctor.

I started filling her in on Shangri-La, but she interrupted me.

She'd never heard of Seth Roberts, but for awhile now she's had 10 patients on an olive oil diet of her own devising and they've all lost lots of weight.

That's 10 out of 10.

Ten out of 10 patients using Erika's made-up olive oil diet have lost weight. She reports this like it's nothing.

Her regimen is to have them take 1 Tbsp of olive oil 3x a day, midway between meals.

She takes at least a Tbsp of olive oil a day herself, I believe, and has been doing so for years.

Erika doesn't have a Unifying Theory of hunger and anti-hunger on the Serengetti plains. She just figures a Tbsp of olive oil 3x a day keeps people full.

I said, "How'd you come up with that?"

Erika shrugged and said, "It's obvious."

more on mitochondria:
Bruce Ames in Discovery
Bruce Ames in REASON
Bruce Ames at fumento.com

The Shangri-La Diet at Amazon
Seth Roberts website

Shangri La diet in freakonomics
Shangri La diet part 2
early adopter
diet, evolution of the brain, & McDonalds
Marginal Revolution on Shangri La
your own lying eyes
progress report 7-23-06
Jimmy 7-24-06
mind hacks & Shangri-La 7-26-06
7-29-06 update
my life and welcome to it - 8-6-06 - success
compare and contrast photo op 8-12-06
9-12-06 update
9-17-06 Jimmy is melting
10-4-2006 Dr. Erika's olive oil diet works, too

shangrila

-- CatherineJohnson - 04 Oct 2006

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MoreTeachingToCrammery 17 Nov 2006 - 01:06 CatherineJohnson




Coming to the end of our 4-day weekend here...

Friday I learned from Christopher that on Tuesday (tomorrow) he would be taking a chapter test on probability.

Seeing as how I don't know any probability, that was bad news.

So I spent the weekend teaching to crammery, big-time.

First I had to teach myself to crammery; then I had to teach Christopher to crammery; then I had to make Christopher learn how to draw tree diagrams; & after that I had to make him do a bunch of problems for practice & to see if he got them right. (He did.)

By Sunday night Ed was in on the act, too, so 3 people in this household have spent a good portion of Veteran's day weekend teaching probability to crammery.

You can make that 4 if you count my neighbor, the statistician.

She spent the weekend on stand-by, fielding phone calls Saturday night and drawing tree diagrams Sunday afternoon. She loaned me her copy of Probability Demystified, which she used to teach probability to crammery last year when her kid was in this course.

The book looked so good I decided I needed my own copy so Ed and Christopher could use one copy while I used the other. So I went to Barnes & Noble to buy one after picking Jimmy & Andrew up from their program at the Y. That was the only time I could go, so they had to go, too.

Normally I don't go to B&N with Andrew.

If I do go, I don't try to buy anything, aside from whatever I'm buying for him.

But yesterday I had to look at books and I had to buy books and I had to take Andrew with me because I had to teach to crammery because my school isn't responsible for individual student learning.

Parents are responsible.

So I had no choice.

At B&N Andrew got so obsessed with the Arthur books that he refused to leave and I had to drag him - literally drag him, by the collar of his jean jacket - from the back of the store to the front & then through the check-out line. The lady who helped me carry my stuff said, "This is the worst I've ever seen him."

So today my neck and shoulder are a mess, but we all know quite a lot about probability.

Which we'll forget in the next couple of days, after the test.



it's official

No child without math-brain or math-career parents could get through the Irvington "accelerated" track.

Which, as we know, is the average, non-accelerated track in the rest of the developed world.

I suppose if you hired your own private math teacher, as some parents have done, you might be able to do it.

But that's the only way.

If I hadn't been studying math for nearly two years I could never have taught myself probability to crammery the way I did this weekend; nor could I have taught probability to crammery to Christopher (and Ed).

No way.



if you thought that was bad —

If you thought spiraling in K-5 was bad, wait'll you get a load of it in middle school.

