Entries from TeachersTeachingKids

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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KtmReaders 29 Aug 2005 - 21:40 CatherineJohnson


Lots of good things from readers, which I'm going to consolidate here:

Dan K's dimensional dominoes

A reminder: Dan K has posted dimensional dominoes manipulatives for teaching dimensional analysis. (I haven't taught myself dimensional analysis yet, but I will. I have to go through ktm and print everything out! There's a bunch of stuff from Carolyn I need to see on hard copy.)

Anne Dwyer observations & question

First, Anne's question:

...my daughter ... is having the worst time memorizing her basic math facts. If you let her count on her fingers or use a number line, she is absolutely fine. And she can solve all of the word problems at her level. I wonder whether I should force her to memorize her basic facts or just trust that the more problems she does, she will eventually memorize what she needs to know. Does anyone else have experience with this?

Offhand, my feeling is that Anne should probably have her daughter actively memorize her math facts, and then practice the facts on worksheets. (Actually, these two activities might be the same activity, I don't know.)

The TRAILBLAZERS material claims that kids in a TRAILBLAZERS curriculum use their math facts so often that they end up knowing them by heart (I think that's a decent summary of their position, but I haven't checked). That sounds good, but I'm not optimistic.

[update: I just checked my TRAILBLAZERS document. They teach math facts conceptually--using counting on & other approaches--& give lots of practice, but no timed work sheets.]

Christopher, who has a terrific memory, didn't manage to learn his math facts cold until we did the Saxon work sheets. Then he got them very, very fast. And remember, we used flash cards & a software math facts program; plus I'd say he was getting a good workout on his math facts at school & in homework. With all that effort, he still didn't have them mastered.

The Saxon work sheets did the trick. I've heard something similar from Joanne Cobasko of SOCMM, too.

I also talked to a mom recently who pulled her son out of their public school in Tribeca (the notorious District 2 NYC HOLD was first formed to deal with, I think) to put him in St. Anne's school in Brooklyn. (sidebar: Ed had lunch with a teacher there who said there is ZERO constructivism at St. Anne's. Apparently it's a FANTASTIC school. Sigh.)

Anyway, her son is now high school age, & is good at math, yet he still does not have a firm grasp on his math facts. She said it's been a handicap (I believe that was the word). She, too, had gone the flash card route back in the day.

I have no idea why flash cards shouldn't be working better for people like me; they're a time-tested teaching method, aren't they?

Last but not least, I used to have a fantastic memory, and I probably still have a good memory for my age. (Boy do I despise age-related memory loss. WHICH BEGINS AT AGE 30, GUYS)

I used to know all my various numbers by heart, and I didn't have to work at learning them, either.

That is no longer true. We got a new credit card number a year or so ago, which I have to write down CONSTANTLY on forms for the kids.....and until this week I still didn't know it by heart. I was constantly having to track down my Mastercard to find the number, which meant, in practice, that I was constantly procrastinating filling out Crucial Forms because I didn't feel like undertaking the whole track-down-the-relevant-information Next Action.

Meanwhile Ed did have the number memorized, along with the number for our pediatrician (who we've been seeing for 7 years now).....so that was making me feel even dumber.

Finally last week I sat down and memorized the number.

Now I know it. (Maybe after I finish this post I'll memorize our pediatrician's number, too.)

Anne's daughter's memory is probably way better than mine, but I guess what I'm thinking is that if a number doesn't take hold in your memory pretty quickly, you're probably going to have to sit down and memorize it on purpose.

Does anyone else have more experience with this?

note: for a slightly older child I very much like the Homeschool Math 6/5: - Tests and Worksheets Booklet, which is the 5th grade book. [ISBN: 1591413222] You don't need to buy the answer book. I'm sure the books for other grades are excellent, too. (I own Saxon 6/5, 7/6, & 8/7 & all of the worksheet books are good.)

calling Carolyn M!

Carolyn is back at school & swamped, but she's checking in from time to time. So, Carolyn M, if you happen to see this & can leave a quick answer, that would be great.

calculus no longer required for b-school

from Andy Joy:

From my experience, calculus is not required for business majors at some schools. I have a degree in accounting, and the year before I attended college, our "Calculus for Business Majors" requirement was replaced with Intermediate Algebra. While nothing in my coursework required calculus, I think that the calculus I took in high school better prepared me to understand economic relationships.

I'm currently working at another college which requires analytic geometry & pre-calc (not calculus) for its business majors.

I advise mechanical engineering students at a college. We've found that 60% of our incoming freshman are unprepared for calculus (which we, of course, require). It boggles my mind that this figure doesn't include all incoming freshmen--just those who think they're suited to become engineers!

This doesn't surprise me at all given what my brother-in-law tells me about the new M.A.'s he hires straight out of engineering school,

from Andy Joy

I went to a private school in California, and I work at a state school in Idaho, and neither requires Calculus unless it is necessary for your particular major. A business, English, Spanish, music, etc. major would only need to complete pre-calc/analytic geometry at the state school, and "Critical Thinking and Problem Solving" at the private school.

A follow-up question: do kids have an advantage in college admissions if they've taken calculus?

Would this be true at all schools?

Are there any scholarship possibilities? (I'm thinking of the WSJ article on kids being given scholarships if they'll pull up a school's stats.)

Also, what is 'Critical Thinking and Problem Solving'? What does this course cover?

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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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AmericanEducator 13 Sep 2005 - 01:19 CatherineJohnson


Via eduwonk, the good news that the Fall issue of American Educator is devoted to the subject of math ed!

While I'm on the subject, I emailed Am Ed asking whether a non-union member can subscribe, and received this reply:

It's possible all you need to do is send a money order or check to American
Educator for $8.00.  See address below   Thanks,  Mary 


Mary Singleton, Temp
American Educator Department
T: 202/879-4420
F: 202/879-4534
E: msinglet@aft.org
American Federation of Teachers, AFL-CIO
555 New Jersey Avenue NW
Washington, DC  20001
www.aft.org

I'm sending my check tomorrow.

what made you quit?

First paragraph in the Editor's introduction, Helping Children Learn Math:

“What caused you to quit school?” That’s the main question that researchers from the United Negro College Fund asked of 62 high school dropouts in a West Virginia Job Corp program last year. Most had the same answer: mathematics.

table of contents

Helping Children Learn Mathematics

Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide?

Mathematical Knowledge for Teaching: A Research Review

Mathematics for Teaching: Then and Now

What I Learned in Elementary School

Harold Stevenson remembered

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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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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

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IBMFundsMissingMathTeachers 18 Sep 2005 - 21:16 CatherineJohnson


Via joannejacobs, a news story about IBM supporting employees to become math teachers.

"Over a quarter-million math and science teachers are needed, and it's hard to tell where the pipeline is," said Stanley Litow, head of the IBM Foundation, the Armonk, N.Y.-based company's community service wing. "That is like a ticking time bomb not just for technology companies, but for business and the U.S. economy."

While many companies encourage their employees to tutor schoolchildren or do other things to get involved in education, IBM believes it is the first to guide workers toward switching into a teaching career.

[snip]

If selected, the employees would be allowed to take a leave of absence from the company, which includes full benefits and up to half their salary, depending on length of service.

In addition, the employees could get up to $15,000 in tuition reimbursements and stipends while they seek teaching credentials and begin student-teaching.

That last is my favorite: 'while they seek teaching credentials.' New York state requires a Master's degree in education--education, not math--to gain certification as a math teacher.

update

I just spotted an interesting comment left on Joanne's site:

This sounds to me like a way of unloading people who are past the peak of their productivity and whose skills are outdated.

Even so, it may be a good move for the individuals involved and for the schools. Second career people should be given some kind of temporary licensure so that they can teach before running the gaunlet of ed school. There are certain characteristics of good teachers that cannot easily be taught or assessed prior to concrete experience in the classroom. I am afraid that many people in their late forties or early fifties could not successfully transition to teaching. I speak from personal experience (failure) and the experience of my wife (huge success).

Stevenson & Stigler, in The Learning Gap, strongly urge that teacher training be done in the classroom, under the supervision of a master teacher.

This commenter is right: ed school doesn't tell you what it takes to be a good teacher, or to enjoy doing it.

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CommentsThreadIntegerProblems 21 Sep 2005 - 20:37 CatherineJohnson


Check out the Comments thread on the Prentice Hall Pre-Algebra problem.


First of all, here's an important resource Dan K has posted before: Mathcounts - a site entirely dedicated to middle school math.

Dan, thanks for re-posting that source. I remember your mentioning it the first time, but it didn't register.


Second, Lone Ranger has advice on improving handwriting. We're just going to HAVE to do this, and it sounds like her idea is less time-consuming than the one I was using. (I was using the book Write Now: The Complete Program For Better Handwriting by Barbara Getty, Inga Dubay. It's a terrific book - I highly recommend it - but it's more than I can deal with at the moment. fyi, the authors give workshops to physicians, teaching them to improve their handwriting sufficiently in just a couple of hours that they can write decipherable prescriptions. I improved my handwriting quite a bit working with the book, and hope to get back to it someday before I'm dead. Their web site: Getty-Dubay Productions)


Third, I think Carolyn & Barry may have given me opposite advice (but I'm too time-crunched at the moment to figure it out...)


Fourth, I'm with J.D. when he says, It peeves me that texts still use the "higher" and "lower" terminology here. To be accurate, they should use "greater" and "lesser."


Fifth, WOW!

J.D. has a lesson on fractions!

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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.

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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.

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IntegerWorksheetsAndWordProblems 22 Sep 2005 - 23:07 CatherineJohnson


The internet is amazing.

Here are 3 worksheets for problems with integers. The last sheet has some good word problems, which I desperately need.

integer addition & subtraction
integer expressions & word problems (pdf file)
sample page of multiplication and division integer problems from Math-U-See (pdf file)

are community colleges an important resource for us?

Math Worksheets with Answers from Central Lakes College looks like a wonderful web site. It has free, printable worksheets on quadratic equations, on 'foiling,' on finding the slope--amazing. Community Colleges, which probably do a huge amount of the math remediation in this country, may be a terrific resource for us. These people are doing the heavy lifting.


Check out this sheet of Number and Consecutive integer problems (pdf file) from a course called Elementary Algebra at Broward.

keywords: community college free worksheets online

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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

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NumberLinesFromDoug 26 Sep 2005 - 18:20 CatherineJohnson


I can die happy now.

Doug sent me the number lines he made up--they are beautiful!!!!!

Thank you!!!

waiting on the printer...

OK, I'm waiting for the first number line to print out.....and.....no number line......

......now I'm getting paranoid.....

ah hah

There's no paper in the printer.

I hope everyone's impressed that I managed to check the paper tray before having a nervous breakdown.

pause

OK, now what?

I want my number lines!

Right now!

The printer just burped. That's a good sign, right?

still waiting

This better not be one of those Restart Your Computer deals.

I hate that.

success

they're beautiful

Doug, are you a graphic designer?

Graphic design is my other love in life.

These number lines are so beautiful I'm going to put them on the wall.

I might frame one.

(I'm serious about that. When I first started drawing bar models I really wanted to paint a big, blown-up black-and-white bar model and have it framed. I love the Japanese character paintings, and it struck me that we ought to have number paintings, too.)

number line attachments

OK, I'm going to attach these first to the comments page, and post a link on the 'math supplements' page, too.

thank you, Doug!

wait!

First I have to post a screen grab, just to show you what these look like:

hypothetical

I just had a heretical thought.

Nobody seems to learn math very well in this country, but it does seem to be true that girls are even less likely to learn math well than boys, or to want to learn it, or to think that they could learn it, etc.

Looking at Doug's number lines, it struck me: if math books were visually beautiful, and lovely to look at,......would more girls find themselves drawn in?

Given the way I remember feeling about my 2nd grade math book, I don't think that's necessarily crazy.

update

All four sheets of downloadable number lines are attached here.

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AlgebraicSymbolsHardForStudents 27 Sep 2005 - 21:22 CatherineJohnson


Another interesting comment from a joannejacobs thread on new research about children's abstract understanding of math:

Imagine what a man like Archimedes could have accomplished if he had had the benefits of Saxon math. It is true that we all have some mathematical aptitude and that certain simple skills develop naturally, but this is far from enough mathematics to function at even the minimum wage level in our world.

I have never met a student who could flawlessly manipulate symbols according to the rules of algebra but had trouble with the deeper concepts of mathematics. Most of my students find poor algebra skills to be an almost insurmountable barrier to deep understanding.

Of course the foundations for success in algebra are those tedious skill sheets we "abuse" our children with in primary school.

Posted by: CRW at September 27, 2005 03:42 AM

hmm.

Now that I re-read this, I'm not sure what he or she is saying....is the point that a student who excels at writing & interpreting algebraic expressions can always also understand algebra?

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BadTeacherStudy 10 Oct 2006 - 01:48 CatherineJohnson


I still have lots more Wayne-Wickelgren blooki-ing to do, plus some tentative thoughts about whether parents have power over their schools, and if so, how much & what kind.

But this thumbnail account of a famous ed study popped up in today's Wall Street Journal & I want to get it posted:

... inept, unkind or unfair teachers can have a huge impact on a child, causing emotional, social and academic setbacks. In a 1996 study that is still widely cited, William Sanders and June Rivers at the University of Tennessee tracked thousands of elementary students' test scores year-to-year and used them to rate teachers as "effective" or "ineffective." Then, they tracked two random groups of similar students who happened to be assigned to either three good or three ineffective teachers in a row between third and fifth grade. The result: a 50-percentage-point difference over three years in the average test-score changes of the two groups, with kids who had the effective teachers progressing more, says Dr. Sanders, now senior research manager at SAS, a Cary, N.C., software concern.

from:
What to Do When You Are Worried That Your Child Has a Bad Teacher
WALL STREET JOURNAL
September 29, 2005; Page D1

I don't know how to put all the different factors together & come up with an understanding of how and why our schools work & don't work.

But I believe this study. I've mentioned this before: after trying to teach Christopher math using the school's textbook, SRA Math, I had higher regard for our district's teachers not lower.

He had learned very little in fourth grade math. He said his teacher couldn't explain things, and I think that's true. (She's not at the school this year, so I hope she won't see this. She was a terrific person; we all liked her very much.)

But what struck me, in my struggle to teach Christopher concepts I was realizing I didn't understand myself, was how thorough his mastery was of the math concepts he'd been taught in K-3. He instantly knew, without thinking about it, that the larger the denominator the smaller the 'piece.' Instantly. And his conceptual understanding was as good as it could be at that age. He could show me, easily, on a drawing, that 1/4 of a pie is less than 1/3. He could generalize this to 1/1005 being smaller than 1/1004, too.

He learned this exclusively from his teachers. His dad and I weren't even paying attention in those early grades, I'm sorry to say. We were leaving things up to the school.

What dawned on me in those first months working with Christopher was the perception that our teachers were so good they could teach math "no matter what you threw at them," as Carolyn would say. They could teach around a book, if the book was bad. And they did.

(SRA Math may not be dreadful, btw; I don't want to be in the SRA Math bashing business. The books have serious content, and are challenging, & I would have opted to keep them rather than change to TRAILBLAZERS though I can certainly understand why the teachers were happy to see it go. BUT I couldn't teach out of SRA Math myself, and I've had several teachers tell me it was murder for them, too.)

So.....there you have it.

Until I know more, I'm sticking with the conviction that A Good Teacher Makes All The Difference.

which means that....

...which means that a lot of good teachers are probably going to de-fuzzify fuzzy math. They're just going to do it. I think Steve has observed that this is what tends to happen; the new fuzzy math comes in, the school works with the curriculum a couple of years, then they start supplementing big-time.

Another commenter, Katherine Prouty had this to say:

I can tell you that my daughter had NO IDEA how to do division at the end of 5th grade. I thought that she didn't get it...

She also wasn't strong in the lattice method of multiplication. Honestly, there were so many addition steps that she was bound to make a mistake -- especially since drilling of any type of math fact was out of the question, although, with my son, now three years later, they are drilling those math facts in the Everyday curriculum like there is no tomorrow. I'm sure the math tests forced them to it (against their better teaching judgement, of course.)

The Schaumberg teacher I met at the airport, the one who was a keen & enthusiastic fan of Everyday Math, told me, 'Well, you have to give them worksheets. Otherwise they're doing this--" and she performed a delightful imitation of a little kid waggling his fingers against his chin trying to add & subtract.

Here was a lifelong teacher who'd spent 15 years doing nothing but fuzzy math, and the idea that kids have to drill & memorize just seemed obvious to her.

I don't understand politics and the nature of social stability and change (I find the subject riveting).

But while my family motto is It's always worse than you think, it could equally be, It's never as bad as you think. Or maybe just, it's never what you think.

That last is true for sure.

rtfm - NOT

This reminds me of the old rtfm line, which I will not spell out, on account of this being a family website and all.

That means no f-words. (No f-words with a few notable exceptions, that is.)

Suffice it to say that the letters r, t, and m stand for read the manual.

Liping Ma & others have pointed out that, in America, teachers' manuals are written with the express & conscious awareness that no one will ever read them.

In the case of constructivist curricula, that's one thing we've got going for us.



^* It's always worse than you think and no common sense-y

worsethanyouthink

---

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

---

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.

---

TeacherProtestsEverydayMath 05 Oct 2005 - 20:46 CatherineJohnson

comment left at SOCMM:

I am a third grade teacher and have been trying to tell my administrators that Everyday Math is not an effective math curriculum. I have taught it for three years and the students coming to me have no mastery of basic concepts. It also does not meet our district or state standards, but the administrators will not abandon the curriculum. I struggle with teaching it and then when I started researching the program, I now feel it is my duty to speak out to parents and be an advocate for my students.

Is there a reason why so many states are adopting this mediocre curriculm? Please respond!

---

TeacherFamiliarityWithStandards 05 Oct 2005 - 00:46 CatherineJohnson






'Teachers who reported “no such document” are not included.'

source:
Mathematics Teachers’ Familiarity With Standards and Their Instructional Practices: 1995 and 1999, EDUCATION STATISTICS QUARTERLY, Vol. 5, Issue 1, Topic: Elementary and Secondary Education

on second thought

Judging by some of the half-baked stuff I've come across today.....a person who's fairly familiar with NCTM standards could be worse than a person who's very familiar.

I still like those 'no such document' folks.

---

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

---

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)

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AnneDwyerOnMathGames 10 Oct 2005 - 22:56 CatherineJohnson



I've tried many different methods for games. The main thing that I have noticed is that the weakest students tend to get the least practice with all these ideas. (For example, in the travel game, the strongest students answer the most questions and get the most practice.) Additionally, the weakest students get embarrassed.

So now, all my games are take turns. Even the weakest students get the same amount of practice. Additionally, I tend to pair weakness with weakness so that they both get pracitice in areas that need it. I may have three different games going on working on different weaknesses for different students.

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MikeFeinbergKIPP 01 Dec 2006 - 21:25 CatherineJohnson




Here, via oldnewschoolteacher, is KIPP's Mike Feinberg on math ed:

You know, talk about curriculum, if I put in front of you a fifth, sixth, seventh, and eighth grade textbook in math and opened up to page 200 and I jumbled them up, and said, “order them from fifth through eighth grade in order,” you'd have a very tough time because they all look the same. That's because, unfortunately, we have this national strategy of “we're not really going to teach to master, we're going to teach to exposure and over lots and lots of years of kids seeing page 200 in the math book, eventually somehow they're going to learn it. We're going to teach them how to reduce fractions in fifth grade, in sixth grade, in seventh grade, in eighth grade, in ninth grade and continue until finally somehow magically they're going to get it.” Instead of thinking, “let's teach the kids how to reduce fractions at a mastery level in fifth grade, maybe spend a little time reviewing it in sixth grade but let's move on to pre-algebra and let's move on to algebra then.” And that's been our take and so it's not that we have a different math curriculum as much as we have a different math strategy and a different math philosophy.

oh, snap

Everyone [in class] was decrying the fact that poor kids don't have the same things, and that they come into pre-K already behind. When they continue falling behind, middle school and high school teachers complain that "there just isn't enough time" to teach them, particularly with the mandated curriculum dictated by state exams.

I pointed out that, if what people were saying was correct, then that would mean that urban kids should have more time in the classroom, longer school days, and longer school years. This would allow them to catch up and give their teachers the chance to cover everything they wanted. I provided the KIPP schools as an example of a school system that does this, and gets amazing results. It works. More time in school and good instruction works.

My instructor was not pleased with this, though. He thought the idea was too "militaristic." He said, "I mean, what's the end goal?" I was flabbergasted, once again. Doesn't anyone get it? The goal is to give kids the skills and knowledge they need to choose the kind of lives they want to live. Period, end of story, I no longer want to talk to you, stupid idiot. But he has this whole notion of making people "good citizens" or getting them to "think critically" about the world. Ask yourself, what would you want for your child? Would you want her to get a great academic education and be able to do whatever she wanted, or would you want someone to teach her "how to be a good citizen" or "how to think critically"? I know, me too. And if the chips were down, my instructor would admit the same thing. The fact is that schools like KIPP are vaulting kids OUT OF POVERTY. They're giving them a fighting chance. And the concept of the schools is not that complex. Their motto is: Work hard. Be nice. And everything boils down to that in the end. There's no magic curriculum bullet. It's just hard work.

what was it Orwell said about people being objectively something-or-other?

Oh, yes.

objectively pro-Fascist


oldnewschoolteacher again:

This guy, this instructor, he so decries poverty and "keeping poor kids poor" and "the pedagogy of poverty" but it is HIS reluctance to accept WHAT WORKS FOR KIDS that keeps them where they are.

I really don't understand. And I'm so angry about it.

I'm adding objectively pro-racist to the list.


[pause]


No. No, I'm not.

I'm going with functionally racist.

That oughta set some hair on fire.


Mike Feinberg of KIPP on spiral curricula
Steve and Susan J on spiral curricula
acceleration versus remediation
parents' stories about spiralling curricula

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KIPPChantsHarrietBall 12 Oct 2005 - 01:37 CatherineJohnson



more from Making Schools Work

Smith: Talking about the land of confusion, in KIPP it's the land of chants. Now, are you personally a creator of mathematics chants?

Feinberg: (laugh) I'm a creator of a couple of them. Most of those chants came from one of our greatest mentor teachers, Harriet Ball, who has the creative musical ballpoints, who learned how to teach in this multi-sensory, whole body style where the kids are singing, chanting, dancing, moving around the room in a way where they're learning from mastery and they're enjoying themselves. And she taught us a lot of those songs and chants. Once you learn her philosophy – how you make the learning relevant and how you make it fun, but also how you make sure the kids are learning what they need to learn – that opens up a whole new world of how to both reach and teach. And we owe that to Harriet. I don't have a lot of rhythm, but I've learned over the years how to come up with some neat chants and songs.

I wish to heck Harriet Ball would finish her book.

God's Ouija board

In 1985, Ball was teaching 3rd grade at Houston's Fairchild Elementary School when she had an epiphany. "My students were struggling to read numbers," she says, "and I was determined to help them. I was standing at the board one day, and all of a sudden it was like a Ouija board. God spoke to me, and I started writing down a rhyme that explained how to change a written number to a numeral."

Ball had used some chants before to engage her students, but this was the first time a lesson had come to her in the form of a song. "It blew my mind," she says. "The kids got it right away, and from then on, I started teaching like that." Other rhymes started popping into her head, sometimes in the middle of the night.

"They were revelations from God," says Ball, who was raised a Baptist but now attends a Methodist church. "A lot of people don't hear me when I say that, but it's true." Later, someone told Ball that there was a hard-to-pronounce word— mnemonics—for what she was doing. But to her, all that really mattered was that it was working.

"When I teach," she says, "I employ the eyes, the ears, and the touching need, the movement need. There's rhythm, and there's singing. I also use wholesome competition. But I don't allow any putdowns; I don't allow the students to laugh at one another." It helps, she admits, to be "a natural ham" to teach her way, but you don't have to be. "Not everyone can teach like I do," she says, "but I can be a springboard for doing something different."

Rap, Rhythm, and Rhyme by David Hill, EDUCATION WEEK 1-17-01 (registration required)

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RonAharoniOnTeachingFractions 27 Oct 2005 - 01:49 CatherineJohnson



Interesting observations via email from Ron Aharoni.

But first, you might want to re-read this post on the fifth operation of arithmetic:

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.”

against pizza

I'd sent him the link to that post, which also included an earlier post of Carolyn's about rectangular fraction tiles being superior to circular pizza-pies:

I agree that sticking to the pie representation of fractions is harmful. I also prefer parts of rectangles.

But: I believe that it is important to take, from the very beginning, fractions of sets. What is a half of 6 apples? A quarter of a set of 8 pencils? And then, immediately, WHAT IS TWO QUARTERS, and three quarters, of that set? This conveys the meaning of "three quarters" better than the manipulatives.

And, an elaboration, from a second email:

I try to start with fractions of all kinds of objects - shapes as well as groups. In first grade, I start fractions with division. I give groups of kids all kinds of objects: one group gets a rectangle, another a circle, another group two rectangles, another group an apple, and another A GROUP OF 4 APPLES, and ask them to divide the objects they got into two parts. Later, each group tells what they did. We then discuss the notion of "a half of". Then each kid is asked to do work on his own - take halves of shapes, and a half of say 4 objects drawn on paper.

Then we can divide into three parts, and discuss what is a "third of something".

Then "two thirds" (just repeat twice the one third), then a quarter - all this can be easily done with second graders, even first graders.

Carolyn says: 3/4 is 3 '1/4's'

This tracks with a point Carolyn made in an email last night:

A unit is rather like the denominator part of a fraction. Many of the rules regarding their manipulation are the same. I intuitively understand why that is, and I am going to try to write it up, but right now words elude me.

Here's a quick try to convey the idea by analogy, though -- the correct way to think of fractions is as a unit -- of the form 1/3, 1/4, 1/5, 1/8, etc. -- occurring some number of times, where that number is given by the numerator.

So you should think of 3/4 as being "the unit 1/4, occurring 3 times".

on not using a child's pre-existing knowledge

One of the common-sense themes of 'metacognitively-aware' teaching, with which I normally agree, is that one should use what's already there, inside a child's head.

When it comes to fractions, the 'friendly fraction' 1/2 is probably more or less innate; children figure it out without having to be taught. (quoting from memory; not fact-checked)

I'm thinking the 'naturalness' of friendly fractions like 1/2, 1/4, 1/3 and so on -- all representing, for children just starting out, one obvious, natural whole divided into parts -- may be a problem as much as an opportunity.

All textbooks begin teaching fractions with the fraction 1/2.

Always, this is illustrated as 1/2 of a pizza.

I think that's probably a mistake. I'm thinking the idea of 1/2-of-a-pizza may be so deeply ingrained in children's (and grown-ups') minds that the jump to 1/2 of a group is that much harder to make.

don't laugh

OK, I finally looked up the page in Christopher's 5th grade textbook that utterly threw me last year.

It was 'Lesson 58 Fractions of a Whole.'

The lesson began:

We've looked at a fraction of a whole unit. Now let's review fractions of numbers greater than 1.

Take 1/4 of three identical sandwiches.

There followed a page of drawings showing that 1/4 of 3 sandwiches is the same thing as 3/4 of 1 sandwich.

I didn't get it.

I could see it was true.

I could see that the drawing was 'true,' and I knew, of course that 1/4 x 3 = 3/4 x 1.

That wasn't the problem.

The problem was, I didn't get it.

I was having an especially hard time with the pizza pie chart image that kept popping into my mind:





My problem with this mental image, which was very strong & vivid, was that I simply could not stop seeing THREEFOURTHS.

THREEFOURTHS, to me, is a highly overlearned mental THING; if you say 3/4 to me, I'm going to start seeing visions of circles divided into fourths with 3 of the fourths shaded in.

Period.

I have no choice. It's like a song that's stuck in your head. Only it's not a song. It's a textbook illustration.

So there I was, trying to think about ONEFOURTH of 3, and forget it. It wasn't happening; it wasn't going to happen.

I just could not make that bright, vivid, 3/4-of-1-whole-circle turn into 1/4 of 3 circles.

I could imagine 3 circles, side by side, each divided into 4.

But after that my brain instantly jumped to the THREEFOURTHS clumps. I kept imagining, in sequence:

• first, the shaded 3/4 of Circle Number One (on the left)
• second, the shaded 3/4 Circle Number Three (on the right)

then

• the left-over 1/4 from Circle Number One added to the top half of Circle Number 2 (in the middle) AND the left-over 1/4 from Circle Number Three added to the bottom half of Circle number 2.....

...which I bet at this point nobody can even follow.

I certainly couldn't follow it. Not because it's hard, but because working memory wasn't put together to perform a sequential circle-dividing task of that magnitude.

the magical number 5

I was thinking.

3 circles, 2 THREEFOURTHS chunks, 2 ONE-FOURTH chunks, and 2 TWO-FOURTH CHUNKS ought to come out to the magical number 7, plus or minus 2.

Apparently I'm down to the magical number 5.

rescue

Finally my friend Debbie came to the rescue. (I bet I can't find her email....nope, can't find it). Paraphrasing:

The way I always think of this is as three 'one-fourths.' There are 3 sandwiches, and you take 1/4 from each sandwich. That gives you 3/4, or 3 separate one-fourths.

That one sentence clobbered my THREEFOURTHS image.

Suddenly I could 'see' separate little one-fourths pulled out of all 3 circles; I could see the individual one-fourths as.....units, I guess. Like Carolyn would say.

in conclusion

This is what makes me wonder whether, in some cases, the 'natural math' a child (or adult) brings to class may not be the best hook.

In my case the problem wasn't just the probably-innate friendly fractions children & grownups understand without being taught. My problem was the image of the circle, which, as Carolyn points out, is not an easy thing to break into parts and then rearrange those parts in new configurations.

That's why circles represent things like 'eternal love' and the like, because we don't see circles as having beginnings, or ends—or pieces or parts.

Culturally speaking, at any rate, a circle is the Ultimate Whole.


All of this is a long way of saying that:

• I'm going to stick with rectangular fraction tiles
• Aharoni's idea of starting with 2/3 as well as 1/3 -- of teaching 2/3 in the same moment that you teach 1/3 -- is an excellent idea

update

Here's a terrific example of why rectangular fraction tiles are superior to circles:





source:
Demonstrating division of fractions with pictures or manipulatives at Math Forum


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)

---

InvestigationsInMilwaukee 17 Oct 2005 - 18:17 CatherineJohnson


Here's a new one:

In a fifth-grade class, teacher Beth Ann Schefelker, who won major national recognition last year for her work, asks students to divide 246 by 12 by creating a story problem. Two girls tell classmates their proposed method: Twelve sisters each had $20, so that gives them $240, with $6 left. You split up the $6 and you get 50 cents more for each sister. So the answer is $20.50.

One of Schefelker's students, Tylar Moore, said it's "kind of like a myth" that kids don't learn their math facts through Investigations, a program used in about two-thirds of Milwaukee elementary schools. Most of the kids in the class know that four times eight is 32, Tylar said, and if they don't know that off the top of their head, they know strategies for figuring it out, such as writing 8 four times on a piece of paper and adding the numbers up.

Schefelker said her class doesn't do a lot of work on basic math facts - what she calls "naked numbers" - but the math is embedded in the work they do, much of it in the form of problem-solving. She said learning math shouldn't be like training circus animals to do tricks. It should be like teaching people to live in nature.

source:
Division flares up over math by Alan J. Borsuk 10-4-03 (lots of interesting materials online with the article)

naked numbers........

I like it!


So now we've got:

guide on the side
sage on the stage
drill and kill
chalk and talk

and

naked numbers


grunt and spit
naked numbers
plug and chug
Ken's buzzwords

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AskeyTeachesTeachers 15 Oct 2005 - 15:42 CatherineJohnson

Askey started teaching a course four years ago in Madison for prospective elementary school math teachers. One of the things he did was ask them a question from an eighth-grade math test that was used in an international study several years ago: Divide 25.56 by 0.004. Fewer than half got the right answer (which is 6,390).

Liping Ma

[Liping Ma] asked teachers from each country to divide 1 3/4 by 1/2 and explain how they would teach that to students.

Only nine out of 21 U.S. teachers even got the right answer, and just one suggested a method of teaching how to divide a fraction by a fraction that Ma listed as "conceptually correct."

All 72 Chinese teachers gave correct answers, and 65 created more than 80 story problems for illustrating the process that were creative, easy to understand and appropriate.

(The correct answer is not 7/8, a common mistake. That's what you get when you multiply 1 3/4 by 1/2. When you divide by 1/2, the answer is 3 1/2. You are, in effect, figuring out how many 1/2's there are in 1 3/4.)

Ma asks in her book, "What kind of 'teaching for understanding' can we expect" from teachers who do not have a profound understanding of math themselves and who are not given much opportunity to work on improving how they do their work, including time to work on developing their teaching skills? Teachers in China work extensively, individually and in small groups, on ways to make sure they are doing their jobs well. American teachers have larger amounts of actual classroom time and very little time to work on improving their effectiveness.

"What U.S. teachers are expected to accomplish then is impossible," she says. "It is clear that they do not have enough time and appropriate support to think through thoroughly what they are to teach. And without a clear idea of what to teach, how can one determine how to teach it thoroughly?"

the Math Summit

A math "summit meeting" held by the U.S. Department of Education in February ended with agreement on a three-point agenda for improving math education: Get the public more involved, launch more research on what works, and spur improved teacher knowledge. Two follow-up sessions have been held, and department officials are looking to the federal education law, No Child Left Behind, as a way to push for more math teachers who have strong backgrounds in math.

Get the public more involved.

So I guess we're doing our part!

this is great

From the other side of the debate, Roger Shouse of Penn State told the same forum that "reformers' attacks on traditional practices appear to reflect a failure to distinguish between 'traditional math' and 'traditional math taught badly.' "

I'll say.

lesson study

Liping Ma is associated now with the Carnegie Foundation in California and is beginning work on a project with a California school district on what is called "lesson study," an approach used in Japan and China in which teachers work together to improve their teaching methods.

I'm strongly in favor of this.

One of the main reasons I started working on Kitchen Table Math was that it was the only way I could rustle up colleagues, mentors, & master teachers for lesson study.

source:
Bottom line for math students: good teaching is what counts by Alan J. Borsuk SENTINEL JOURNAL 10-4-02

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TeacherReleaseTime 16 Oct 2005 - 21:19 CatherineJohnson



The 3 best books I've read on math ed are:

Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma

The Learning Gap by Harold Stevenson and James Stigler

Principal's Guide to Raising Mathematics Achievement by Elaine McEwan


All 3 are amazing, but we haven't talked much about McEwan's book, for some reason.

McEwan is a frank foe of constructivism, unlike either Ma or Stevenson & Stigler; she also comes from a long career as a public school teacher and administrator. If you were going to buy one book to give to your own school's principal or school board, this would be the choice.

This is a woman who actually did take over a school and raise math achievement; she's done it, not just studied other people who've done it:

In 1983 I became an elementary school principal in a small district, kindergarten through eighth grade, in the suburbs of Chicago. Although the district was home to affluent areas where upwardly mobile young executives moved their growing families into burgeoning subdivisions, my school fronted on railroad tracks in the central downtown. The building was old, the playground was rusty, and the paint in the hallways was fading and peeling--a fitting backdrop for a demoralized veteran faculty. The standardized test scores in both math and reading were abysmal. Students in grades 2 through 6 as a group were at the 20th percentile in reading and the 17th percentile in math on the Iowa Test of Basic Skills. We tackled reading achievement first, with great success. With each succeeding year we reduced the number of students who scored in the bottom quartile. Our scores jumped to the 60th, 70th, and even the 80th percentile in reading. But we soon realized that we could not neglect our math deficiencies.

We discovered that the majority of our sixth-grade students failed the junior high school math proficiency test. They were doomed to the low math track for the rest of their academic careers. They would never master algebra, the 'gatekeeping' course to advanced learning. Even the doors of our local community college would be closed to them unless we drastically improved student achievement. We determined that it wasn't enough to give our students literacy; we had to provide numeracy as well.

In the eight years I served as building principal, student achievement in mathematics rose as dramatically as it did for reading. The junior high school mathematics chairperson noticed the trends. 'What are you doing over there?' she wondered. 'We're phasing out remedial math classes and adding another section of fast-paced math for next year...."

The book is a page-turner, and I'll try to get lots more posted about what she and her teachers did. (Her section on the 'Gambill method' of teaching algebra is a tour de force.)

But since we're on the topic of teacher release time, here's her most succinct statement on the importance of giving our teachers the same ability to work with colleagues teachers in high-achieving countries have:

One of our most effective programs for improving instruction was the periodic release of teachers individually or by grade level from their classroom responsibilities for one-half day. Teachers can use this time for many activities, any one of which has the potential to raise achievement. They can talk about each of their students' progress with the principal and the student assistance team, meet with a math specialist to learn about a new strategy or method to teach problem solving, meet with other teachers at their grade level to plan a unit of study, or visit a colleague and observe a math lesson.

I have a vague memory that her teachers may have been able to videotape their lessons and study them together, the way athletes study game tapes....but I may be mixing up a couple of sources, so I'll have to check.

I do recall that her teachers got so good at teaching math they were being bused around the state, along with their students, to stage demonstration lessons for teachers in other schools!

teacher release time!

Singapore does it, China does it, Japan does it; as far as I know, most high-achieving countries have time structured into the work day or week for teachers to confer with colleagues. Plus we've got Liping Ma, Stevenson & Stigler, and McEwan, a school principal who led her school's successful effort to raise math achievement, all telling us teachers need colleague time.

That's why I say that if I had my druthers, this would be my first reform (in part because we could do it if we decided to. You don't have to defeat the entire NSF-NCTM matrix to get teacher release time put in place.)

Which reminds me.

The first time I met our new superintendent I raised the issue of teacher release time. She nodded, agreed it was very important, and said she'd had teacher release time every single Wednesday afternoon in her Connecticut school district.

Then she said we couldn't have it in Irvington, because it would cost too much.

We had just adopted a new Character Ed program, which was taking up 20 minutes a day, each and every day, for 6 months of the school year.

We could afford 20 minutes a day for NO PUT DOWNS (the program's name) but we couldn't afford 20 minutes a week for teachers to study math. (I'm dimly remembering one of these 3 books saying that the time teachers need per week to work together on math ed is an hour. I think.)

There are times when I understand why Jimmy used to bang his head against the wall.


McEwan has written lots of books, including The Principal's Guide to Raising Reading Achievement, Making Sense of Research: What's Good, What's Not, and How To Tell the Difference , Solving School Problems: A Guide for Parents & Educators: Kindergarten Through Middle School and How to Deal With Teachers Who Are Angry, Troubled, Exhausted, or Just Plain Confused. She's very interesting on the subject of managing staff, and she's terrific on the issue of kids who aren't doing well in a subject. She puts such kids on a 'principal's list,' which requires her to sign their report cards as well as the parents. She doesn't let kids fall off the track. As soon as a child is having trouble, she's on the case.

update

I was looking for something else, and came across this post on Chinese teachers from Liping Ma's book.

update, update

The one-hour a week figure comes from Liping Ma:

Chinese teachers not only study teaching materials individually, they also do it with their colleagues.

Chinese teachers are organized in jiaoyanzu or "teaching research groups" ... These groups, usually meeting about once a week for one hour, get together formally to share their ideas and reflections on teaching. During this period of time, a main activity is to study teaching materials. In addition, because Chinese teachers do not have their own desks in a classroom, they share an office with their colleagues, usually with other members of their teaching research groups. Teachers read and correct students' work, prepare their lessons, have individual talks with students, and spend their nonteaching time at their offices. Therefore, they have significant informal interactions witih officemates outside of the formal meetings of their teaching research groups.

Obviously, they have quite a bit of informal interaction with colleagues as well.


Susan S on teacher training in China
how Chinese teachers learn math
teacher release time & Liping Ma & Elaine McEwan's Princepal's Guide

---

DirectInstructionWorkshop 19 Oct 2005 - 15:37 CatherineJohnson



from Carol Gambill, on teaching algebra to 8th graders:

I have developed totally scripted lessons for each algebra unit that require absolute focus and attention, constant oral responses, and intense involvement from every student.

Demanding and receiving absolute focus and attention isn't that hard once you've had enough practice.

I'm sure if we could watch a video of KIPP instructors at work, we'd see rapt attention.

The way to command rapt attention is to call on the students constantly.

For mainstream teachers, calling on students means asking a question.

KIPP does lots of class chants, which I'd like to incorporate into my own small class if I could find out what the KIPP chants are. I suspect all kids would profit from learning math chants. (I had to do whole-class phonics chants when I was a kid.)

But outside KIPP, 'constant oral response' means constant question-and-answer. Everyone has to be ready with an answer at all times.

The art of Asking a Good Question is almost never mentioned in math ed writings. The constructivists talk about real-world problems and 'challenges'; domain-knowledge folks talk about 'direct instruction' or 'scripted instruction.'

But the problem with the phrases 'direct instruction' and 'scripted instruction' is that they call to mind a teacher delivering a lecture.

I don't know how Zig Engelmann teaches his classes, but as far as I can tell, scripted instruction for most of the educational world actually means asking excellent questions you've thought about, written out, and committed to memory before hand. The Saxon Math books in the early grades have tons of questions scripted in.

Another problem: many of us think of questions as a query that arises spontaneously in the course of a class. The teacher is lecturing away, and suddenly the spirit moves him or her to stop and ask a question.