Christopher's class has been studying probability for maybe two weeks.

The chapter covered at least 18 different topics, so we had to teach all 18 to crammery, instead of teaching 4 or 5 to mastery as you would if you cared about the kids actually learning something.

If you want to see what I mean, take a look at the TOC to Probability Demystified:

Chapter 1 – Basic Concepts of Probability

Chapter 2 – Sample Spaces

Chapter 3 – The Addition Rules

Chapter 4 – The Multiplication Rules

Chapter 5 – Odds and Expectation

Chapter 6 – The Counting Rules

Chapter 7 – The Binomial Distribution

Chapter 8 – Other Probability Distributions

Chapter 9 – The Normal Distribution

Chapter 10– Simulation

Final Exam

Answers to Final Exam

Appendix: Bayes'Theorem

Index

The book has twelve chapters.

The contents of five of them are covered in one chapter of Christopher's math book. (Chapters 1, 2, 3, 4 & 6)

Does a spiraling curriculum lead to negative learning?

I'm thinking it does.

I'm thinking the effects of a spiraling curriculum are worse than a simple FWOT.

When you teach 18 brand-new topics in 2 weeks, you may actually be degrading knowledge.



UPDATE 11-20-2006: Christopher got a 77!

Class average 80 or 81.

This test wasn't loaded with "Honors" level questions (turns out that's what the tests have been - Honors level tests given to a merely accelerated class in which no Honors level material has been taught).

But it had a couple, and it was long.

Christopher messed up some minor computations, misread the "spinner" on the spinner problem....and one of the word problems is all wrong. (More later)

He could easily have earned a grade in the 80s.

He picks up new math concepts much faster than he used to. This started last spring, and has continued this fall.

It's cool.

Demystified series
gap anarchy
Engelmann on reteaching material learned incorrectly

teachtocrammery
degradingknowledge
negativelearning



-- CatherineJohnson - 14 Nov 2006

---

WhoSpeaksForTheChild 01 Dec 2006 - 21:30 CatherineJohnson




Karen A pointed me to a post at Ken's, who pointed me to this passage from Siegfried Engelmann:

The problem with the current educational system is that it has no advocacy for the children. In fact, it is a very strong non-advocacy system, which is supported by all major components of the system—the law, colleges of education, local school districts, educational publishers, federal and state grant supports, and teacher unions.

I find this moving.

Every once in awhile I wonder what on earth Ed and I are doing.

Why would we be taking on our entire school district?

Why would we be pushing for systemic reform?

Why aren't we just getting what we can for our 3 kids?

That's what other people do - and that's what they say they're doing.

It's not that they don't care about other people's children. They do care.

They don't see any other way.

Most of the time they're right.^*


Engelmann's opening line reminded me of the last conversation I had with our departing head of special ed.

We were saying goodbye, and in the middle of the conversation she said, "You and Ed are very good advocates for your children."

Then she gave me a meaningful look for emphasis.

That took me by surprise.

Of course, I guess we are pretty good advocates for our children (she meant Jimmy & Andrew)....but I didn't realize that others might see us this way - or that they might see this as a good thing.

I guess I assume others see us as a pain in the tuchis, which we are when we need to be.


Over the past couple of years I've learned the lesson a lot of parents with special needs and typical kids learn: you have to advocate for the normal ones, too.

That was a surprise. I guess it shouldn't have been, but it was.

Anyway....reading Engelmann's opening line I thought: that explains it.

Advocating for systemic reform in our district is what we have to do to advocate for our typical child.

That's why we do it.

I'm sure we've got some civic duty motives mixed in there, too.

But if you ran an fMRI on both our brains right now, I expect you'd see the "good advocates for your children" areas lit up like a Christmas tree.

At some point I began to see the sameness of all the stories I was hearing.

I came to see that allowing a school to treat your child's problem as if it were his and his alone lets the school off the hook.