Scripted instruction means you don't ask questions off the top of your head. You think about the questions you're going to ask. Some questions are better than other questions, and you think about that. You test-run your questions with real students; then you throw out the good ones & revise & modify the good ones to make them even better.

The questions are in the 'script.'

Wickelgren on asking questions

[T]eachers should present information to the class, but stop every minute or two to ask questions or pose problems based on this information. This produces far faster learning than asking students to discover answers with little help. It is also much more effective than straight lecturing, as most kids will not pay attention to a long lecture--but they will if forced to respond frequently to the information given.

The benefits of balancing questioning and information delivery in learning are underscored by a classic study by psychologist A.I. Gates. In that study people spent different proportions of time reading (absorbing) information versus attempting to recall what they read. People learned the most when they spent about 80 percent of their time trying to answer questions about the material. If they spent less time recalling facts, they learned les. But if they spent more time in recall, their learning also tapered off.

A similar ratio should be employed in the classroom. Math teachers can query students in a variety of ways. They can pose general questions about a math concept to test students' understanding of it. They may explain a problem-solving method using an example problem and then ask the students to solve similar problems. Teachers may even given students a chance to figure out the answer to a new type of problem while providing feedback and hints, and ultimately the answer when none is forthcoming.

Using direct instruction, you don't talk for longer than 2 to 3 minutes at a time. Then you ask a question or pose a problem.
source:
Math Coach, page 30-31

direct instruction on direct instruction

The Sweetwater Union High School District has posted videos of what looks to be a professional development workshop on direct instruction. I've watched all of them; they're terrific.

The video on guided practice goes over reserach on teacher effectiveness:

• effective teachers typically ask an average of 24 questions during a 50 minute period; ineffective teachers typically ask an average of 8.6 questions during a 50 minute period

• effective teachers typically ask more process questions ('how did you get the answer'); ineffective teachers ask far fewer process questions

• effective teachers devote more time to guided practice (there's a video lecture on guided practice at the site)

• effective teachers give more quizzes than ineffective teachers

The instructor in the video mentions one teacher who writes 50 questions beforehand for each lesson she is going to teach.






The questions a teacher asks in class are the near-equivalent of the problem sets in a textbook.

Ourside class you learn math (mostly) by doing problems; inside class you learn math (importantly) by answering the teacher's questions.

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DirectInstructionEngelmann 19 Oct 2005 - 20:56 CatherineJohnson



from KDeRosa:

Zig has the answers to all your direct instruction questions and a few more you probably haven't even thought of yet. There's been a lot of experimentation, research, and field testing incorporated in his teaching techniques.

Check this article out:

Student-Program Alignment and Teaching to Mastery (pdf file)


Thanks!

update

Wow. I just started skimming the article; it's terrific.

Back later.

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NewYorkStateMathStandardsChart 23 Oct 2005 - 12:26 CatherineJohnson

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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.

---

FormativeAssessnent 19 Dec 2005 - 01:30 CatherineJohnson



Doug's comment reminded me that I'd pulled an OECD article on formative assessment to post:

Formative assessment – the frequent assessments of student progress to identify learning needs and shape teaching – has become a prominent issue in education reform. In fact, Studies have shown it to be among the most effective educational interventions ever reported.

Between 2002 and 2004, CERI examined exemplary practice of teaching and formative assessment in secondary schools in eight OECD countries – Australia (Queensland), Canada, Denmark, England, Finland, Italy, New Zealand and Scotland – and brought together literature reviews from English, French and German research traditions, relating all this to the broader current policy environment.

The resulting publication, Formative Assessment: Improving Learning in Secondary Classrooms, combines those elements to clarify the concept of, and approaches to, formative assessment and its relation to teaching strategies. The culmination of this study was a major international conference organised by CERI in Paris, on 2-4 February 2005. The conference highlighted international research and case study evidence from the CERI study.

CERI will co-sponsor a regional conference on formative assessment in Budapest, on 29 – 30 September 2005....

Beginning in 2005, the project has just started to look at assessment strategies for adult learners. The study will highlight the issues of why, what and how institutions should assess adult students, and implications for policy.

I think this may be the web site that assured me 'adult learners' don't remotely learn the way young learners do, a fact I decided not to learn.

Being an adult learner, not learning that I can't learn was easy.

update

ah-hah

yes, indeed, I have done a bang-up job of not learning the bit about adult learners not learning, because the CERI web site, far from being the bearer of bad tidings about adult learners, is in fact the bearer of the Certain-To-Be-Correct observation that one can learn at any age. (pdf file)

In recent years, brain science has captured the interest of policymakers and educators. Many believe that new discoveries about the brain yield new insights into early childhood and adolescent learning. However, most of the brain science policymakers and educators cite is not new and even this “old” brain science tends to be oversimplified and misinterpreted in policy and educational contexts. Contrary to popular understandings about the brain, most learning is not limited to early critical periods in development. Furthermore, there is no simple relation between the number of neural connections in the brain and rate or ease of learning. What we do know, from psychological studies of the mind, is that rate and ease of learning depend critically on what one already knows, not on one’s age. We should attempt to use what we do know about learning across the lifespan to provide optimal learning environments for all our citizens.

Does that sound like domain knowledge to anyone else?

oops

Nope, wrong again.

This is the web site with the bad news about adult learners, a fact I seem to have learned in spite of the many obstacles created by my advanced age.

Here's the Good Word from Manfred Spitzer, Psychiatric Hospital, University of Ulm, Germany (pdf file):

You cannot train 15 year olds and 50-year olds in the same way, as the younger ones will perform better.

I'm going to forget that now.

what does this mean?

Spitzer recently attended a meeting on the retraining of employees where he said he noted that the official dogma of every learning institute for retraining of employees stated emphatically that age does not matter. However, he says you cannot train 15-year olds and 50-year olds in the same way as the younger ones will perform better, and that this causes anxiety in the older subjects. But this is not officially recognised, and so when Spitzer told them about the declining learning rate and what the consequences should be for educational programmes it was evident that they were doing exactly the opposite. He explained his theory of a more cost-benefit effect: if this type of retraining was more focussed on split groups according to age decline, it would ultimately produce a curve effect, and in turn produce a cost benefit effect. He says when you start to think about such issues it becomes evident that there is an endless list of possibilities of things you can do, and this is what he will now be exploring in his new Transfer Center.

I wonder if the author of this passage is too old to learn to express himself clearly?

Surely not.


KUMON & formative assessment

---

TourDeForcePartTwo 22 Nov 2005 - 18:24 CatherineJohnson



via Eduwonk, I've just found the KDeRosa of the teachers' unions:

It has fascinated me to see the reaction to Part I in this series in which I urged teacher unions to become responsible advocates for controlling the waste in our public schools. Over night, thanks to Mike Antonucci at the Education Intelligence Agency, I’ve become the darling of the political right, the Goldwater Institute hailing me as the second coming of Al Shanker. Not bad for a dues paying member of the Democratic Socialists of America. If teacher unionists can build coalitions with the right to curb waste and use the taxpayers’ money more productively, that’s fine with me. I’m weary of the political left surrendering all thought of economy and good school management to the right.

It is also time teacher union leaders end all their sanctimonious rhetoric about professionalism. The fact of the matter is, in most of America’s public schools not only are teachers not permitted to function as professionals, their working conditions are deteriorating and are horrifyingly reminiscent of those that gave birth to the teacher labor movement to begin with.

In the name of serious educational reform, we need to tell the truth about the agony of many elementary school teachers who if they get an uninterrupted hour a day with their whole class, it’s been a good day. We need to explain to a world that is largely ignorant of what we are up against, that even when they occasionally get some time, how they use it is often determined by some administrator type who having taught for a few years is empowered to shove the latest fad of an imagination-sapping program down their throats. We need to talk about the absurdity of all the so-called push-ins and pull-outs that fracture the coherence of the school day, creating a rhythm of school activity more akin to a computer game than what most people would understand as learning. We need to talk about how these circumstances defy the ability of even great teachers to practice their craft in anything approaching a professional manner and which thwart the ability of novice teachers to develop their teaching skills. A revitalized teacher labor movement would organize these hardest-working of hard-working teachers to take back control of their work - to regain the pride that comes from developing an individual style of teaching as unique as one’s fingerprints.

A revitalized teacher labor movement would speak out forcefully about our middle school teachers and the absence of professional conditions in most of their workplaces. They are inundated with criticism these days, sometimes even from colleagues in the upper and lower grades, for the falloff in test scores that almost universally occurs at this level. They are caught up in a wave of so-called middle school reform that has swamped the academic program, leaving us psychobabble about emotional learning as a substitute for the kind of intellectual challenge that would probably raise their scores. Not too long ago, I heard a principal of one of our middle schools tell the Board of Education that, “The goal of middle school is the emotional education of our students.” How can it be that he wasn’t fired on the spot? When has anyone seriously engaged middle school teachers about their thoughts of what might improve the educational outcomes of their schools? Professional? Indeed! Can anyone imagine hospital administrators prescribing medical treatments without consultation with the physicians on staff?

Teachers are always called to an ill defined professionalism by those who wish them to do more for less and with less. Union rhetoric too often aids and abets this exploitation. It encourages members to believe they are professionals even though they have minimal participation in determining good teaching practice, no say about who enters and remains in their line of work and are constantly second guessed by supervisors with little to no appreciation of the art of teaching and parents who believe they know more about teaching than we do.

Not to put too fine a point on it, but I think every word of this is true.


Part 1 is even more amazing.

Opening line: If the United States is to preserve our system of free public schools, teacher unions are going to have to stop accepting the status quo and making excuses for the poor performance of our students.

oh boy:

With entrepreneurial aplomb some crafty educators have gone corporate, developing and skillfully marketing programs for everything from mathematics to values education. School districts employ large numbers of central office administrators who then turn around and hire consultants who often come selling their programmatic wares. Where are the NEA and AFT to challenge this pentagon-like waste in our schools?

The world of marketed education packages is opaque and impossible to penetrate. Apparently there is a huge 'health' industry peddling its wares to school districts, as well as a very large 'character education' industry, or so I gather. All of these things cost money, are based on no data whatsoever, and are virtually unknown to the taxpayers who fund them.

Some of the data on D.A.R.E., for instance, a program we've had for years here in Irvington, show that it is associated with increased drug usage in teens. Whether or not D.A.R.E. encourages kids to use drugs, it certainly doesn't discourage them; no one thinks it's effective. I talked to a federal prosecutor who just laughed when I brought it up. Irvington 5th graders spend weeks attending D.A.R.E. classes instead of academic classes, and the school holds a graduation ceremony at the end, which the Superintendent attends. All this without examining, or even collecting, outcome data. And we pay for it.

In middle school this year our kids all took a test to determine their 'learning styles.'

Presumably, the reports would come back, and.....and what?

They would be taught according to their individual learning styles?

I don't see that happening. They must have the results back by now. (The test can't be scored by regular teachers; it has to be sent away to the company that manufactures it for Special Scoring.) I've heard nothing about Christopher's Learning Style; nor have I seen evidence of homework and/or teaching geared toward his learning style.

It's a good thing, too, since cognitive science tells us that teaching to learning style is almost certainly the wrong way to go.

But who needs research when you've got Mel Levine writing bestselling books on learning styles? Irvington has purchased a fancy learning-style testing program and we're paying for it.

I doubt Irvington administrators came up with the idea of purchasing a fancy learning-style testing program on their own.

My guess—my guess—is that the company that produces it pitched it to them.

Either that, or Scarsdale was using it, and we followed suit.

(Have I mentioned Scarsdale uses TRAILBLAZERS?)


and here's this:

Surely some of the budget defeats on Long Island were aided by the local newspaper’s articles on teachers earning over one hundred thousand dollars a year.

Yup.

I'm in a state of permanent dismay over the Main Street School 5th grade teacher, earning $100,000 a year, who told M.'s mom last year that he wouldn't be grading any math homework because he had 'too many students.'

Average class size in Irvington: 17.

---

MyContractToImproveChristophersGrades 19 May 2006 - 16:27 CatherineJohnson



OK, I need help.

Christopher came home with this "Report Card Evaluation Contract to Improve My Grades," which he has filled out and signed.

I'm going to write a contract for his teachers to sign.

If I get really ambitious, I'm going to write a contract for the principal and superintendent to sign, too. (The superintendent, by the way, has created a 'Wellness Committee' open to parents and members of the community. I guess we're branching out from character education.)

I could crib the whole thing from War Against the Schools' Academic Child Abuse, but that wouldn't be as much fun.

What items should be on a teacher/principal/administrator contract to improve student grades?

I'll definitely have a line about formative assessment and teaching to mastery.

I also need a line about giving clear assignments and making sure students understand assignments, about not telling an entire class their short stories are 'horrible' and 'don't deserve to be published in a book,' and about not saying 'Stop making all that noise, you're not retarded.'

What else?


UPDATE 11-29-2006: Rejecting this "contract" turns out to have been a good call. We learned this fall that Christopher's grade 6 math teacher was instructed to hold down the number of As in her class, which she did. This directive runs counter to standard practice in New York state, which is to grade students in Honors and Accelerated courses up slightly so as not to punish them for taking more difficult classes. Parents were not informed of this policy, yet we were asked to sign a "contract" stating that our child was "responsible" for his grades.


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract

---

WhyPublicSchool 07 Dec 2005 - 18:35 CarolynJohnston


On the Doug and Ken take on Ed Wonk thread, JD left this comment:

I remember reading a comment left on a different site that alleged that the public school was, in essence, an institution whose main purpose was to remove the burden from parents of the work involved in educating their children.

I always thought the main idea of public school was to educate those children whose parents could not or would not educate them, for whatever reason.

Early on, in our agricultural years, there must have been a lot of parents who thought it was a waste of time to have perfectly able-bodied farm kids spending most of their day at school. But that didn't matter: the law had decreed that their kids would get educated. Did educators at that time assume that kids would have the whole-hearted involvement of their parents at home -- or that their possibly illiterate parents would be able to help them with their homework? I doubt it very much. So the argument that kids can't be taught unless their parents are involved is beside the point; these are the conditions that schools were intended to function in.

Whether it's possible to teach kids against their will and without their parents' support is perhaps unsettled, but the original intent of public school was definitely to educate kids whether their parents liked it or not. So really the question public schools ought to be trying to answer is this: what's the best we can do for these kids if there's no support at home: how do we ensure they learn anyway?

I'm now going to say something very politically incorrect: unwilling children CAN be made to learn (at least when they are young).

We've educated Ben against the most incredible odds; he had Asperger's, severe Tourette, and severe inattentive ADD. They don't come more unwilling than Ben; there was a time when you could stick your face an inch from Ben's, yell at the top of your lungs, and get only a Buddha-like smile in response; not because he had an attitude, but because he had gone someplace where he couldn't hear you.

We got through to Ben mainly by keeping a close eye on what was working and what wasn't, incentivizing him heavily*, and changing tactics if something wasn't working (that's behavioral analysis). You concoct a set of things you want the kid to learn, and you concoct a set of incentives, and you keep an eye on both to ensure that the goals are being met, and that the incentives are working. Schools have kids for around 6 hours a day; that's a lot of time.

But I feel for Ed Wonk and for all teachers, because schools are very hierarchical and autocratic; teachers can't necessarily do what they know will work.

* i.e., we bribed him shamelessly.

---

IepsForEveryChild 19 May 2006 - 21:47 CatherineJohnson



Rereading Parent Pundit's post about her daughter's experience with Everyday Math and ALEKS, this passage caught my eye:

...they give a pretest and a posttest for the curriculum. In other words, they give the final at the beginning of the year and at the end of the year to track the learning. My daughter received a 25 at the beginning of her 5th grade year in math, but she only received a 69 at the end of the year....

Clearly, intervention was needed. In the summer at the end of 5th grade, I had her try the Aleks computer program in math, www.aleks.com. The Charter School in my town uses it, and I decided to try it for my own daughter. A tutor would have been expensive and less than optimal in this situation because my daughter does get concepts, she just needs more drill (how can most kids hone their number sense if they aren’t ever asked to multiply and divide numbers continuously), and she needs algorithms that have fewer steps so there is less possibility of error (everything that Everyday Math does not provide.)

I give Parent Pundit's school—and the authors of Everyday Math—credit for the pre- and post-testing.

My problem is: what comes next?

They give this child a pre-test and she scores 29; they give her a post-test and she scores 69.

And then......nothing.

"Clearly intervention was needed."

I'll say.

Why is intervention the parent's responsbility?

The school has failed to teach this child 5th grade math. When she takes the ALEKS test, the program tells her she knows only 21% of a typical 5th grade curriculum. (I'm wondering whether ALEKS allows people just to take the grade-level tests, and if so, how much they charge. I'll check.)

If this child were classified as having special needs, she would be entitled to be taught the content that is listed on her 'IEP,' which stands for Individualized Education Program.

Of course, in my experience the content on the IEPS doesn't get taught, either, but still.....it's there; the parent has a leg to stand on. (And in my own children's case, in fact it's extremely difficult to know what they are and are not able to learn, though I suspect Engelmann would make short work of some of the IEP meetings we've had.)

But with a typical child with normal intelligence, there's no mystery. She can learn 5th grade math in 5th grade. It's the school's job to teach it to her—and to reteach it if they failed the first time around. If that means providing tutoring or summer classes, so be it. It's the school's failure; the school needs to fix it.

This mother was in the same position I was in at the end of 4th grade. My child was failing; the problem was the school's, not his or mine. (In his case the problem was almost certainly the teacher, who I liked very much, but who apparently just could not teach math at that early stage of her career. The school didn't give her tenure, which was the right move. But children who lost a year of math in 4th grade weren't given any help or remediation. No one came to parents of these children and said: Your child failed to learn math this year, because his teacher was inexperienced and didn't manage to teach the subject to mastery. Here's what we're going to do to re-teach the material he missed.

American schools, by and large, teach for coverage.

Not for mastery.


free assessment at ALEKS?

It looks like ALEKS offers a free assessment. (I haven't tried to use it, because I'm not sure I can run the test twice on one computer, and I'm most interested to see where Christopher scores.)

If this assessment really is free, and is easy to use, it could be a useful tool in talking to teachers and administrators.

What we really need is our own simple-to-administer, at-home assessment, 'rolling' assessment tools.

I'd like to be able to send my school a report each month on where Christopher is in the curriculum.

Of course, that's another project.

report cards for the school

---

FirstDaysAtSchool 06 Dec 2005 - 19:52 CarolynJohnston


The discussion on the WhyPublicSchools post about girls and boys, and the differences in their personalities and needs, reminds me of a story that Bernie told about his teaching approach on first days in math classes that he taught in colleges.

The first impression, of course, is critical, and Bernie used to play those kids, especially the boys, like violins.

The boys, he said, needed some tough love on the first day. You could scare them with the notion that you were the strictest math teacher ever on the first day, get them braced and working, and then back down later, as necessary, if you wanted to. If you let them get the initial impression that you weren't the alpha dog in the classroom, then you'd lose them.

This approach, he said, backfired like crazy with the girls. A lot of them would run right out of the class on the first day and go drop the class like a hot potato. He really wished that he had a way of secretly conveying to the girls that his bluster was all an act put on for the boys' benefit, that he was really a sensitive guy who would treat them well. And he was, as the girls who stuck around found out.

I didn't try to moderate anyone's impressions of me on the first day, but in general my hand-holding style went over a lot better with the girls than the boys. Since math is pretty much just as difficult no matter who is teaching it, after a while some of the boys would be failing, and would stop coming to class. Bernie's approach on day one would have served those guys better.

Maybe this, more than any difference in math aptitude, is the reason to have single-sex classrooms.

---

TheBook 19 May 2006 - 22:11 CatherineJohnson



So today, in Study Skills, Christopher had to Sign The Book.

This is one of their punitive things, The Book. Mrs. Roth has one, too. She's proud of it; she talked about The Book for at least 10 minutes on Back to School night, and held it up for all of us to see, then kept pressing both hands down on the cover, her fingers splayed out, to stress her points. When kids do something wrong, they have to Sign The Book.

Christopher had to Sign The Book twice today in Study Skills.

Once because he didn't have his Grade Contract, and once because he didn't have a Number Two Pencil.

sheesh, no pencil? Why didn't have a pencil?

I'm majorly unhappy with the school at the moment, but I do want my child to show up in class equipped with writing implements.

Turns out he did have a pencil; he had a mechanical pencil. The reason he had to Sign The Book was that the teacher couldn't tell if it was a Number Two Pencil.

Why did he need a Number Two Pencil?

Because he had to take a test on study skills.

He doesn't have any study skills, but he has to take a test on study skills, and he has to have a Number Two Pencil that says Number Two Pencil on the side in order to take a test on the study skills he doesn't have.






I was thinking about the Grade Contract.

Ken pointed out that a 'contract' in which only one party promises to do something isn't a contract.

In a contract both parties promise to do something.

Tonight I realized that document is more like a Signed Confession.


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract

---

WhoseFaultIsIt 09 Dec 2005 - 03:21 CatherineJohnson



I need to find the Galen Alessi article:

Parents frequently report that they are intimidated, patronized and made to feel guilty and inadequate by staff at their child's school. After a few negative experiences, these parents feel increasingly helpless, frustrated and defensive.

Not surprisingly, parents behave exactly like other human beings when they are blamed or attacked. Feeling internally threatened and uncomfortable, most respond by trying to explain and justify their position, hoping that they will be understood. A few go on the offense, firing volleys of blame back. Many parents find these experiences exquisitely painful and humiliating. If they withdraw and try to avoid school functions, they may find themselves labeled as "uninvolved parents" - which accounts for their child's learning problems.

Sometimes, emotions get out of control. Feelings of intense anger, bitterness, and betrayal consume parents and school personnel - who are then completely unable to work together in educational planning and decision-making. In these cases, everyone loses - and the child may be the biggest loser if his parents and educators cannot work together effectively.

What is the basis for these negative experiences? Are parents too sensitive? Do they misperceive and misunderstand what happens in their contacts with educators? Or are parents just loyal and over-protective of their children, as many educators claim?

If anyone has a copy, let me know:

Diagnosis Diagnosed: A Systemic Reaction, Professional School Psychology, 3 (2), 145-151




I, for one, am loyal, over-protective, and married to a man who can sling the lingo like nobody's business.

PLUS I am a card-carrying member of this organization:





I was a member of Mothers From Hell 1, too.

I can't sling the lingo, but I have my own specialty, which is complete and total rejection of Other People's Categories.

I once had a horrible situation with Jimmy's special ed program at BOCES. It was a mess. The program was a mess; the children were a mess; the staff was a big, fat, demoralized mess. It was such a mess that other BOCES staff members, in other programs, were telling parents, openly, 'yeah, that program's a mess.'

So I was handling the situation, and we'd pretty quickly reached the Universal Agreement That Mom Is Crazy point, only without my realizing it, when the new head of the program called.

The line they'd been taking with me was that they 'had to be realistic.'

Roughly translated, this meant, 'Your son is a retarded ax murderer and you expect us to teach him stuff?' (I also have a knack for reading subtext.)

So I'd been hearing this We-have-to-be-realistic cr**, and I was in no mood.

The new administrator calls me up, he's in the Reasonable Administrator zone, he let's slip the fact that everyone involved has had a conference about me. Not about the fact that Jimmy is learning nothing in their program, and is deteriorating by the minute — no, nothing about the student. They've held a meeting about me. (I forget how he let this slip, but he did.)

Then he says, "I have to be realistic."

I said, and this stands today as my greatest triumph, "In this house we do not believe in realism."

That set him back.

You could hear the stunned silence on the line.

I said nothing. Just let him hang there.

Finally he said, in a tone of voice filled with exploratory caution and dread (Can an insane mother reach through the phone lines and strangle me? Is that possible?), "Maybe we're not talking about the same thing. Could you fill me in a little?"

I said, "In this house, we reject realism. We do not believe in 'being realistic.'"

Then I stopped talking. Again.

Oh, it was great. Great, great, great.

Eventually we worked our way around to the revelation that 'in this house we do not believe in being realistic' meant 'in this house we believe in you people doing your job,' and the point had been made. Made and double made.

Things never improved with that program, but the Crazy Mom stuff came to a screeching halt, which was something.

Then our school created a terrific program for Jimmy and brought him back to district.


key words: blame the student school psychologist
Pamela Darr Wright summary of Galen Alessi study
Evolving Functions for the School Psychologist
Whose Fault Is It?
educational rights of special need children versus typical children
Engelmann on Galen Alessi study
Pamela Darr Wright posted to ktm
"public school has never been about outputs..."

---

StudySkillsTeacherClimbDown 19 May 2006 - 22:08 CatherineJohnson



So where did we leave things?

• Superintendents bigfooting Singapore Math class

• Mrs. Roth distributing Ds and public shamings

• Study skills teacher calling to berate hapless parent

• Study skills teacher hanging up on hapless parent

• Big Meeting with principal cancelled due to snow

I think that's where we were.


further developments

The Study Skills teacher has come to her senses. (Come to her senses or been told to come to her senses, more likely.)

Christopher came home from school and reported that the Study Skills teacher had said to the class that she 'could tell' which children have to be reminded to do their homework.

Then she named four children, all of them boys. Christopher was one.

Next she said she could tell which children did not have to be reminded to do their homework.

She named a girl (who promptly said, 'Yes, I do have to be reminded to do my homework.')

So then it was back to the Email Factory. Writing emails to the school is becoming a full-time job. I don't like writing emails to the school. I certainly don't like writing emails to the school on an hourly basis. But I'll do it if they keep this up. (My friend M. tells me she knows moms who send hostile emails to the school every day. I believe it.)

Christopher never has to be reminded to do his homework. He always does his homework; he likes to do his homework. He's done his homework without being reminded since he was a tiny boy.

He has to be reminded to do my homework.

He has to be bludgeoned to do my homework.

He is, however, devoted to doing the school's homework.

So I sent an email, the tone and content of which I would characterize as terse, to the Study Skills teacher, copying it to the principal, to Ed, etc., etc.

I closed with the line, "Another item to add to tomorrow’s expanding agenda."

I heard back promptly.

Chris has always been a wonderful student. She was 'half teasing' when she said he has to be reminded to do his homework. She is 'puzzled' and 'surprised' by his recent lack of preparation. She 'meant no harm,' and she is 'concerned.'

Fine.

This isn't what I would call an apology, as in I'm sorry I hung up on you, it was rude and unprofessional, it won't happen again; and it's simply a softer version of the your defective child theme, but fine.

She can be taken off the agenda, because there's already too much stuff on there.

Of course, we are going to be talking about the Grade Contract. We are going to be talking about the punitive, child-blaming nature of the school's educational philosophy. I know I said we'd be concrete and specific, but it turns out we're going to be abstract and theoretical. Then we'll be concrete and specific.

The highly abstract and theoretical point we'll be making from now on is:

If Christopher is getting Ds on essays, it's the school's fault.

If Christopher is getting Ds on math tests, it's the school's fault.

If Christopher is coming to class without his freaking Contract To Improve My Grades, it's the school's fault.


I know J D has debriefed many an ex-teacher who thinks parents are crazy. I know, because I've debriefed them myself.

I know our school administrators are going to attempt to think we're crazy.

But we're both writers, and we're both educators, or have been. Educators treat educators and writers differently. They just do. We've gone into situations like this before, and we've made our point.

One last thing.

We've been at this for 15 years. You have to think longterm, not short-term. (I realize I say this as a person who stinks at strategy.)

We won't Change Things tomorrow.

We don't have to.

We'll get what we need for Christopher, or, at a minimum, we'll be one step down the path toward getting what we need for Christopher. (Pupil personnel is the next stop; then an Advocate, etc.)

Meanwhile the school will know they have two highly educated parents demanding that the school perform systematic formative assessment and teach students to mastery.

This concept is not unknown to American educators, no matter how much edu-blah-blah they've been forced to regurgitate for their Ed.D.'s. We're tapping into thoughts and ideas they already have, and we're talking about techniques some of their teachers are already using. There are teachers at the Irvington Middle School who are using formative assessment. The administrators know this.

I've learned over the years that taking a radical stance 'works.' At least, it works for us. Being 'unreasonable' on purpose shakes things up. It refuses to play the game of I-have-to-be-realistic, when what I-have-to-be-realistic means is I don't have to teach your child.

What we're confronting now is the regular-ed version of I-have-to-be-realistic.

The regular ed version is Your child is responsible for his grades.

or, alternatively, 'I am concerned.' (See email from Study Skills teacher, above.)

When I taught writing, I had the students go through each and every sentence in an essay and answer the question, 'What is the underlying assumption?'

What is unspoken because it goes without saying?

The underlying assumptions, in each and every conversation parents hold with Irvington Middle School personnel, are:

1) My child is responsible for his grades.

2) My child's character is not what it should be. ('Your child will be a better person.')

We reject both assumptions, and we'll say so.

Then we'll keep right on on saying it.


the bell curve

This is rich.

My friend M. just told me that someone actually came into her son's math class, drew them a bell curve on the board, and explained to them that a grade of 'C' is average and normal, so they shouldn't expect to get As. Just a few children can get As. Not everyone.

Christopher says this didn't happen in his class, but that all the teachers tell them 'C' is average. They're supposed to be happy to be average; that's the message.

That explains a lot. Christopher has been constantly telling us that 'C' is average and good. We've been very unhappy with his recent Cs and Ds, and his answer is 'C is average, it's a good grade.' Obviously there's a systematic effort underway at the school to convince the 6th graders that their Cs are OK.

M. said, 'How can they tell these kids C is average and then have them sign a contract promising not to be average?'

Good question.

She also told her son, who just got a C on his math test, 'You're not average.'

Meanwhile I'm learning that the high school won't let kids into various courses if they do have Cs, which means the middle school is handing out Cs left and right, Cs that will track them into lower level courses in high school, without informing the parents that this is the case.

That's another agenda item for the Big Meeting. We want a precise list of all high school courses and tracks, the requirements for being admitted to AP courses and tracks, and the school's plan for making sure Christopher is prepared to enter these courses and tracks and succeed.

"The mission of the Irvington School District is to create a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning."

I'm certain the new superintendent didn't contemplate the possible consequences of creating this mission statement.

Too bad.

That's the mission and we're holding them to it.


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day

---

SmartestTractorsAssessmentForm 19 May 2006 - 21:54 CatherineJohnson







"Attached is a page from our Guide to the Provincial Report Card. It is not required we use it in our classrooms, but I find it helpful in focusing some students. At worst, it is an alternative to the page you have been handed."


thank you





my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract

---

PlugAndChugInSixthGrade 19 May 2006 - 21:57 CatherineJohnson



Quick question.

My thoughts about Christopher's math class are starting to cohere.

Here's what I'm wondering.

The chapter tests are plug and chug: they're 4-pages long, small fonts; at least 25 questions to finish in 45 minutes (with work shown, so no super shortcuts or 'just knowing' the answer allowed).

Is that a good idea?

As things stand, the chapter tests have the glaring problem of offering virtually no space on the test itself for kids with large, immature handwriting to do side calculations—and so far the teacher hasn't told anyone it's OK to use scratch paper. I've sent an email asking if Christopher can use scratch paper; no response as yet.

I don't know if the teacher doesn't allow scratch paper, or if it's just that no child has asked.

Ed and I are asking. ('Asking' as in formally-requesting-slash-demanding.) The kids need scratch paper and plenty of it, especially given the fact that the elementary school did not see fit to teach handwriting. (The BRILLIANT Ms. Duque was ferocious on this point: MAYBE if you'd taught them HANDWRITING IN THE SECOND GRADE, she would fume, THEY COULD LINE UP COLUMNS OF FIGURES IN THE FIFTH.)

Good point.

We're prepared to go to war on the subject of scratch paper if we have to, so I figure scratch paper will soon be part of the test-taking scene in Phase 4 math.

We'll see.

(If we don't get scratch paper we'll demand testing for occupational therapy & we'll bring in Christopher's vision therapy records to prove he has a visual processing disorder & make everyone read them and hold meetings about them—and that's just what I come up with off the top of my head. Have I mentioned that once, back in Los Angeles, when the special ed people were playing hardball about a placement we wanted for Jimmy, we told them, laughingly, that we were thinking if we couldn't get the placement we'd ask for full inclusion? I think I was the one who said it; then I chuckled. Our attorney, who was present, probably chuckled, too. The special ed people smiled wanly. I'd read about people smiling wanly in novels, but until that moment I'd never seen a person actually do it. We got the placement.)

Back to Christopher's math class. Apart from the mechanics of having 11 year olds with terrible handwriting take a plug and chug test, the course itself has problems, namely little or no formative assessment and no practicing to mastery ever.

But suppose all of those things were in place. Suppose systematic formative assessment were happening every week or every day, all students were practicing all skills to mastery, and the kids had all the scratch paper they needed to do a plug and chug math test in their lopsided, too-big handwriting.

Would a plug-and-chug test be a good idea?

Does plug-and-chug testing tell you the students not only have mastery, but have mastery to the point they can get through a 4-page test without folding?

Is that important as you head towards algebra? (I'm not asking whether mastery is essential; it is. What I'm asking about, I think, is stamina.....or is it?)

I have no idea.


observation from Tracy W

Tracy just left a comment that made me realize my question isn't clear.

At the moment, I'm not concerned about the heavily procedural nature of the course. There's probably too much teaching of 'math tricks' like cross-multiplication without reference to the general rules that make shortcuts possible, which of course means you're going to be giving the kids plug and chug tests, since plug and chug is mostly what you're teaching.

But at the moment I'm wondering only about the question of giving a 'killer test' to 11 year olds. (I don't use the word 'killer' to prejudice the answer, believe it or not.)

I assume that the reason the teacher does give killer tests is that she's whipping through a vast amount of material in a very short space of time, so there's a huge amount of material to cover in each chapter test.

However, if that's the only reason she's giving massively long tests (massively long for kids this age who are new to the material) she could just as well test all of the material through frequent administration of shorter quizzes and tests.

I'm wondering if there's a specific gain from giving a long, hard test in pre-algebra. It strikes me that there may be, but on the other hand I can't say what it would be.

---

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....

---

MetacognitiveTeaching 15 Dec 2005 - 17:05 CarolynJohnston


I had an interesting email this evening from a Jenny D (I don't know whether it was Jenny D the blogger):

One of the reasons that reform math gets a bad rap is that many programs stop at the hard part.

Let me try a different way. Traditional math is good because it has one way to solve a problem. But higher math never has one way to solve a problem. So what teachers need is a better framework for teaching math that allows for different ways to solve problems.

But that means the teaching is harder than simply marking a problem incorrect and showing the one way to solve. It means thinking more deeply about student problem solving skills and actually diagnosing the slipup in computation or set up of a complex problem.

Deborah Ball did an NPR program about this last year. Here's the website. On the left is a math problem and three students' answers who got it wrong. But each got it wrong for a different reason. The understanding of what went wrong in each case and the subsequent student understanding is the best of reform math. Sadly, it rarely happens in classrooms.

One of the reasons traditional math is so beloved is because it's easy to teach.

Love your site. Good luck.

This brings to mind some discussions that Catherine and I have had regarding 'Metacognitive teaching', which is a fancy term for anticipating the misconceptions and errors your students will make.

Jenny D is suggesting that that's a feature of 'reform' math, whereas 'traditional' math teach emphasizes learning and applying correct procedure.

I would suggest instead that it's a feature of good teaching in every approach. As Liping Ma has shown, underprepared teachers make many of the same errors themselves that the kids make.

But I agree that one reason traditional math is beloved is because it's easy to teach. And I think that's a good thing, although it doesn't make up for a weak teacher.

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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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IfTheStudentHasntLearned 23 Dec 2005 - 22:16 CatherineJohnson









revision

From Catherine:

Our new pretend-shirt specifically says "If the student hasn't learned, the school hasn't taught," not 'the teacher hasn't taught'.

No more thoughtless (and unintended) teacher-bashing.

Seriously. I'm the last person to want to make teachers feel blamed and bashed, seeing as how half my relatives have been or are currently teachers. I'm sure I'll be one again at some point, too.

The problem is that, when you talk about schools, it's the teachers who are visible. They're in the trenches, so they get the blame. (I realize I'm not telling teachers anything they don't know.) I know better than that, but I've been sounding like I don't.

Time for a course correction.

From Carolyn:

Hey, my entire family on my mother's side were also teachers, every man and woman Jack of them. I've been a teacher too; so has Catherine.

My observation is that policy flows downhill in a school, and the buck stops with the teachers. They get the responsibility, but not the authority; policy changes really have to start with upper management.

We're here to put the pressure on upper management, and support the teachers in doing what they know how to do.

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ImSorry 19 Dec 2005 - 19:42 CatherineJohnson



I'm realizing belatedly that the 'Students Haven't Learned' t-shirt is insulting to teachers. That is radically not what I had in mind.

I'm sorry!

The slogan on the t-shirt actually comes from a Siegried Engelmann program where the teachers themselves wore shirts that said, "If the learner hasn't learned, the teacher hasn't taught." The teachers wore the t-shirts because they were part of a Direct Instruction program that gave them the means and the administrative backing to make this promise and keep it. They were making a professional statement.

I took the slogan out of context, and I ought to know better seeing as how my job is writing.

Writing means knowing what the words you use mean to other people, not just to you.

What the shirt should say is "If the student hasn't learned, the school hasn't taught."

That, I do believe, although I'm afraid there may be caveats here, too. How much can a middle school do to teach kids who've lost ground in K-6 and now have the hormones, emotions, and preoccupations of pre-teens?

I don't know.

In any case, I'm sorry for posting an image that made people feel slammed when they saw it. That wasn't the effect I intended, but I know it's the effect I had.


what can one teacher do?

All of this leads me to a question I think about fairly often.

How much can one teacher do?

Formative assessment is, I think, a fantastically powerful tool. I'm convinced that a policy of systematic formative assessment would allow a school to make a fair amount of headway even with middle-school and older students who have, as Rudbeckia put it, 'baggage' when they get to a teacher's class.

But it's the principal's job, not the teacher's, to put in place a policy of systematic formative assessment. The principal is the educational leader, and the ultimate authority inside the school. It's the principal who can supply the institutional resources and support to embed formative assessment inside all courses and classes.

My question is, if the school doesn't adopt a policy of formative assessment, can one teacher do it alone?

It's obvious that one teacher, on his or her own, can do formative assessment to some extent. There are at least two teachers using formative assessment at the middle school. And ktm Contributors have left comments describing math teachers they had in high school who used formative assessment.

But how far can one teacher take this without institutional support?

Another thought experiment: could Christopher's math teacher create her own system of formative assessment, as Carol Gambill did?

Again, I'm not sure.

She's required to get through a huge amount of content—way too much for Christopher and at least half the class or possibly more.

Given how material she has to cover (and I do mean 'cover,' not 'teach'), could she justify taking time in class each day for formative assessment?

I'm thinking this might be time well spent, in spite of the coverage requirement.

But I don't know.

I've had one teacher describe her frustration with the Irvington administration for not having an answer to the question: "Am I teaching for mastery, or teaching for coverage?"

She had asked this question more than once. No one had given her an answer.

That is an administrative failure, not a teacher failure.

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OnwardAndUpwardWithMsKozak 23 May 2006 - 22:25 CatherineJohnson



Oh boy, Christopher is a happy guy.

He's in heaven.

He moved to Ms. Kozak's class today, and came home filled with Ms. Kozak stories.

"Ms. Kozak is giving us spelling," he said. "She gives a weekly spelling list. We have to take a spelling test on Friday."

"Ms Kozak taught us all the verbs, and she made us take notes. She told us about active verbs."

"Ms. Kozak taught us what constructive criticism is. Then she made everybody trade their drafts with their 5 o'clock peer partners."

Apparently Ms. Kozak has the kids fill out a clock with different peer partners, so they can switch around amongst the different kids when they exchange their work. Today they were looking at the subparagraph (something like that), the lead, and the 'hook.'

"They were really good," Christopher said, speaking of the other kids' works in progress. "I read them. They were really good."

"She gives us homework, too," he said, sounding like homework from English class was a gift.

So that's the silver lining, one of them anyway. Christopher now believes that a teacher who teaches isn't someone you take for granted.

"I did a good impression," he said, too. "I answered all the questions. I did a good impression."

That frosts me.

Here is a child so eager to please, so wanting to do well in school, that he's thinking how to make a good impression even though he's still too young to know that people 'make a good impression,' not 'do a good impression.'

Mrs. Roth has a criminal heart.



meanwhile, back at the ranch

The other kids are still ragging Christopher about Mrs. Roth.

"You made Mrs. Roth feel bad." etc. The girl who's Mrs. Roth's perceived favorite gave him the finger. They don't make teachers' pets like they used to.

Another child reported that Mrs. Roth had said to the children, in class today, that the grade she gave Christopher 'was fair.'

Needless to say, that prompted an email to the principal.

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TeachingMathToTeachers 19 May 2006 - 21:52 CatherineJohnson



Susan J left a link to Racial Equity Requires Teaching Elementary School Teachers More Mathematics (pdf file) by Patricia Clark Kenschaft.

I'm just beginning it, but so far it's right up my alley:

Seventy-five black people with at least one degree in mathematics responded to a variety of questions, including, “What can be done to bring more blacks into mathematics?”

[snip]

[the most common answer by far was] “Teach mathematics better to all American children. The way it is now, if children don’t learn mathematics at home, they don’t learn it at all, so any ethnic group that is underrepresented in mathematics will remain so until children are taught mathematics better in elementary school.”