It's something about him, not something about them.

Of course, it is something about him....he's having a problem.

But he's having it at school.

So let's talk about the school, too.

I haven't written about the Princeton Charter School yet.

I'll do so soon, because it's important - and because I discovered yesterday that two of the signers of the anti-constructivism letter to Secretary of Education Richard Riley were founders of PCS.

For now, here is a passage from Chiara R. Nappi's account, "Why Charter Schools?": (pdf file)

When parents complained about their child's experience in school, even if they explicitly complained about the deficiencies of the curriculum, teachers and principals tended to treat each case as new and unrelated to any previous one, preferring to come up with solutions specific to a particular child rather than trying to modify the program to improve it for all children.

Engelmann is right: in American schools there is no one to advocate for the children.

It's not a case of bad people.

It's a case of bad structure.

Not to get into detail, it's been obvious to us everywhere we've been that the structure makes it quite difficult, perhaps dangerous in some cases, for teachers to advocate for children. And still they do it, often enough.

Here's Engelmann again:

Basically, the laws associated with teaching and student performance are two-faced. In one sense, the laws were instituted to protect the students and thereby protect the state's interest in a valuable resource. The other face of the law denies that teachers have any sort of professional skills that are not possessed by the person on the street, asserts that teachers have only "responsibilities," protects schools or teachers from liability, and refuses to recognize rights of students to receive a quality education. Although special education children are modestly protected by laws, the appropriateness of programs is not determined by anything approaching tight standards.

... there is not help from the law, no hope of malpractice suits (because these suits imply that teachers have professional skills, which the law denies), and no hope of support from state boards of education or state agencies because these agencies are not accountable for achieving their stated mission.

That's Engelmann, writing in 1982.



Accountability at Princeton Charter School

"A school that holds itself accountable is one that states its objectives, assesses its success in achieving those objectives, and reports to students, parents, and the community on its achievements.

Princeton Charter School (PCS) holds itself accountable to its various constituencies, including the taxpayers who largely support the school. School accountability begins with a curriculum that includes clearly stated, measurable outcomes logically developed within and between grades. PCS assesses and reports on many measures of student academic achievement and other important outcomes of the school's program."



The Princeton Charter School is a Blue Ribbon School.

^* I don't know if there is any other way normally. If Ed weren't a professor, if I weren't a writer, if Ed hadn't worked on the History-Social Science project in CA, if we didn't see eye to eye, if we were lots younger and less impatient with tomfoolery than we are at this stage of the game......things would be different.

-- CatherineJohnson - 19 Nov 2006

---

ReTeachers 04 Dec 2006 - 15:08 CatherineJohnson




from NYC HOLD:

Letter #1

I am a physician who was initially [a] mathematics major in college. I just found your Web site today and wish I had known about it 6 years ago when my oldest daughter began kindergarten in District 2. It was not until third grade that I realized just how little math she was learning, and how behind she was in basic skills. According to her teachers, everything was fine, but then no testing or assessment was done, other than the state wide tests - and I recently discovered that our teachers do not even get access to their student's individual results!

Needless to say we've been struggling ever since - we tried Kumon, had a private tutor, and have used the McGraw Hill Math series workbooks as well -. Unfortunately, attempts other than tutoring, such as workbooks don't teach -they just provide for practice of taught skills.

My daughter is a bright child, but math is not "natural" for her. She has never done well "inventing" her own ways to do problems, and I have been stymied as to why the school was not teaching her how to add, subtract, multiply and divide, etc. Once taught, and after sufficient practice, she gets it. I was never asked to invent math - I was taught the ways that math scholars developed over the centuries - why are we asking our children to reinvent the wheel? Our best year of math at PS --- was 5th grade, when all the teachers were new to NYC, all three having come from teaching in the Midwest. Suddenly there were worksheets coming home and quizzes in class, and my daughter had a sense of what she was expected to know, and I did too. All too late as far as I am concerned. Now in sixth grade we are still catching up I have now ordered the Saxon series to aid me in teaching both her and her 2nd grade sister (who unlike her older sister gets math almost intuitively, so it will be much easier going)

At any rate your mission statement summarizes everything I have been saying to friends and other parents at school for the past 4 years. I too, am convinced that our school has for far too long been taking credit for the extra work that the parents are doing in math - this is why our children are doing well, not because of the curriculum!