[snip]

Like most Americans, I found it difficult to believe how poorly prepared mathematically they are.mathematically by our system. They need to be taught. I have found them eager and quick to learn—and appallingly ignorant of the most basic mathematics.

“Teach us math! Teach us math! Teach us math!” chanted dozens of elementary school teachers during one after-school workshop. There was an amazed silence while we all absorbed what had just happened. Then one of them said, “If you taught us math the way you did just now, we could teach it to the children.” They all nodded emphatically. This incident followed my statement that those of us who thrive mathematically have had some good mathematical experience early, typically at home. Someone had asked for an example out of my own childhood, and I had explained how my father had described the meaning of pi to me several months before I started kindergarten. Their response was the chanting, “Teach us math!”

The rest of the article is an account of Kenschaft's math classes for elementary school teachers.

I believe we need far less ed school and far more on-the-job training.

For me, that would include classes like Kenschaft's.

It's not reasonable to expect thousands of math majors to pour into K-8 education.

It is reasonable to expect that the dedicated and able people who've gone into K-8 education can continue to learn elementary school mathematics on the job, as Chinese teachers do. Chinese teachers typically have the equivalent of a high school education here, and their knowledge of math is not astonishing when they begin work. I imagine they start at a higher level than our teachers do—I'd have to check to see whether Liping Ma addresses this—but the fact is, Chinese teachers gain profound knowledge of elementary mathematics by studying the high-quality textbooks they must teach and meeting with colleagues to discuss those books.

If we think all kids can learn math, why don't we think all teachers can learn math?

The fact that they didn't learn math in their own schools & colleges is no reason to think they can't possibly learn math now, when they're employed and motivated to do their jobs well.

Ed ran summer institutes for high school history teachers. They were starved for real history and real colleagues, and they were smart.

That's the kind of professional development I'd like to see.

Let's have fewer Workshops on Differentiated Instruction, and more Summer Institutes in math, reading, writing, and history.


kids teaching kids

It has been my observation that the reason that scores are higher in white districts is that some parents teach their children mathematics at home, and these children teach many of the others. It has appeared to me that the teachers are no better prepared in the high-scoring districts.

I wouldn't be surprised to learn that elementary school teachers in high-scoring districts are no better prepared in mathematics than teachers in low-scoring districts—although I guess I'd been assuming that they were.

What did take me by surprise was Kenschaft's blunt statement that we parents are the entire reason high-scoring schools are high-scoring.

And I was gobsmacked by her assertion that kids like ours, who are being taught math at home, are in turn teaching math to other kids at school.

That possibility simply hadn't crossed my mind.

Which is funny, because Christopher taught his fourth grade partner-in-flunking how to do two-digit times two-digit multiplication.

Christopher. A kid who a couple of months before had been flunking math.

His friend hadn't gotten any remedial teaching at home, so Christopher taught him multiple-digit multiplication.

Our assistant superintendent told me that another kid in his school taught him algebra. A kid! The teacher was impossible, he said (and later on took credit for the Asst. Superintendent's progress.)

Of course, I was suitably scandalized by this story.

But it didn't occur to me to wonder how it was that the friend happened to know algebra.






You hear it said, often, that schools like Irvington's have high scores because their parents have high SES.

It's time to operationalize that statement.

How exactly does a high SES translate to my kid knows how to divide fractions?

Forget IQ differences, real or not; no one has an IQ so high he just naturally knows how to divide fractions. People have to learn how to divide fractions, which means someone has to teach them.

If Kenschaft is right, those people are the math brain parents and their kids.



it's always worse than you think

[The] principal invited me to consider that school “my school”. He and the teachers really wanted to help the students. Its students had a median achievement in mathematics of about the 25th percentile on the “Iowas”, one of the lowest levels in Newark. I am now convinced that its rank was due to the fact that the principal did not pressure the teachers to cheat in any way on standardized tests. When I told him this years later, his eyes widened. He was president of the principals’ union. “What? You are saying…” I nodded. Since then I have read numerous reports of systemic cheating on standardized tests and other forms of deception by school administrators...

A friend of mine was, I think, president of the PTSA in an affluent district when it was discovered that a teacher was cheating on the tests. She was walking around the room telling the kids the answers, IIRC. The principal put the teacher on leave, and the school blew up. The other teachers were bitterly upset; the parents went to war (many parents supported the teacher and attacked the parents who had complained as whistleblowers); many, many students left.

I lost contact with that friend not long after, so I have no idea whether the school even survived.

This was not a school in Newark.



communication skills for the 21st century

During my first class teaching elementary school children, a fifth grader raised his hand and asked, “What is that word you keep using instead of take away?” Enter “minus”—for fifth graders!

fast change

The best first-grade teacher told me she never bothered to teach subtraction during the first half of the year because the children couldn’t learn everything at once. I started visiting the school in October, and it seemed to me natural to teach addition and subtraction together. She told me she would not reinforce my teaching of subtraction between my weekly visits, and I said that was no problem.

One of the games I played with the children was holding five unifix blocks in front of me, putting them behind my back, and bringing forward three. “How many are behind my back?” I asked. The children could answer correctly. Then I told them that one way of writing this was “5 – 3 = 2”.

“Oh, no!” said the teacher.

“Why not?” I asked.

“Because subtraction means “take away” and you took away two blocks. So it should be written ‘5 – 2 = 3.’” I explained that subtraction could mean “take away”, but it could also mean “missing addend”. It seemed to me that since the children could see three blocks, “5 – 3 = 2” was preferable, but “5 – 2 = 3” is not wrong. The next week we explored the “difference” meaning of subtraction and the “motion” meaning. (I walk five steps toward the window and three steps away. How many steps am I from where I began?)

She was startled when half the children passed the subtraction part of the November standardized test—without any reinforcement from her. She had never had a child pass it before. The crucial role of mathematical knowledge on the part of the teacher was becoming obvious to me.

white people can't jump (update 6-26-06: what does this heading mean?)

My first time in a fifth grade in one of New Jersey’s most affluent districts (white, of course), I asked where one-third was on the number line. After a moment of quiet, the teacher called out, “Near three, isn’t it?” The children, however, soon figured out the correct answer; they came from homes where such things were discussed. Flitting back and forth from the richest to the poorest districts in the state convinced me that the mathematical knowledge of the teachers was pathetic in both. It appears that the higher scores in the affluent districts are not due to superior teaching in school but to the supplementary informal “home schooling” of children.

The only thing wrong with this observation is: it's not so informal.

I'm working my tushie off here.

(more t/k)


original thread about teacher preparation

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CoffeeAtCaffeSole 03 Jan 2006 - 00:42 CarolynJohnston


One thing about being frustrated with your job; any day you have off is almost automatically a good day, and this was a good day.

This morning I had coffee with Greta Frohbieter, a KTM visitor who, until recently, taught math at one of our district's charter schools; we met at a local coffee shop not far from my son's middle school (if you look at the second picture on the coffee shop's website, imagine us sitting in that room -- but the paintings in that photo are long gone). Greta is working on a Master's (and perhaps a Ph.D.) in curricular studies at CU in the school of education; when she met me, she had a copy of Parker and Baldridge in hand in case I hadn't seen it, and another book I actually hadn't seen (The Man Who Counted, by Malba Tahan).

What a good time! It's rare that I get the chance to talk in the flesh with someone who is as interested in this stuff as I am! We yakked nonstop for perhaps an hour and a half.

Greta's undergraduate degree is in civil engineering, and she has worked in the aerospace industry, so she is someone who has really used math. Although we never talked about this explicitly, I imagine she left her aerospace job because she loved teaching math and wanted to go back into it; now she is drawn to teaching teachers about mathematics (an idea that appeals to me as well; but unlike me, Greta has the courage of her convictions and is actually studying to do this). In her experience, teachers of elementary school math are eager to learn more mathematics so they can teach kids more effectively; not resistant, as one might fear. Greta was excited by the TeachingMathToTeachers post -- discussing the idea that what's required in order to have racial equity in performance on mathematics standards (which is an important issue in schools of education these days) is to have elementary school teachers who know more math.

Greta and I agreed that mathematical weakness in kids -- whether it's procedural weakness (which she has seen in many students over the years) or conceptual weakness -- follows from a lack of access to adults who can teach math. It's just as Catherine said in the post I mentioned above -- if we are to assume that any child can learn math, then surely any teacher should also be able to learn math. Surely a good way to enable kids to learn math is to empower their teachers with knowledge of the mathematics they need to teach.

Greta also gave me some advice on pre-algebar and beginning algebra texts, which I've been sorely wanting. Ben is doing pre-algebra this year -- next year, he'll need a pre-algebra/beginning algebra text. Most of the books that Greta recommended to me are from the 70s; from a time before math texts were full of colorful graphic distractors. She had good things to say about the Smith, Brown, and Dolciani algebra text, and about Paul Foerster's Algebra 1 text (which also received a high rating at Mathematically Correct). She recommended a Holt pre-algebra textbook from the 1970s ("it had a space shuttle on the cover," she said, "you know the one?" ... I didn't.. does anyone else?).

You know, I just went looking for a place where I could buy the Dolciani text -- is that as hard a book to find as it appears to be?

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SusanOnPartsAndWholes 11 Jan 2006 - 16:04 CatherineJohnson



This way of looking at the edu-world has been terrifically helpful to me:

Part of the problem is that, like New Math and Whole Language, there is a movement afoot to push what I consider middle school skills down into grade school, all with the assumption that grade school skills will just be learned by osmosis (or shoved onto the middle school teachers...again.) These are your two camps.

In the beginning this new way of teaching writing [beginning in Kindergarten] looks very impressive as little persuasive essays come home and state tests appear to improve. Like math, we didn't learn it that way and so what do we know? I believe this is what you would label teaching Whole to Parts.

The traditional way of learning writing (or math, for that matter) has always been Parts to Whole, starting with building blocks for younger children (handwriting, grammar, sentence structure, punctuation) and then moving to more complicated techniques requiring better critical thinking skills (notetaking, outlining, etc.) that actually match the child's growing opinions and ideas. This strikes me as common sense, but what do I know?

Whether this new way is really better in the long run is still unsure, from everything I've read, yet one can't help notice that something is wrong when college professors complain loudly about students' bad writing skills, and then even request a grammar section on the SATs.

key words: parts to whole whole to parts two camps

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StupidInAmerica 12 Jan 2006 - 17:55 CatherineJohnson



Ken left a link to John Stossel's special 'Stupid in America' tomorrow night at 10. (January 13, 2006)

Jan. 9, 2006 — American students fizzle in international comparisons, placing 18th in reading, 22nd in science and 28th in math - behind countries like Poland, Australia and Korea. But why? Are American kids less intelligent? John Stossel looks at the ways the U.S. public education system cheats students out of a quality education in "Stupid in America: How We Cheat Our Kids," airing this Friday at 10 p.m.

"We're not stupid. & But we could do better," one high school student tells Stossel. Another says, "I think it has to be something with the school, 'cause I don't think we're stupider."

That's the question Stossel examines in his special report: What is it that's going wrong in public schools?

There are many factors that contribute to failure in school. A major factor, Stossel finds, is the government's monopoly over the school system. Parents don't get to choose where to send their children. In other countries, choice brings competition, and competition improves performance.

Stossel questions government officials, union leaders, parents and students and learns some surprising things about what's happening in U.S. schools. He also examines how the educational system can be improved upon and reports on innovative programs across the country.

"Stupid In America: How We Cheat Our Kids" with John Stossel airs Jan. 13, at 10 p.m.

I'm setting up the TIVO.

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HighSchoolAssignment 14 Jan 2006 - 20:35 CatherineJohnson



I've been thinking about entraining attention.

Curriculum designers who are concerned with capturing & holding student attention often use speed and choral response. That's why KIPP & DI have scripted call-and-response lessons. The pace and the talking/chanting/rapping/rhyming (depending on the program) capture attention and hold it.

That's why KUMON uses timed worksheets. Speed captures attention.

How to Double Your Child's Grades in School teaches an active question-asking, text-highlighting, book-within-the-book-finding mode of reading to achieve the same goal: capture the child's attention, as opposed to relying on the child to force himself to focus.

Here's another tactic:

Ohio High School Porn Homework Canceled
Jan 13 4:03 PM US/Eastern

BROOKLYN, Ohio

A high school research assignment on Internet pornography was canceled after parents in this Cleveland suburb complained.

Superintendent Jeff Lampert said that although the teacher's apparent goal — to discuss the harmful effects of pornography — was well- intentioned, he agreed with parents that the assignment was inappropriate for 14- and 15-year-old freshmen at Brooklyn High.

The assignment asked students to research pornography on the Internet and list eight facts about pornography. Students also were asked to write their personal views of pornography and any experience they had with it.

Lampert said he doubted the teacher would face any punishment.

They were probably planning to spiral the assignment for the next couple of years.







off topic, but worth it

When you Google 'pay attention' you get this:

Also this and this.

pay attention!




update: a dog paying attention





Obviously this dog is not of middle-school age.

In dog years, I mean.

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StupidInAmericaPart1 16 Jan 2006 - 18:39 CatherineJohnson


Of course I missed the show, but the message boards are a hoot.

This one is from sharpeteacher:

Stupid in America does not start in the schools. It is the stupid adults that produce these lazy, under-achievers. When the parent see no reason to act like civilized people why would you expect the children to. The problem I have in my classroom is parents. Parents support their disrespectful children. They defend them when they get suspended or act like fools. [ed.: true! case in point!] (Parents like the one on tv that said her child was in high school and could not read.) It is the parents responsiblity more than the teacher to be sure the child is progressing. Maybe if parents suck it up and quit being selfish, stupid people then there children would care and learn about the real world and do well in school. You are comparing these countries and states that do not have the same rules or even the same tests. If you take a test and I take another test we can not compare our scores because we did not take the same test. Parents do not care enough to change their childs school. What we need is for someone to stand up and broadcast a show about stupid parents in America!!!!!

Here's a school administrator:

I agree as an administrator we have more stupid parents that bad teachers. It only takes discipline.

Another satisfied customer:

It's funny, that only teachers are responding to this thread. Let me tell you that I have read to my 2 children since day one, have helped with homework every night, volunteered uncountable hours in the public school system and am probably over involved in my kids lives. But just recently I have encountered this problem. My 10th grader just dropped 2 grades in Geometry in 4 weeks and I did not know about it until the week before Christmas break. After a conversation with the teacher she tried to tell me that I "should have known" that my child was in trouble. She said that she had done everything she was supposed to do to inform me. She had sent a letter home at the beginning of the year, stating that she would eventually send a password home to log on to an account to check grades and that my son, "if he were doing his job" was keeping a running tab of grades. I never received either. She obviously does not have children, thinking that they are going to come to you, saying, "mom, I'm flunking Math". Give me a break! The teacher gets paid for making sure my child learns [ed.: a common misconception! no! she doesn't get paid to make sure your child learns! she gets paid to spiral!] and obviously, my child was not learning, and his teacher felt that I did not need a note concerning this fact. Hey, as long as she can pick up that paycheck for putting in those hours, what makes the difference whether my child learns or not. Let me also tell you that I am not an absentee parent. I have volunteered in the public school system for 13 years, and am always available. This "teacher" also went on to say that it was all three of our responsibilitys' to make sure that my son was progressing. [ed.: hey! I got the same line from the Study Skills teacher who hung up on me!] I can't fix what I do not know about. She also said that she had 132 students and couldn't keep track of everything. Well, then maybe she should only get part of her paycheck, if she is only doing part of her job. Let me also add, that in the week since we have found out about the grade drop, we have gotten him two tutors, (pretty bad when a child has to go to another teacher for tutoring), have helped him more at home and he has raised his GPA by 5% in one week! [ed: I Should Have Homeschooled, Part 100-something] Teachers are always saying that the student needs to take responsibility....just once I would like to see a teacher step up and take responsibilty for what they have done...or in this case what they haven't. Public Education in America really stinks!

why do new teachers quit within 5 years?

I spent three years as a high school teacher, getting a job at a public school straight out of college. Three other rookies started with me. One quit after one year; the second year another quit; I quit the third year; the other rookie is now the high school’s activities director, eyeing a vice principal position.

Most new teachers leave the profession within five years. Teachers like to point at this statistic as proof of how hard their job is. It isn’t. It’s proof of the job’s meaninglessness. It takes a month or so at the job to realize that it doesn’t matter how hard you work, or how well you do. Your students will appreciate it, a little, but they are gone when the bell rings, and at the end of the year, they’re out of your life. The administration will take no notice. Your pay isn’t attached to it in any way.

Beyond that, your class of 25 becomes a class of 40 with ten special ed students. You’ve got a future felon you’d like to throw out of your class but can’t, because no one cares how well you teach, but cares a lot if you deem one kid a bad apple. For someone young, who has visions of a rewarding career, it quickly becomes apparent that public school teaching is an empty profession.

Career public school teachers come in two flavors, both shown in the John Stossel special.

a) the lazy bum who likes the free ride. That teacher who had his geography students playing Monopoly isn’t the exception, he’s the rule. I guarantee you that the teachers on this message board and in your lives who speak of working 60 hours a week are LYING! At my school, all the teachers arrived five minutes before the first bell and left five minutes afterward, and didn’t take any work home with them. They ran personal errands during their prep periods, and milked the image of the overwork teacher to anyone who wasn’t in the club.

b) The activist. The Union President who made such a fool of herself on the show is the other model. This teacher is also prevalent in the schools. She doesn’t care that kids learn math, science, English, or history. She got in this business to become a brainwasher, and uses her classroom as her personal political forum.

I’ve left the profession, and now work for a corporation in a cubicle. And despite the fact that my job is much harder now, at least it feels like I am accomplishing something!

uh-oh

The sad state of affairs on this matter is that the majority of us have personally experienced a really bad teacher on more than one occasion. That's too many bad teachers!

Me? I personally spent from the beginning of my junior year to the month of February teaching myself AB Calulus. Why you ask? Because my teacher was too busy planning the annual math club ski trip during my class period. I also, by my choice, went to a local college that summer to take AB Calculus to be sure I was ready for BC Calculus my Senior year.

I then spent my daughter's 6th grade year giving her the math lesson she should have been taught at school everyday by the teacher who couldn't stay off her cell phone long enough to teach. Her idea of teaching was handing out worksheets, reams of them, for the children to do without any lesson. The proverbial straw was the worksheet asking to calculate areas and perimeters of squares, triangles, parellograms, circles, etc. The worksheet had a diagram with measurements and an A = under each one. No formulas. I asked my daughter where her notes were from class on this. She said Mrs. Teacher didn't teach that day. They did worksheets with 5 digit numbers multiplied by 5 digit numbers...busy work.

helicopter parents of the world, unite



update

eduwonk likes this book, from Brookings:

Apparently the Wall Street Journal called it, "The education book of the year . . . an icon-smashing book on school reform."


There's a terrifically interesting-sounding (awkward modifier alert) list of books under "People who bought this book also bought":

• Tinkering toward Utopia: A Century of Public School Reform David B. Tyack, With Larry Cuban
• Managers of Virtue: Public School Leadership in America, 1820-1980 David B. Tyack, Elisabeth Hansot
• What Works in Schools: Translating Research into Action Robert J. Marzano
• American Public School Law Kern Alexander, M. David Alexander

the politics of vouchers (interview with Terry Moe)

---

ImCollectingStoriesAboutGaps 22 Jan 2006 - 16:02 CatherineJohnson



Engelmann's Student-Program Alignment and Teaching to Mastery is still rumbling through my Hebbian networks, toppling every domino in its path.

It's kind of fun. I'm experiencing my very own Paradigm Shift.

I don't know where I'll be when things calm down, but one thing I do know: I'm never going to see 'gaps' the same way.



killer Gaps

We're constantly hearing about Gaps, of course. Achievement gaps, learning gaps, teacher gaps — everywhere you turn, there's another Gap.

I've read so much about Gaps I never really stopped to think what a gap actually is, or might be.

I guess I've thought of gaps as static and predictable. All the gaps seem to grow wider over time, until they look like an ice cream cone lying on its side in a PowerPoint slide.

That was then.

Suddenly, gaps seem dynamic, dark, and entirely unpredictable — more properly a phenomenon belonging to Chaos Theory (does anyone talk about Chaos Theory any more?), not Excel charts.



Anne on diagnosing Gaps

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 teachers 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.

Susan J on diagnosing Gaps

I think it is very, very hard because it is so personal and unique to the student.

I'm 65 and a computational scientist and I still remember odd and embarrassing gaps that had huge negative effects even in graduate school. Even when you get to the point where you are in charge of your own learning, you can miss these things.

For the mathematicians on the site, I'll admit that it took me more time than it should have to understand that when one solves a differential equation, one is solving for an unknown function rather than a variable.

I still remember puzzling over a textbook diagram of a simple mercury barometer when I was a freshman in college. The difficulty (for me) was that the diagram was simplified and didn't show the support stand for the glass tube with its closed end up and its bottom end part-way submerged in a dish of mercury. So I could never figure out why the tube simply didn't fall over!

here's what I'm wondering

Although I believe that the gap between our kids and kids in high achieving countries starts in first grade or thereabouts, I do trust research showing that achievement slows in middle school. (This finding may not be confirmed, but at the moment I take it as probably true.)

Here's what I wonder.

When you don't teach to mastery — when you teach a spiraling curriculum — kids end up with gaps.

That much we know.

But kids probably don't all end up with the same gaps, except for the Universal American Fraction-Decimal-And-Percent gap.

So think what a middle- or high-school math teacher is up against. Ninety or more kids, each with different gaps affecting different areas of the new content they're supposed to be learning and/or spiraling.

It's Gap Anarchy.

At the moment, it seems logical that the further you go, and the more gaps you accumulate, the slower your learning curve is going to be, until finally you hit the wall.

I don't know whether that's true, but it seems logical.

More than logical.

It seems inevitable.



what do we know about learning gaps & how they work?

Here's Engelmann:

When students are not taught to mastery, they often mislearn the skills and concepts the teacher attempts to teach. For instance, they may learn to guess at words in sentences. Reteaching them requires many more trials and much more work than that required to teach them to mastery initially. Initial teaching may require only 10 or fewer trials on some skills. Reteaching the same skill after students have mislearned it and have practiced inappropriate strategies for years may require several hundred trials.

Here he's talking about the case of a student having learned the wrong thing, rather than merely having failed to learn the right thing. The news is bad.

What else do we know about gaps?

Or about reteaching?

And what have your own experiences been?

I'd love to hear.


key worsd: 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 and Richard Nixon
Terminator





-- CatherineJohnson - 17 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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DirectInstructionRant 31 Jan 2006 - 21:49 CarolynJohnston


OK, I know I'm the quiet one, but I'm going to have to speak up.

Consider me not sold on Direct Instruction. Teaching to Mastery for all, certainly. Direct Instruction for all, not in any world I'm king of.

I've read some of Zig Engelmann's articles. He's arrogant. He comes off as the sort of person who not only knows he's right in this one matter, but who has never admitted that he's wrong about anything, ever. I just can't trust someone who never dithers.

There's a heck of a lot to be said for using behavioral analysis methods (which is what Zig's methods are) in a typical classroom. Constantly taking data on how well children are learning -- formative assessment in the vernacular -- is a great idea; this aligns very well with most people's common sense, that a bunch of quizzes are better in the classroom than giving one big honking test. Frequent assessment can be used far more effectively than it typically is.

And I don't mind the idea of using scripted instruction; Carol Gambill, whose methods I will emulate if I ever end up in the classroom again, uses scripted instruction. The difference is that the scripts have been developed by Carol herself, in the process of becoming the great instructor that she is.

I do dislike the idea of scripts being handed down to the mass of uninformed teachers, from the brow of Engelmann. He has some good ideas, I know, and I'd like to see them disseminated to teachers (along with Carol Gambill's scripts) as part of the process of their developing a good method of teaching from a good curriculum.

But I really feel that the secret to good teaching is to have teachers that know math; that are learning math all the time, and who are learning about the ways that kids learn math, and the misconceptions that they have. Not only that -- it's personal growth, in the form of knowledge about math, and development of knowledge about how kids learn math, that keeps a teacher in the game; not perfect delivery. Not perfect pedagogy.

The core notion behind DI is applied behavioral analysis; using trial and error, over time, to unmuddy the communication channel for everyone, so that a concept is learned with maximal efficiency by everyone. This method has been used, very effectively, to teach the ultimate at-risk kids, autistic kids. Even among autistic kids, however, learners vary in what they take away from a lesson. To illustrate behavioral analysis/direct instruction, here's a snippet from a page on DI:

Faultless Communication: Concept Definition

Imagine that one could design instruction in such a way that it would communicate to the learner one and only one interpretation. There would be no misunderstandings, no confusion and no misdirection. Concepts would be learned perfectly. If this were true, then if one wanted to teach the concept "vudged," one would be sure that the instruction was going to allow the learner to identify cases where "vudged" was appropriate and cases where "vudged" was not. Vudged? What is vudged? Let's try to learn it.

First it will be my turn to communicate the concept of "vudged." I'll show you some examples and some non-examples. Then there is a little test to see if you've learned the concept. Relax. Remember I'm going to communicate the concept so that there is no possibility of misinterpretation.

Did you learn vudged? If you labeled the first, third and fourth items in the second row as vudged, then you got it. If we were to state "vudged" as a rule, it might be something like "not aligned horizontally," or more simply "tilted." Did you come up with something like that as your worked your way through the examples and non-examples?

The instruction presented you with examples of vudged and non-examples of vudged, isolated the feature that made things vudged or not vudged, and then tested to see if the instruction generalized to other stimuli. Logically, the instruction had to succeed. When instruction conveys the concept so accurately, Engelmann calls it logically faultless.

Such faultless communication leads learners precisely to a single interpretation of the instruction, and ideally that same instructional communication would work for all learners. When instruction is faultless, it provides us a way of studying the learner. We can present faultless instruction to a number of learners and observe the effect of the instruction on their learning. Because the instruction is the same for all learners, we can rule out instructional factors accounting for observed differences in learning. Thus, each learner's response to the instruction provides precise information about the learner.

Did you get vudged? Probably you did, but I didn't. Really, I didn't.

That's the problem; there's no faultless way to deliver a lesson to a whole bunch of kids at once, or even to one kid at a time. An applied behavioral analyst, working flat out, is constantly doing course correction. That's why autistic kids get taught using behavioral analysis 1-on-1; the whole experience is a process of formative assessment, with the teacher watching how that one child is responding to the lesson, and changing tactics as necessary.

Streamlining your lessons over time so you don't throw curveballs like sticking a fly at the end of your second example of the concept of 'vudging' -- great idea.

Utilizing Zig Engelmann's already well-prepared lessons as you develop your own -- great idea (although if they're anything like this vudging example, forget it).

But please, let's take Zig Engelmann down off his KTM throne. I'm extremely leery of the idea that there is one right pedagogy that will solve all our problems. There's no royal road to geometry, and what I really believe teachers need isn't more training in more pedagogy; it's more domain knowledge, more respect, curricula to work with that aren't ridiculous, and the opportunity to grow.

What kids need is the expectation of mastery, lots of practice, curricula that aren't just crazy, and special help when they need it -- teachers who know three different ways of explaining something, so any given kid can find one explanation that he can understand.

-- CarolynJohnston - 28 Jan 2006

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ProgressReport2 08 Oct 2006 - 22:16 CatherineJohnson



I've just written an email to Christopher's math teacher filling her in on what's going well and what we're still working on around here. Thought I'd post it as an fyi.

(I figure if schools can buy Comment Banks, we parents should have Email-to-the-Teacher Banks....)

This email is longer than it should be, so if you don't feel like wading through the whole thing, the points are:

• Christopher got 9 out of 10 questions correct on last night's homework (that was amazing; just great)

• this is the second time he's been able to do a homework assignment independently & correctly since he began seeing Ms. Kahl for extra help (GREAT)

• we're very happy she assigned them a Review Problem set covering material in previous chapters for homework this weekend

• saga of the latest quiz debacle (C. did study for the test, didn't study the review sheet, did study the book, didn't generalize book problems to the harder problems on the review sheet, etc., etc.)

• segue to: latest quiz debacle illustrates frontal lobe/organizational/study skills problems we've discussed, i.e.:
  
  • forgets things easily & thus forgot he had a review sheet
  
  • has trouble reading directions on tests & thus hosed the re-take, too

• segue to: we're making some progress on 'knows what he doesn't know', & would like guidance counselor to reinforce the point

• segue to: at this stage content matters most to us, and we're seeing important gains there

• segue to: THANK YOU!

improvements

I've just recently discovered the concept of kaizen, which sounds cool....

Seeing as how I believe in 'tipping points,' I probably shouldn't also be thinking that every small change makes a difference.....

Nevertheless, apparently I believe small changes make a difference and I also believe in tipping points. Never let consistency be a hobgoblin; that's what I always say.

Since our Team meeting with the school, we've seen some small but, I think, important changes in the math class. (This course, I'll add, was created long before Ms. Kahl was hired to teach it):

• teacher has given what I take to be at least one formative assessment, a pop quiz on integer operations, which the kids did well on

• teacher has given one homework assignment that was entirely review/distributed practice, pulling problems from previous chapters

• teacher has seen Christopher once a week for extra help

• Christopher has been able to do at least two homework assignments on his own and arrive at the correct answers (this hadn't happened since the very beginning of the school year)

• I think there's probably been more guided practice and informal assessment during class-time (not sure, but that's the way it sounds - I never quite got a fix on how much guided practice was going on, so it's hard to say for sure that it's increased....)

The latest quiz debacle aside, Christopher does seem to be doing quite a bit better.

Now, maybe that's because he's 'de-traumatized'....he has a lovely new English teacher, and he's being given quite a bit more support by the school in the form of visits to the guidance counselor, etc. So maybe he's just gotten back onto the 'good' side of his performance curve, where he has just the right amount of pressure to improve his performance, but not so much that he falls apart.

On the other hand, he could also be doing better because Ms. Kahl is zeroing in on student performance in a way she hadn't been prior to our meeting.

Certainly the fact that he's suddenly had a pop quiz on material from the first chapter they studied conveys the message that all of the material is important & must be remembered after the chapter test has come and gone.



how much can one teacher do?

This is something I've thought about a lot.

Ms. Kahl is a new young teacher; I think this is her first job.

The Phase 4 6th grade course was created before she got here, and the course is HUGE and FAST.

As far as I can tell, this course is Algebra 1 with geometry & without word problems.

Algebra 1 with geometry & without word problems taught to 6th graders.

Here's what Paul Miller had to say when I asked how a mathematically gifted child would fare:

How would a mathematically gifted child handle this course, in 6th grade? Of course, it depends how mathematically gifted the child is, but I think someone who's moderately gifted would probably choke on the pace. For comparison, in my graduate courses this past semester, we covered approximately 6 or 7 chapters worth of material in each course. I'd say there were probably about 5 or 6 broad concepts per chapter or so. Given that, I'd say the pace of a course using this textbook for a 1 year course for 6th graders is approximately the same as a graduate level course.

There are certainly a good number of kids making it through this course in one piece. On the other hand, the class average is usually around 85, which means that unless everyone is clustering at the 85 (I don't think they are) a fair number are getting Cs and lower. That is a long distance from mastery, which is typically defined as 90%. On one test, in one of the other classes, the class average was 74.

So, judging from what Christopher tells me, and from the fact that one child burst into tears on one of the tests, and from the fact that for years I've heard tales of kids dropping out of this class because 'it's not worth it, I want him/her to be happy, it's not worth all the pain, etc.' there are plenty of kids struggling.

aside: this is funny. There's one child who's been getting 60s and 70s on tests, and has a perfect record of 100s on his or her Extended Response problems.

I don't think this course can be taught to most of these 6th grade kids, period.

I do think some will get As. But this is the ultimate mile-wide, inch-deep math course. (pdf file) Most of these 6th graders will have to re-learn all this stuff as 7th and 8th graders.

So my question is: how much can one teacher do?

It looks like Ms. Kahl is adopting some of the core features of direct instruction, namely formative assessment and distributed practice.

How far can she go with these improvements in a course that's not premised on teaching to mastery?

I'm thinking.....maybe pretty far.

I guess we'll find out.



here's the email

(I’m going to copy this to Griffin, because Griffin is seeing Christopher tomorrow morning. Griffin – if you have a chance to reinforce some of the concepts at the end of this email, that would be great. )

Hi Deanna--

We’ve had another good night with Christopher & math that I wanted to tell you about.

Yesterday, Christopher got 9 out of 10 of his math homework problems correct on the review assignment you gave (simplifying expressions).

The 10th problem was wrong ‘only’ because he left out the negative sign (though I feel that’s a problem in and of itself – I’d say he’s pretty shaky on the meaning of negative numbers.... I’m going to require him to do some more negative-number-line calculations whenever I can work it in. We’ve had him do a few, but not enough.)

This is the second homework assignment he’s been able to do correctly on his own since you began seeing him for extra help. That’s an enormous change. It’s fantastic.

We’re also thrilled that you gave him a Review Problem Set for homework. Last year I could ‘assign’ Christopher review problems myself, but he’s so defiant this year that it’s a huge battle getting him to do the extra work he absolutely must do if he’s going to succeed in math.

I read an interesting factoid about the difference between gifted & non-gifted kids a couple of weeks ago. Supposedly, a mathematically gifted child takes half the number of ‘trials’ to learn a particular concept or skill that a non-gifted child does.

I believe it. We spend a lot of time telling Christopher, Practice, practice, practice.

Last but not least, thanks for letting Christopher take the last quiz over again.

The problems he had with the quiz are a perfect example of the problems he’s apparently having with organization & study skills in general.

He studied pretty hard for the quiz. He and Ed worked on it both Saturday and Sunday.

BUT he studied the wrong thing. Ed & Christopher studied the exponent lesson in the book, not the exponent problems on the review sheet. (Christopher wasn’t able to generalize the book’s lesson to the problems on the sheet, which is what I’d expect for newly learned material.)

Apparently Christopher forgot you’d given them a review sheet. He may have been absent the day you went over it; I’m not sure. He had the sheet; it was in his binder where it was supposed to be. But he didn’t remember it, and thus didn’t use it—and it didn’t occur to us to look for a review sheet since we’ve always had him study the book. (Ed and I are still getting the hang of middle school, too...)

A second organizational/study skills issue: apparently Christopher isn’t great at reading directions, since he managed to mis-read the directions on both the first and the second quiz.

I’ve now told him that he should treat the directions the same way he treats the problems: he should use his pencil to underline and/or ‘cancel’ them, just as he cancels factors.

After he reads each sentence in the directions, he should either underline it or lightly cross it out. That will tell him he’s read them.

We’ll see if that helps.

Anyway, my point is: he studied the material for the test twice, and knew it well.

Yet he still managed to do badly on both quizzes. That’s what I mean by ‘frontal lobe’ issues getting in the way of performance.

I do think we’ve made some progress on the ‘metacognitive’ skill of ‘knowing what you don’t know’. We mentioned in the Parent Meeting that because Christopher follows what you say in class, he thinks he’s ‘got it’ & will ‘remember’ the lesson when it comes time to do homework or a test.

Now he’s at least starting to get the concept that understanding what your teacher says in class is only the first step. This is still a struggle; often he’ll get insulted if one of us tells him he doesn’t know something. He’ll think we’re telling him he’s stupid, or didn’t listen in class, etc. So we’re not there yet.

But we’ve made progress.

All of this will take awhile, but certainly in terms of course content, which is what matters to us at this stage of the game, things are going much better.

Thanks!

Catherine

yes, it's an animated Comments Bank!

-- CatherineJohnson - 30 Jan 2006

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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

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SmartestTractorOnTeachingAlgebra 02 Feb 2006 - 03:06 CarolynJohnston


Catherine dared our contributor SmartestTractor to write up a brief description of her teaching methods -- which are inspired partly by the Carol Gambill method -- and she actually did! Like Matt Goff, she is very aggressively checking her kids' understanding of the previous night's homework every class period -- doing constant assessments of their understanding -- but there are some differences.

from Smartest Tractor:

I started using the Gambill Method this year. Unfortunately, the textbook I use does not have the answers in the back of the book. I have created solution pages and I put them on-line for the kids to look up.

I have attached the one of the files. I am looking for suggestions.

Is it clear? Easy to follow? Too cluttered? Should the solutions have a written explanation beside each line of the equation? As a parent, would this be useful or useless when trying to help your child?

[snip]

I teach grade eight English, math, history, geography, physical education, health, visual arts, and science in a JK to 8 school.

[snip]

The Gambill Method has been a rather interesting, and effective, strategy in my classroom. Needless to say, the kids have never been exposed to the idea. I really messed up the other day when I tried to combine two ideas, like terms and the distributive property, into one day. We went over Thursday's lesson again (Lesson Nine - Solving Equations in More Than One Step). [ed. note: ktm contributors have been discussing formative assessment. Smartest Tractor is using daily formative assessment, in the form of a brief quiz, to discover whether her students grasped the previous day's lesson.]

The current results for the unit (pdf file).

Smartest Tractor In a Nutshell. (pdf file)

also see:
Smartest Tractor's Solution Key (pdf file)
Algebra to date(pdf file)




Rory Donaldson at brainsarefun.com

Smartest Tractor links to Rory Donaldson, who has this to say about Carol Gambill:

In all my years of teaching I have only met one teacher, Carol Gambill, who thoroughly understood the effectiveness of "solution keys."

Solution keys are not the same as "answer keys." A real solution key does not skip any of the steps required to reach the final answer. Solution keys never try to trick the student, or force the student to fill in missing gaps, or require the student to extrapolate. Solution keys provide the student with an ideal solution, every step spelled out.

When creating solution keys the teacher must sit down, and with pencil in hand, thoroughly write down every step required to solve the problem. What ends up on the page are the steps students are required to take to successfully solve the problem, with written comments under each step, or off to the side, adding explanation.

Let me see if I can create both a good and bad example.


Problem: Jerry and Jenny have $1.50 in cash. Jerry has twice as much as Jenny. How much does each have?




The reason that solution keys are ignored is that they require a lot of extra work on the part of the teacher. However, they are very effective when used with homework. Armed with solution keys, and problems that follow the solution keys step by step, students have a great deal of success. Little is more frustrating than the modern crop of textbooks that present no solution keys, and then a bunch of unrelated and dissimilar problems. The work is left to the teachers who really want to consider themselves "good."

Carol Gambill method in a nutshell
brainsarefun.com
Smartest Tractor's algebra class In a Nutshell
Smartest Tractor's Solution Key for students & parents
Smartest Tractor's current results for the unit

formative assessment: Black & Wiliam recommendations
formative assessment: summary of principles

-- CarolynJohnston - 01 Feb 2006

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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

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NoCommentPart3 07 Feb 2006 - 12:00 CatherineJohnson






I'll Take Retention For 500, Alex








update from Janet at 'Art of Getting By'

Since I am the author of the post, I feel like I need to respond. I actually welcome questions like this to be made directly on my blog or to me because I am very open to answering them, no speculation needed.

Google Master was right. No one had to memorize anything. The test was assessing the skill of how to read a simple map. All the children had to do was count pictures. They also had to know a little bit about a compass. That was it.

As for this test itself, it might seem harsh, but this is precisely the kind of questions they need to answer on the NJ Ask and tests just like it all across the country. I'm not saying that sometimes some of the material isn't tough sometimes but this is not an example of such material. My job is to try to get them to understand stipulated grade level material as well as they possibly can.

This is where my somewhat sarcastic attitude came in. If you were in my classroom you would know I have done anything BUT give up on these children. The problem is bigger than this post alone can measure, and that is why I plan to address it in multiple posts that I'm spacing out over time. In short though, there are many contributing factors to the frustration: homogeneous grouping and low motivation just being two of them.

If there are any additional questions about my particular classroom, I would be more than happy to answer them.

Thanks, Janet!


"Ask the Cognitive Scientist":
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Practice Makes Perfect, But Only When You Practice to the Point Beyond Perfection
Allocating Student Study Time: "Massed" versus "Distributed" Practice
Why Students Think They Understand—When They Don’t


formative assessment:
formative assessment
formative assessment in a nutshell


teaching to mastery
CA report on quality ed research
accelerating low performers
Gambill method of teaching algebra
Smartest Tractor's algebra class
Matt Goff's algebra class
TERC, KIPP, & mastery


other posts:
overlearning
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
failing algebra in Los Angeles
Yonkers middle schooler tutors a student who is failing



-- CatherineJohnson - 03 Feb 2006

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BoyTroublePart5 04 Feb 2006 - 18:07 CatherineJohnson



Just spotted this "Remark from the Fray" in reaction to Slate's article on self-disipline & achievement:

Any high-school teacher will tell you why boys do more poorly than girls:

Boys are jerks.

Sure, there are exceptions, the occasional aesthete or scholar...but generally speaking, boys between the ages of 13 and 22 are uncouth vulgarians interested primarily in either prodding or pounding on each other, only expanding their limited interests to include such complexities as beer and breasts as age and situations permit.

If the SAT answer sheets used more mammilary shapes instead of the current oval bubbles, or phrased their instructions in terms like "Dude, shove your fist through the best answer to this question," scores would soar.

--Robert P.
High-school teacher since 1985

yoo-hoo

Robert

It's not nice to call other people's children uncouth vulgarians interested primarily in either prodding or pounding on each other.

My advice?

Don't make me come down there.