Christopher tells me he is to bring in $11 for a state test prep booklet.

ELA? I asked. The ELA test is coming up in January.

No. Not the ELA.

Math.

Christopher is to take $11 to school to purchase a state test prep booklet for math.

uh-oh

Houston we have a problem.

I don't feel like spending $11 on a state test prep booklet.

Why don't I feel like spending $11 on a state test prep booklet, you ask.

I don't feel like spending $11 on a state test prep booklet because:

• in preparation for the state test last year class spent 3 days writing about failure and disappointment in their math journals

• resulting in: class using only a couple of pages in the state test prep booklet

• resulting in: parent forced to assign bulk of pages in the state test prep booklet

• resulting in: screaming, yelling, crying

• also resulting in: parent having to work bulk of problems in the state test prep booklet herself, because answers to state test prep booklet were supplied only to teachers, not to parents
  

In conclusion, I don't feel like spending $11 on a Top Secret state test prep booklet because if I'm going to do the school's job I want the school's materials — all of the school's materials, not just the materials the school sees fit to share with me.

Actually, even if the school did see fit to make my reteaching life a tad easier, I'm not sure I'd want to shell out $11 for a state test prep booklet.

Last year's actual grade 7 math test is here.

The sample tests teachers use for training on the scoring rubric are here. (I believe that's what these tests are.)

So we've got two sets of actual New York state math assessments with answers available free online.

Why spend $11 for a booklet?

Wait!

Don't tell me!

I have the answer to that!

If the school doesn't have to pay for it out of the school budget, it's not really money.

Table of Contents NY math standards
New York State standards: grade C
sample problems, NY state test
"vacation"
impending doom
math journal, day 2
math journal, day 3
thank you, Saxon Math
don't study for the test
state test

math standards- intermediate (pdf file)

State Assessment
State Assessment mathemathics
sample state tests 2005
State Tests 2006



-- CatherineJohnson - 30 Nov 2006

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NationalInstituteForLiteracy 09 Dec 2006 - 01:57 CatherineJohnson




Is this what I think it is?

Is this a federal agency directing parents to a homeschooling website for help assessing their children's reading level?


and....


If it is....then why?

Is there a particular reason why our federal government can't provide parents with help assessing their children's reading level?

-- CatherineJohnson - 02 Dec 2006

---

ReadingLevel 12 Dec 2006 - 18:27 CatherineJohnson




I found 3 resources for assessing the difficulty of a book or article yesterday:

• Dale-Chall Readability Index (pdf file) (used in conjunction with Dale-Chall Word List (pdf file)
  

• QUEST book list

• Lexile Book Search (use in conjunction with Lexile FAQ) (I think Mark Roulo put me onto Lexile, but have lost the note I remember having made about it...)
  

And here is Hoagie's Gifted Education Page on readability tests.

When it comes to figuring out your child's reading level, I found the San Diego Quick Assessment helpful. I'll let you know how well it jibes with Christopher's ITBS scores.

Scholastic on the San Diego (pdf file)



-- CatherineJohnson - 04 Dec 2006

---

IowaTestOfBasicSkills 09 Dec 2006 - 04:33 CatherineJohnson




I have now mentioned ad nauseum the fact that my district no longer gives standardized tests that would provide actionable intelligence to parents or anyone else.

We have no idea what our kids' scores mean.

Nor does the school have any idea what our kids' scores mean. This is the state's fault, not the school's. The new ELA test is a mess — even the score reports are a mess. Some kids got score reports with one score on one side, a different score on the flip side. At this point the school doubts the validity of either the test or the scoring or both. Not sure.