-- CatherineJohnson - 04 Feb 2006

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SecretBallot 06 Feb 2006 - 13:25 CatherineJohnson



I'd never heard this:

It is especially noteworthy that San Antonio dropped Everyday Math shortly after [Diana] Lam departed, following a secret ballot by the city’s teachers, 80% of whom voted against it.

source:
Mathematics in the NYC Children First Initiative
Fred Greenleaf
Professor of Mathematics
New York University
Prepared for the Courant Initiative for Mathematical Sciences in Education Forum:
“Delivery on the Promise of Mayoral Control”
Courant Institute of Mathematical Sciences
New York University
October 2, 2005

Our assistant superintendent for curriculum has told me that our teachers like TRAILBLAZERS very much.

He's heard no complaints at all.

Of course, he says the same thing about the parents.

-- CatherineJohnson - 05 Feb 2006

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JohnnyAndKarin 06 Feb 2006 - 15:52 CatherineJohnson



This is so beautiful, I'm posting the whole essay.

From the Los Angeles Times
X = Karin (Johnny) {gt} 95%
What does it take to learn algebra? First you have to master the fundamentals.
By Karin Klein
KARIN KLEIN is an editorial writer for The Times.

February 4, 2006

JOHNNY PATRELLO was a greaser. I was a dork. And yet, despite our rigidly stratified school culture, we came together in the spring of 1968 at Walt Whitman Junior High School, where I tutored Johnny in algebra.

I thought about Johnny again as I read The Times' series this week on L.A.'s dropout problem. Algebra, the reporters found, is an insurmountable stumbling block for many high school students.

What struck me was that the reasons why Johnny can't do algebra in L.A. today are remarkably similar to why Johnny Patrello couldn't do algebra almost four decades ago in Yonkers, N.Y.

Johnny and I were brought together by Mrs. Elizabeth Bukanz, the algebra teacher. Mrs. Bukanz wore her sandy hair in a frizzy French twist and her glasses on a chain. But she was gentle and smiling, and she had passion — at least for what she called "the beauty of algebra." I, too, loved its perfect logic and tidy solutions, so unlike my messy teenage life.

But Johnny was deaf to algebra's siren song. He was flunking, and Mrs. Bukanz hoped that if I used my study halls to tutor him, he might score at least 65% on the New York State Regents exam. Passing the exam allowed even failing students to move on to high school, which started in 10th grade; otherwise, Johnny would be left behind.

Johnny wore his leather jacket in class despite the spring warmth, and he habitually tilted his face toward the floor so that when he looked up at me, he seemed embarrassed. Yet for such a cool guy, he was surprisingly friendly and committed to giving this a try.

Things looked pretty hopeless to both of us those first couple of sessions, as Johnny stumbled through algebra problems while I tried to figure out exactly what he didn't understand. Then, as we took it down to each step of each little calculation, the trouble became clear: Johnny somehow had reached ninth grade without learning the multiplication tables.

Because he was shaky on those, his long multiplication was error prone and his long division a mess. As Johnny tried to work algebraic equations, his arithmetic kept bringing up weird results. He'd figure he was on the wrong track and make up an answer.

This discovery should have made us feel worse. How could we possibly make up for a dearth of third-grade skills and cover algebra too?

But at least we knew where to start.

We spent about half of those early sessions on multiplication drills. Seven times eight, eight times seven — Johnny could never remember. As an adult, in memory of Johnny's struggles, I would rehearse my kids at an early age in that one math fact. Get that 56 down, I would tell them, and the rest of multiplication is a snap.

Today's failing high school students, though plagued by more poverty and upheaval than Johnny or I ever knew, bring the same scanty skills to algebra class, according to The Times' series. They never quite grasped multiplication tables, but still they moved on to more complicated math.

Who can focus on the step-by-step logic of peeling back an equation until "x" is bared when it involves arithmetic that comes slow and slippery, always giving a different answer to the same calculation?

Yet in all these decades, the same school structure that failed Johnny goes on, dragging kids through the grades even if they don't master the material from the year before. This especially makes no sense for math, which is almost entirely sequential.

Leaving children back isn't a solution; it simply makes them feel stupid. They learn, like Johnny, to look at the floor. The floor can't embarrass them.

What I learned from Johnny — aside from the fact that greasers could be sweet-natured and very, very smart — is that schools are structured to help administrators feel organized, not to help children learn.

Young children's skills are all over the map, yet we corral them into second grade, third grade and so forth, where everyone moves at one pace in all subjects. Better to group them according to their skills in each subject, without the "grade" labels, and let them move on to the next skill when they have mastered the one they were on. If they're not getting it, give them extra tutoring, but don't push them forward until they're ready. This way, there is no failure — only progress.

It requires a sea change in thinking, but it's not impossible or even all that hard. Back before standardized tests put classes in lockstep, some progressive schools already were using team teaching to do this in math as well as reading and writing.

Johnny finally nailed seven times eight, then with amazing quickness worked his way through basic "x" problems up to multiple variables and beyond. Still, I couldn't quite catch him up to a year's worth of work in a couple of months. And on a sweltering June day, with humidity that neared 100%, the regents exam came, faster than we felt ready for it.

A couple of weeks later, I saw Johnny in the hall. He shot me a dazed look and broke the news — 95%! That moment has wiped from memory my own regents score. But I won the algebra award at the graduation ceremony. Johnny cheered, apparently undaunted by the fear of appearing uncool.

We lost touch in high school. I was college-prep, he was voc-ed. We would pass occasionally in the halls, and he would glance up from the floor and say, "Hi, teach!"

I know he received his diploma because I see his picture in my old yearbook, wearing a suit and tie instead of his leather jacket. His eyes still look up cautiously from his slightly downcast face, as though he is a bit surprised to be there.



BEFORE I USED Johnny's full name in a story that would reach more than a million readers, it was only right to try to contact him for permission. Directory assistance found one John Patrello, not too far from Yonkers.

The phone was answered by his wife, Joann. It was the same Johnny, but he had died a year and a half ago of a massive stroke, leaving behind Joann and four children.

As she and I talked, both of us in tears at times, it was amazing how much of what I remembered about Johnny continued throughout his life — the tough outer look, the sweetness a millimeter underneath, the quick mind, the habit of tilting his face toward the floor. His eldest is a doctor; the second, a teacher. His teenage daughter wants to be a journalist, and I'll see what I can do to help her along the way.

Johnny became an auto mechanic. ("He loved math, and you know auto repair involves a lot of math," Joann said. Yes, it does.)

Another thing Joann told me about Johnny: He was incredibly fast at multiplication.

-- CatherineJohnson - 05 Feb 2006

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CarolynOnMasteryLearning 07 Feb 2006 - 19:54 CatherineJohnson



I was just doing some Librarian work on ktm (linking like posts with like, dropping 'back doors' into existing posts, posting links in the book-style index) — and I discovered that Carolyn wrote a post on mastery learning back in May!

How good is mastery learning? Two of the review studies looked at mastery learning by itself and with combinations of other curricula, and found that mastery learning by itself produces better results than what was termed 'conventional instruction'. However, mastery learning got its best results when used with other teaching techniques. One study got decent results for "mastery learning with corrective feedback" (meaning -- electric shock? The review didn't say), but got its best results from mastery learning with 'enhanced cues' -- extremely detailed instructions to the students on how to do problems.

Another study found that mastery learning and cooperative learning strongly enhanced each other (note: cooperative learning is structured working-together among students, as opposed to simply being stuck in groups to do your homework together: see part two of this series).

It's interesting, reading this post now, not least because I recognize one of the author's names: Doug Carnine.


Report to the California State Board of Education

-- CatherineJohnson - 06 Feb 2006

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SchmidtInLosAngelesTimes 08 Feb 2006 - 15:44 CatherineJohnson



The LA Times series on Los Angeles high schools includes a terrific interview with William Schmidt, U.S. TIMSS NATIONAL RESEARCH COORDINATOR 1998.

I love this line:

...we know that by the end of eighth grade, U.S. students are probably some two years behind their counterparts in most of the rest of the world…. Middle school in the rest of the world is about algebra, geometry, chemistry, physics. In this country it's still about a lot of arithmetic and what I call "rocks and body parts."

rocks and body parts

Never heard that one.



elementary school & fractions

A: Studies show that middle school is where we lose a great deal of ground, at least internationally. The middle school in these other countries in mathematics is much more demanding. And it's much more of a transition into what we in this country first do in high school. So when our kids come into high school, they're a couple of years behind already. And our high schools just can't make it up.

Basically, the middle school is not preparing kids adequately. But it actually goes all the way back even into primary school, where, again, the kids are not being prepared well, don't understand and aren't able to do the computations associated with simple arithmetic.

Q: So it starts in elementary school?

A: We need to really start a much more serious, clearly defined, coherent curriculum all the way back there, and then we'd have a better shot at doing better with our kids. A lot of mathematics in this country is not designed very coherently. It doesn't progress from the simple to the more complex in ways that are reflective of the mathematics discipline. There's a sequence of things that make the most sense. And very typically in American schools, these sequences are not very clearly laid out.

Q: What do you mean?

A: Fractions, for example, are very difficult for students. Instead of introducing the concept clearly enough so that they understand fractions as numbers on the number line, we oftentimes try to move too quickly to other parts of fractions, such as the operations, before they really have a clear understanding of what fractions are and how they fit into the broader number system.

So kids are trying to learn how to operate on these things, and at the same time they really don't understand what they are, so things get very muddled in their minds.

For me, this is very helpful.

I have yet to meet a mathematician, engineer, or applied-math professional who didn't tell me that fractions are the bottleneck.

I believe it, but I don't quite understand what it means. That's due, in part, to the fact that I haven't begun to re-learn algebra. (Algebra starts in April.)

But I'm also confused, at this stage of the game, over what exactly K-6 kids should be learning about fractions in order not to fall apart later on.

The idea that kids need to understand fractions as numbers on a number line before performing the four operations on them is extremely helpful.

I tend to think he's right about this, though not in quite as literal a sense as this passage implies. Based entirely in my experience of teaching math to Christopehr & re-teaching math to myself, I wouldn't say you need to nail down fractions are numbers before here's how fractions are added & subtracted.

I'd say that fractions-are-numbers can be illustrated and taught via fractions-are-numbers-that-can-be-added-and-subtracted.

My sense is that you want to spend a great deal of time using the number line and using rulers to show both that fractions are numbers and that fractions are numbers that can be added and subtracted.



Saxon Math & fractions

Saxon Math has a number of interesting approaches to fractions:

• kids are asked to count in fractions: 1/4; 1/2; 3/4; 2; 2 1/4; 2 1/2; 2 3/4; 3

• kids do mental math with fractions

• I believe kids are asked to do some skip-counting with fractions as well (not sure)

• fractions, especially fractions of groups, are taught via bar models

is there one perfect method?

Q: Are the nations throughout the world using a different curriculum? Do they have different teaching methods?

A: That's actually a point I want to make very clearly. There doesn't seem to be one perfect method for doing this across the world. Different countries have different methods, just like we do here in the United States.

The real issue is the what. What it is that they're studying, in what grade levels in what sequence and at what level of rigor. Those are the issues that become important, not the how. It's more the what.

Q: We're just not being hard enough.

A: Yes. That's it, in a certain sense. As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.

In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

Here's where I suspect he's missed — or perhaps slighted — a key issue, which is teaching to mastery.

I'd put money on it that in fact there is one 'perfect method' of teaching math, which is to make sure students learn to mastery.

I also suspect that in some (or perhaps many?) countries parents, not schools, are responsible for seeing to it their children learn to mastery. I'd almost bet the ranch that's the case in Singapore.

If this is so, classrooms could in fact look very different to researchers. Once parents take on the job of formative assessment, schools gain a great deal of leeway, to put it mildly.

Wherever the learning-to-mastery is actually taking place, whether at school, at home, or in both locations, you're going to see the same things. You're going to see massed practice, you're going to see distributed practice, and you're going to see overlearning.

Assuming I understand the findings of cognitive science correctly, and I think I do, there is no other way.



mile-wide, inch-deep

....As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.

In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

Again, why is it we 'keep repeating topics,' and why is it that as a result our kids have 'too much to learn'?

Kids in other countries end up learning far more than our kids do.

This is a perfect description of Christopher's accelerated math class, I must say. They're covering a zillion topics; it's far too much to learn in the time they have.

Schmidt is right about that.

What he's not mentioning is the fact that when you cram too many topics into one school year, the kids end up learning nothing well.

Easy prediction: 'mile-wide, inch-deep' is going to be interpreted, in the next cycle of math reform, to mean we should teach fewer math topics, period. Teach fewer topics and continue not teaching to mastery.



teacher prep

Q: In Los Angeles, some educators say they have a hard time finding qualified teachers. Is that a problem for other nations?

A: For some. In the elementary grades, everybody struggles with this, because elementary teachers have to teach all the subjects. But once you get into about middle school, this is more of a problem in the United States, where our teachers are not as well prepared as the teachers in these other countries.

We are doing a study right now across six countries in which we very clearly find that U.S. teachers — U.S. teachers from middle school — are not being … required to take the same level of mathematics that is true in other countries. Teachers that are going to teach middle school mathematics have to have a stronger background.

IIRC, in Asian countries teachers begin to specialize as early as the 4th grade. I'd like to see that in our schools. Teaching both English language arts and math well in 5th grade is a huge undertaking.




By the numbers

A 2003 study found that U.S. 15-year-olds scored low among industrialized nations on the PISA* mathematics test.

Rank	Country	Score
1.	Hong Kong (region)	550
2.	Netherlands	538
3.	Japan	534
4.	Belgium	529
5.	Australia	524
6.	New Zealand	523
7.	Norway	495
8.	Hungary	490
9.	Latvia	483
(tie)	United States	483
11.	Russia	468
12.	Italy	466

* Program for International Student Assessment -
Source: American Institutes for Research






Chapter 1 Why Schools Matter (pdf file)

1998 press release, TIMSS findings

-- CatherineJohnson - 07 Feb 2006

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WholeSchoolReform 11 Feb 2006 - 01:38 CatherineJohnson



A series of links, starting with Carnival of Education, then moving to Jenny B & on to Foundations of Teaching and Learning brought me to a professor's notes taken on a lecture about bringing "research-based practices to scale in school."

I'm out of my depth here. I've begun reading books & articles on 'whole school reform'.....and that's about it.

Translating the findings of cognitive science on the nature & process of learning, which I do understand, into public policy and systemic institutional reform — I can't make that jump.

This lecture, and the study to which it refers, appear to come out at least moderately in favor of very early grades scripting, which I know sets a lot of people's teeth on edge —

As far as I can tell, it appears that scripting was effective in Kindergarten, but not in grade 3 (please correct me if I'm wrong).

I think I've mentioned that the Saxon books are scripted early on. I know the Kindergarten book is scripted, because I have it. I know the 1st grade book is scripted because my sister-in-law uses it in IL.

I don't know when Saxon stops scripting lessons, but I'll bet it's somewhere around 2nd or 3rd grade. (Again, if anyone knows for sure, chime in.)



leadership in schools

Although I don't understand public policy well, this passage doesn't surprise me:

ASP - focused on "cultural control" aimed at promoting "powerful learning" that schools needed to define themselves. Instruction is not specified in any centralized way.

AC - focused on "professional control" in which the emphasis is adhering to standards of teaching and learning. A key feature was a very aggressive leadership training program focusing on principals and coaches.

SFA - focused on "procedural control" in which instruction is highly scripted. What students should learn and how they should be taught are quite clear, particularly given the scripting. Coaches and leaders teach the design and monitor fidelity of implementation.

Teachers report that SFA and AC (compared with controls) have greater design specificity and consistency, and more interaction with leaders, but ASP has more support for teacher autonomy.

[snip]

Effects on achievement (using the TerraNova test).

SFA had a 1.5 month grown effect at K but not at grade 3.

AC had a positive effect of 2 months at grade 3, but not at K

ASP didn't have any significant effects.

As far as I can tell, for years researchers have been saying that strong principals are the key.

Until someone proves that to be wrong, I believe it. 'The person at the top sets the tone.'

It doesn't surprise me that a reform focusing only on 'culture' or on 'teacher autonomy' would produce no results. Schools need strong educational leadership.



question

Ken may know the answer to this.

What is the difference between Success for All & Engelmann's Direct Instruction?



update: Vlorbik on SFA

i'll take that one after barely glancing
at "success for all": engelmann is clearly
a human being with actual opinions of his own
but "s.f.a" is a committee of mushmouth obfuscators
with nothing in the world to say but feel-good cliches.








-- CatherineJohnson - 08 Feb 2006

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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

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RenaissanceLearningAndAcceleratedMath 13 Feb 2006 - 23:57 CatherineJohnson


ok, I am now officially too sick to carry on. (head cold; bad one)

I'll drop in these links, and come back later:

• School Renaissance (page from Catalogue of School Reform Models)

• Renaissance Learning (has bought AlphaSmart, and manufactures Accelerated Math — company was started by a mom who created a software program to help her children learn to read

• very brief description of Accelerated Math

• STAR Math 12-minute assessment program (part of Accelerated Math)

• Assessment Master

• The Center for Comprehensive School Reform funded by U.S. Department of Ed

• Center for Comprehensive School Reform page mentioning Renaissance Learning, Success for All, & Direct Instruction

• Apple page discussing Renaissance Math

• someone's wiki page on Renaissance Math (includes posts from Math Forum)

This sounds like a good idea, especially seeing as how a parent invented it. I almost always like teaching systems and ideas parents come up with.

Does anyone have experience with Accelerated Math?

The 'wiki' page is excellent — seems to be written by a teacher actually using the program.



can formative assessment be done by software?

Offhand, it strikes me that formative assessment is the area of math ed most compatible with software & programming...

A couple of teacher comments:

"I am thoroughly convinced that Accelerated Math can do things for students in math that are almost impossible to accomplish otherwise. The instant feedback and the emphasis on mastery ensure that students do not just coast through the program without truly learning the material. While the teacher (or someone) still has to do much of the teaching, students can be much more independent much of the time, and can cruise quickly through objectives that come easily to them. I have never made it through the end of the math book with any of my classes - I'm lucky to get past the halfway point with some of them. But with AM, motivated students can master EVERY SINGLE objective for the grade level library they work through, eliminating the gaps I see in the math skills of most of my students."

"The true power of AM is its ability to collect data about each student and to report that information to the teacher so he/she can act upon it. AM will notify a teacher whether a student is struggling in any given topic. It is then the teacher's job to act accordingly. The teacher may re-teach a lesson to the whole class, assign a peer-tutor to a struggling student, or to meet with the struggling student himself/herself. AM notifies the teacher of a struggling student much faster than the teacher ever could have figured it out if left to his/her own devices. I could continue singing the praises of this wonderful teaching tool, but I fear I've gone on long enough."

One last thing: Joanne Cobasko, of SOCMM, had a horrific experience with a software math-teaching program her school used with her son. I'll get her story posted at some point. The school wouldn't let her son advance, because the software, which was broken (IIRC, the headphones may have been defective...?) said he wasn't ready.

Apparently they put Hal in charge of math.



update: Joanne Cobasko on SuccessMaker:

Fairfax County, VA Evaluation of SuccessMaker Computer Curriculum Corporation (CCC) SuccessMaker Program Final Evaluation Report (pdf file)

From page 5 of the pdf file above under the heading Findings then sub heading of Student Achievement comes the following:

"For the most part, no significant differences were found between the performance of students at the CCC [SuccessMaker] program and comparison schools on the Stanford 9 mathematics tests. In all three years of the evaluation, students at both groups of schools demonstrated significant growth over the course of the year, and not many differences were found in terms of the rate of growth. Student gains from fall to spring on the Stanford 9 showed modest correlations with the gains made on SuccessMaker's own assessments, but did not show direct correlations with time spent on the system. In several instances....Students who spent under 20 hours on the program outperformed those who spent more than 20 hours on the program..." [bold emphasis is mine]

To put these findings in plain language there were only SMALL correlations with actual standardized test outcomes and the SuccessMaker reports teachers print out which show glowing results in student achievement. The students who spent the least amount of time on the SuccessMaker program scored better on standardized tests.

To further illustrate the lack of effectiveness of this program, Aspen Elementary has been using SuccessMaker since December of 2003 and their API scores have not shown ANY improvement. 2003 and 2004 API reports on the CA SBE web site (posted before 2004-2005 adjustments took place, show a 5 point drop from 879 down to 875, then a one point increase to 876) California Department of Education Academic Performance Index (API) Report

Why on earth is the administration requesting that the district finance this ineffective intervention? It is expensive and shows little in the way of results.

The IES has indicated there is NO VALID RESEARCH to show this program is effective: What Works Clearinghouse.

The district is further crippling CVUSD math education by using this program as it's sole intervention for students who are struggling with math.