We certainly have no idea what decline growth in our children's scores means. Judging by the conversations I'm having, more than a few students seem to have experienced decline growth last year.

But of course there's no way of knowing, because all data in Irvington goes straight to the Data Warehouse.

It's Top Secret!



I'm serious about this.

Ed and I have requested subscores for gender and race.

The school is not going to give them to us.

At some point they'll have to; it's the law.

At some point the state of New York will give the data to us — or, alternatively, at some point I'll put on my Girl Reporter cap and go out and get the info myself, then spray paint it on the school wall right next to the statistics about wife-beating.

WAIT!

WAIT!

DID I SAY THAT!

DID I SAY SPRAY PAINT?

Surely not.


[pause]


I will not be spray painting state test subscores on the middle school walls.



Anyway, the main reason I want the gender data is that if there is a large gap between boys and girls on the new ELA test, which I suspect there is (lots of writing on the test; writing typically skews test results to girls) I would be inclined to view the results as incorrect.

But since the school has opted to stonewall I will carry on being upset about my son's decline growth in ELA scores, and I will carry on encouraging other parents of boys to be upset about their sons' decline growth in ELA scores, too.

This is why political consultants the world around recognize stonewalling as the brilliant form of damage control it so obviously is!



Of course, I can kind of see why the school might not like me getting my hands on the subscores for race.

Especially when you take a look at our local achievement gap in years gone by.

Irvington is no KIPP.



defensive testing

The point is: I need information.

Where exactly does Christopher stand?

Enter the ITBS, a test favored by E.D. Hirsch.

You can order the ITBS from two places:

• Piedmont

• Bob Jones^*
  

The ITBS is one long test. About 6 hours worth; 13 separate tests.

• vocabulary

• reading comprehension

• spelling

• capitalization

• punctuation

• usage and expression

• math concepts and estimation

• math problem solving and data interpretation

• math computation

• social studies

• science

• maps and diagrams

• reference materials
  

wow

The science test was so hard I couldn't score it (informally score it, I mean — the tests are scored by computer after you return them).

The maps and diagrams test was impossible.

Everything else was doable.

Ultimately I'll have scores on each separate scale that tell me where Christopher ranks in terms of his fellow-students throughout the country.

For the time being, I'm assuming Christopher is fine on reading comprehension. That scale had 46 questions; he missed 6.

So we'll see.



what the middle school is doing right

The one terrific moment vis a vis our school happened when Christopher took the usage and expression test.

He looked at the first couple of questions and said, "Ms. K taught us all this stuff last year." (And she taught it in one semester, too, in his case.)

He missed 3 out of 41

That's teaching.

The schools here have tremendous teaching talent.

What they don't have is a decent curriculum and a focus on academic achievement.



Math was somewhat disheartening.

My take is that Christopher is exactly where Ed keeps saying he is: his procedural skills aren't bad, but his comprehension is poor.

• mathematics problem solving and data interpretation MISSED: 3 out of 35 (91% correct)

• mathematics computation - hmmm... I didn't record my scoring .... he wasn't great on computation (back to KUMON?)

• mathematics concepts and estimation MISSED: 14 out of 52 (73% correct)

I think I'll probably start giving Christopher the ITBS once a year. That's what Jerry Moore at My Short Pencil does.



^* I know this thanks to Nick's Mama.


-- CatherineJohnson - 04 Dec 2006

---

LindaMoranListserv 11 Dec 2006 - 19:25 CatherineJohnson




I think everyone here knows about Linda Moran's Teens and Tweens blog.

I've recently (re)discovered that she has a listserv attached to the blog.

I joined last week, and I think some of you might like to join as well. There have been some very interesting posts to the listserv that I don't believe have been posted to the blog itself — and that I don't expect to see posted to the blog itself.

-- CatherineJohnson - 09 Dec 2006

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