If all students are required to spend 20min twice a week in the computer lab on this program you must add in the time necessary to line up and walk to and from the computer lab. There is probably 1.5 hours per week taken out of classroom instruction time to accommodate this intervention. THESE ISSUES MUST BE ADDRESSED BEFORE APPROVING GENERAL FUNDING FOR SUCCESSMAKER At the very least the district needs to perform a scientific evaluation of standardized test scores from the CVUSD schools that have been using SuccessMaker and the ones that have not. A teacher survey of their perception regarding outcomes will NOT be sufficient. The board members have a responsibility to protect taxpayers by insisting on a cost benefit analysis of this intervention.

Scarce funding would be better spent on tutors for after school Math and Reading programs staffed with human instructors, not computers.


-- CatherineJohnson - 11 Feb 2006

---

LindaSchrockTaylorOnMathAtSchool 16 Feb 2006 - 02:17 CatherineJohnson


I was just trying to de-code the mysteries of Saxon Physics, when I came across this observation from Linda Schrock Taylor:

Frequently we are asked, "When do you end the school year in homeschooling?" My answer is always, "When the last math lesson has been completed and the final exam passed with flying colors." I think it is important that students complete books, especially math books. Each year I would note that even the best math teachers in the public school where I taught were only completing about 42% of each math book prior to the start of summer vacation. The students then went home for eleven weeks, and returned to face the next book in the sequence—even though they were never taught the last 58% of the material in the prerequisite class! Still people wonder why American students fall ever further behind in math!

update: more on not finishing the book

from a Math Forum thread on Accelerated Math (haven't read the thread yet):

I am thoroughly convinced that Accelerated Math can do things for students in math that are almost impossible to accomplish otherwise. The instant feedback and the emphasis on mastery ensure that students do not just coast through the program without truly learning the material. While the teacher (or someone) still has to do much of the teaching, students can be much more independent much of the time, and can cruise quickly through objectives that come easily to them. I have never made it through the end of the math book with any of my classes - I'm lucky to get past the halfway point with some of them. But with AM, motivated students can master EVERY SINGLE objective for the grade level library they work through, eliminating the gaps I see in the math skills of most of my students.

update: question

I remember reading somewhere — and posting — that math textbooks have approximately 23% new content each year....the rest being review of content taught in years before.

I have no idea where I read this, or where I posted it — and am now wondering whether I dreamed the whole thing up.

Does this factoid sound familiar to anyone?



Saxon Physics mystery

Charles found a site selling Saxon Physics, which a Saxon rep told Carolyn is out of print, at a nice price....but I can't figure out what comes with.

The same site also offers the Solutions Manual ($27.99) and Saxon Physics, Answer Key Booklet & Test Forms (99 cents!)

Maybe I've gone blind or lost my capacity to read, but I simply cannot tell whether the Saxon Physics Home Study Kit — "Offering 100 physics lessons, tests, answers, periodic table, charts, and more: all you need to teach a complete physics course" — also includes a Solutions Manual and an Answer Key & Test Forms.

I'm guessing it does not include a Solutions Manual (but why would that be?) & does include an answer key & tests, seeing as how it says it includes an answer key & tests, & does not mention a Solutions Manual.

Nevertheless, I'm confused.



Megawords 14% off

The site offers Megawords at 14% off the regular price.



I love this

Linda Schrock Taylor...is a free-lance writer and the owner of "The Learning Clinic," where real reading, and real math, are taught effectively and efficiently.

I'm going to have to get in touch with her.


-- CatherineJohnson - 12 Feb 2006

---

CarnivalOfEducation 16 Feb 2006 - 02:53 CatherineJohnson



54th Carnival of Education

I think I've got most of Smartest Tractor's pdf files attached to this post. She has also been adding material to the User page on teaching writing.

I would kill to have Christopher in Smartest Tractor's class. Ed read her 'in a nutshell' course description last night & felt the same way. I'm hitting my friend Kris with a copy tonight!

In fact, I'm giving Smartest Tractor's work to everyone who'll read.

I'm very eager to hear how Smartest Tractor's students are faring. (I'm also interested in how Smartest Tractor organizes larger tests, such as Chapter Tests & the like...)

One more thing: Smartest Tractor must be working 18 hours a day on her teaching. Has to be.

wow




Smartest Tractor's algebra class In a Nutshell
Smartest Tractor's Solution Key for students & parents
Smartest Tractor's current results for the unit

Carol Gambill method in a nutshell
brainsarefun.com
Brains are fun: examples of good & bad solution keys

formative assessment: Black & Wiliam recommendations
formative assessment: summary of principles



-- CatherineJohnson - 15 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

---

ImpendingDoom 27 Sep 2006 - 17:37 CatherineJohnson





The kids took a sample state math test today. It was a debacle. Especially the 'short answer' questions, where you have to actually do some math and find an answer. Christopher got 13 out of 24 right. The smartest kid in the class scored 19.

Meanwhile the kids in Phase 3 are coming up with scores like FIVE.

I'm sure TRAILBLAZERS will solve these problems.



update

Remember Christopher's friend-in-flunking from 4th grade?

This was the boy who was in Christopher's math class, getting the same Ds and Fs Christopher was getting. He's in Phase 3 to this day, and hasn't made up the lost ground as far as I can see.

He just called. He got 4 answers right. Out of 24.

So all my hard efforts are paying off!

Christopher is now flunking math at a much higher level!



Glencoe top secret test prep

The kids are preparing for the state test using a Glencoe booklet called Mastering the Intermediate Level Mathematics Test: Diagnose - Prescribe - Practice Workbook.

Apparently, this is a booklet only Official School Personnel can purchase. Its existence is mentioned nowhere in any materials available to parents or students. You can Google it all you want; you can look up the ISBN number; you can drill down into the deepest, darkest recesses of the Glencoe website.

It's not there.

This kind of thing makes me nuts. A couple of years ago I tried to buy the SRA spelling curriculum, Spelling Through Morphographs. It's a remedial program, co-written by Seigfried Engelmann. I had no idea who Engelmann was at the time, which makes Spelling Through Morphographs the second Engelmann book I picked out 'cold,' the first being Engelmann's book about teaching your kid to read.

Apparently Seigfried Engelmann and I are as one.

Here's the description:

Spelling Through Morphographs
Grade Levels 4 - Adult
Successful spellers in just 20 minutes a day!

Spelling Through Morphographs is a remedial program, designed to give older students the tools they need to learn to spell. The program teaches a variety of morphographs -- prefixes, suffixes, and word bases -- and a small set of rules for combining them so that students learn a spelling strategy they can apply to thousands of words.

Fast-paced lessons and a systematic review of every morphograph, combined with a few simple spelling rules, ensure that spelling strategies are mastered. In the first half of Spelling Through Morphographs alone, students learn over 252 morphographs and the rules needed to spell over 3,000 words. By the end of the program, they learn over 500 morphographs, and are able to spell over 12,000 words. And the fact that morphographs have meaning not only helps students remember their spelling, but it also helps them figure out the meaning of unfamiliar words.

Features:

• Students learn to spell over 500 morphographs and are able to spell over 12,000 words
• Students learn to generate correct spellings from morphographs, not memorization
• Expanded writing and proofreading activities reinforce the connection between spelling and composition

So that's right up my alley. Mathematically speaking, a kid who can't spell has to have some kind of 'lever'; there's not enough time between now and adulthood — or now and the SATs — to memorize each one of however many gazillion words in the English language are known & used by smart people. You have to learn the component parts and a finite set of rules for putting them together.

Naturally, nobody teaches spelling that way any more.

Today spelling is taught 'thematically,' meaning kids are supposed to learn to spell whichever words happen to be used in that week's social studies or ELA units. At the beginning of the week kids are handed a vocabulary list of words they'll be seeing and using that week. Then, at the end of the week, they're supposed to be able to spell them.

This has created a generation of what spelling researchers call 'Friday spellers.'

I'm sure there are many excellent Friday spellers out there.

Christopher is not one of them.

If Christopher's going to learn to spell, he's going to have to have a rational, coherent, intelligent curriculum that's been specifically designed to teach spelling. As in spelling per se.

I figured Spelling Morphographs was it.



foiled again

So I called up the folks at SRA.

They said Forget it; they wouldn't sell me the program unless I could prove I was a bona fide homeschooler. I had to have papers.

I was furious.

My school wasn't teaching my kid to spell, I was spending hours trying to figure out what the he** spelling was in the first place (turns out spelling is reading, only harder), I was trying to find the relevant research fast and get a handle on it fast, and I wasn't having fun doing any of this. Learning math & math ed so I can teach math at home is fun. Learning spelling & spelling ed so I can teach spelling at home is not fun.

I was ready to be done investigating spelling.

I wanted to get whatever book I was going to get and go back to doing routine stuff like earning a living.

I wanted Spelling Morphographs.

But no.

I couldn't have Spelling Morphographs, because I'm not CERTIFIED. I'm not OFFICIAL.

I MIGHT BE TRYING TO CHEAT.

The big textbook publishing outfits have all kinds of bans on selling to parents.

Think about that.

The big textbook companies have formal, fully-enforced rules against selling educational materials to parents.

The big textbook companies are cheerfully oblivious to the fact that it's our money that supports their products in the first place; without parents and other tax-paying citizens, SRA could hang it up. But their products are Top Secret. Can't be sold to us. If our school district elects not to send the textbooks home in the backpack, we don't even get to see what we've paid for.

The customer service rep was a sweet-sounding Texas gal who in fact was homeschooling her own kids. Sounding sympathetic, she rattled off a list of online Christian textbook outfits I could try, and told me she'd give me the phone number for my local rep so I could maybe twist his arm and get him to bend the rules.

This just made me more furious, although I managed not to bite her head off. You're telling me I'm gonna have to dive into the whole arcane world of online Christian homeschooling bookstores (until that moment I hadn't even known there was a whole arcane world of online Christian homeschooling bookstores)^* and figure all that out, too???

You're telling me, Go back to Google and start all over again?

No!

Wrong!

I don't want to start all over again!

I don't want to Google online Christian homeschooling bookstores!

I don't want to call my local SRA rep and beg him to sell me an illegal Spelling Textbook!

My kid can't spell, my school isn't teaching him to spell, and I can't buy a remedial spelling book from SRA?

Because why?

What is the reasoning here?

What am I gonna do with my own personal Parent Copy of a remedial spelling textbook?

Tell my kid the answers before he takes the test?

Wait!

Wait!

That's exactly what I'm gonna do!

I'm gonna tell my kid how to spell the words that are gonna be on the test and make him practice until he can spell them!

The reason I'm gonna do that is: THIS IS SPELLING.

THERE'S NO 'MEMORIZED THE ANSWERS'-TYPE CHEATING IN SPELLING.

MEMORIZING THE ANSWER BEFORE YOU TAKE THE TEST IS SPELLING.


So then naturally I got sidetracked trying to find some way for the state of New York to certify me as a part-time homeschooler, which went nowhere and got me even more aggravated.....and at some point in there I discovered Megawords, thank the Lord.



So now My Tax Dollars are paying for a Top Secret Glencoe Test Prep Diagnose Practice Assign grade 6 workbook that I'm (apparently) not allowed to purchase as a mere parent of a kid who has to take this freaking test.

I can't stand it.






New York state math test prep over vacation
state test impending doom

SRA spelling research

How many words in the English language?
How many words in the English language? (another view)
a million or more words in the English language
FAQs: how many words?



^*Now, of course, I get invited to special Christian homeschool days at Six Flags. I am among the initiate.


-- CatherineJohnson - 03 Mar 2006

---

KippAcademyContract 04 Mar 2006 - 12:40 CatherineJohnson







via Eduwonk, a US News & World report on the KIPP Academy with this passage on contracts:

Under a contract signed by students, parents, and teachers, students go to school from 7:30 a.m. to 5 p.m. every weekday, every other Saturday morning, and for an extra month in the summer--over 60 percent more class time than the average school year. Teachers are on call 24-7 to answer questions about homework (the better they teach, the fewer the calls), and parents are held accountable.

I suspect that the wording here — 'parents are held accountable' — comes from the writer, not from KIPP.

My understanding of KIPP is that they're careful to ask no more of parents than what parents really can, and should, deliver.

No parent is asked to serve as his child's re-teacher; hence the 24-7 on-call policy for teachers. IIRC, the parent's job is to make sure the child does his homework, gets enough rest, and gets to school on time. And that's it.

Here's another passage that gives the flavor of what really goes on at KIPP:

Once, when an exasperated Feinberg couldn't get a student to do her homework, he went to her home and, with her mother's permission, hauled the family's 37-inch TV out of the living room and installed it at the front of his classroom. When the student delivered, she got the TV back.

In that case the parent was failing to do her job. The school stepped in and helped — without resorting to a lot of blather about 'holding parents accountable.'

Here's more:

A bigger question for KIPP's founders, and for public education in general, is whether the success of their program can be replicated elsewhere. Some observers argue that KIPP parents, however underprivileged, are inherently more motivated than the parents of other public school kids. To which Feinberg responds: "More motivated? They have to answer a knock on the door and listen to us for an hour and sign their name? How difficult." Levin invites doubters to compare the statistics of KIPP kids when they enter the program and when they leave. "The kids in fourth grade started out with the same low scores, the same sorts of disciplinary problems," he says.

Again, we see 'observers' attributing a child's learning to something the parent is doing, not something the school is doing. This cuts both ways. If the child fails, it's the parent. If the child succeeds, it's the parent. KIPP kids are succeeding; therefore KIPP parents are different.

Richard Rothstein is big on this idea. KIPP parents aren't normal poor people. They're abnormal poor people. I find that shocking coming from an advocate for the poor. The poor are bad parents by definition? Awful.

Here's Rothstein:

But [KIPP] schools do not enroll black children from typical low-income families....Parents who send their children to such schools are already unusually interested in their education; children are accepted only if parents agree to monitor their homework, enforce approved disciplinary measures, and limit television-watching. If children or their parents violate these agreements, the children can be expelled—a rare occurrence, but a threat nevertheless.

source: Must Schools Fail? by Richard Rothstein
New York Review of Books $
Volume 51, Number 19 · December 2, 2004

There you have it. KIPP parents are not typical, because KIPP parents are 'unusually interested' in their children's education.

A typical poor person doesn't care.

Awful.



the parents

Looking back over a decade in the classroom, Feinberg and Levin cite the sorts of triumphs and failures familiar to any adventurer in the blackboard jungle. "There have been so many nights being up until midnight after waking up at 5 a.m. and voice mails from parents yelling at me like I'm a little worse than the devil," Feinberg says.

nope

There's not a lot of talk from either Feinberg or Levin about 'holding parents accountable.'

In fact, there's none.

These two guys are running a superb school for difficult students who are far behind their more affluent peers when they show up.

They hold themselves accountable, first and foremost.

Then the kids, then the parents.

Sounds like the parents are holding the school accountable, too.

That's the way it should work. As Ken pointed out when Christopher brought home the Contract to Improve My Grades, which I signed but then refused to hand in, a contract is signed by all parties, not just one.



preview of coming attractions

I've got to start writing down Christian's stories.

Christian is Jimmy's & Andrew's 'res hab' aide. He went to school in Yonkers, and has tales to tell. He has so many tales to tell that he wants to write a book, and I want him to write a book, and it's conceivable we'll write a book together. His mom lived in a cozy little row of townhouses built down below the enormous Projects there in Yonkers; Christian says they used to call their place Little House by the Projects.

Christian's mom spent a lot of time hassling school officials, let me tell you.

Before he moved to Yonkers, Christian was going to school in Mamaroneck. After they moved, he used the same book as a senior in high school he'd already used in 7th grade in Mamaroneck.

This is why we need KIPP.

And this is why Richard Rothstein doesn't know what he's talking about.

I wonder if Christopher would learn more at KIPP?

I wonder if Christopher could go to KIPP?

It's not that far away. We could get him there.






my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract



-- CatherineJohnson - 04 Mar 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

---

PiWeekComingRightUp 07 Mar 2006 - 02:03 CatherineJohnson




For five bucks I can purchase a pi t-shirt for Christopher.

-- CatherineJohnson - 06 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

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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

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MathJournalDayThree 12 Mar 2006 - 21:40 CatherineJohnson


State test starts on Tuesday next week, and today is Thursday. It's getting close.

So today the kids wrote in their math journals about two quotes, not just one. Assignment was the same as always: give their reaction and say how the quote would help them on the test.

Christopher remembers today's quotes as being:

If you want the rainbow, you have to deal with the rain.


and


You'll always face challenges, but you should never be defeated.

I'm thinking I should send in the quote Jeff Boulier found about automaticity, and suggest she have the kids journal about the importance of having utterly mastered one's work.

That would be a novelty.

They have so utterly mastered their work that they work without thinking;
Holding three-fifths of their brain in reserve for whatever betide.
So, when catastrophe threatens, of colic, collision or sinking.
They shunt the full gear into train, and take that small thing in their stride.

I have to go find my collection of Margaret Thatcher quotes about hard work and why people like to do it.

Have I mentioned that in the state of New York it's against the law to homeschool your child in just one subject?



back again

Can't find the Thatcher line I was thinking of. It's buried somewhere on the basement PC, so that's a project for another day. However, I did scare up a bunch of alternate quotes I'd like to throw up on that board....

In the meantime, here's Stephanie:

I cannot believe they're still writing in the journals! Do they have stress counselors standing by, too? At this point, they should be giving the kids practice in problems that the kids already know how to do, and that will appear on the test. How 'bout giving the kids some feelings of actual success on actual math problems before the testing starts?

As usual, a KTMmer has read my mind.....you guys are starting to get psychic.

Check this out.

I've (obsessively) mentioned the fact that Christopher is not one of the straight-A students in math (or anything else).

So today Christopher comes home full of pep, opens with his 500-millionth 'THE TEACHERS SAID YOU'RE NOT SUPPOSED TO STUDY FOR THE STATE TEST' protest, then stands there in the middle of the living room looking cocky.

'What's up?'

Math journal, two quotes, rainbow, rain, etc.

'Did you do any math in math class?'

oh, yeah!

We did problems about cups.

'Cups?'

Yeah, how many cups in something. There was a really hard problem, and I was the only person who could do it.

With some prompting, he finally remembered the problem:


______ quarts = 48 ounces


The kids were given a chart showing what all of the various liquid measures equal, and they had to go from ounces to quarts.

This is the accelerated class.

Christopher was the only kid who could do it.

She's psyching them out.

update: Christopher wasn't the only kid who could do it — though he was one of only a few — and no, she's not psyching them out.



dimensional analysis rocks

One of my Mental Categories now, when I think about how to teach math, is to prefer to teach procedures that instruct while also solving the problem.

For instance, I don't think cross-multiplication — which I would teach (it's just too powerful & easy to remember to forego) — has a lot of instructional value. (That's my guess.)

Dimensional analysis, I think, is the exact opposite.

Not only is it an incredibly useful, simple, impossible-to-forget procedure, BUT it gives you 'instruction' in converting units of measurement every time you do it.

When you set up a sequence of unit multipliers, you see the conversion process all laid out in front of you. You see that to convert from ounces to quarts you're going to go through 4 steps (ounces to cups to pints to quarts). You see that sometimes you multiply & sometimes you divide.....You're getting a mini-lesson in what you're doing while you're doing it.

Christopher didn't use unit multipliers to solve the conversion problem in class today. (Dang!)

But the reason he could do it when everyone else couldn't (apart from the fact that we're not sitting around journaling about COPING WITH MATH FAILURE) is that he's done a bunch of dimensional analysis problems here at home.

Thank you, Dan K.


Ms. K teaches dimensional analysis



-- CatherineJohnson - 09 Mar 2006

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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

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GregMatteoProblemsThatTeach 11 Mar 2006 - 19:29 CatherineJohnson



For excellent examples of problems that teach, try Math TV at Action Math. The video solutions for some of the fraction and ratio problems even use Singapore methods. Christopher may really enjoy these.

Greg DeMatteo
Norwood Middle School





I'm thrilled to get these — will report as soon as I've watched!

(Sorry. I'm developing a slight THING for animated gifs....)



back again

Action Math is a BLAST!

Here's the first problem:


A new movie theater opened up in town.
The theater contains 40 rows of chairs.
The first row has 10 chairs.
Each additional row has two more chairs than the row before it.
What is the seating capacity of the theater?


This brings up something important.

I think early word problems should be written exactly this way, as a list of sentences, not a paragraph. This helps 'disaggregate' basic working memory and 'environmental dependency' issues from the math problem itself.

The child isn't constantly having to search back and forth in a paragraph to re-isolate the individual sentences.


These videos are incredible!

You MUST go see them.

Wonderful.

I've just gained more conceptual understanding of algebra watching one video than I did in 3 years of high school! (I'm pretty close to serious about that....)

Greg, THANK YOU!







OK, now I'm sick.

If Christopher had had a teacher like the one on this website all year long.....we wouldn't be studying for the state test.

Compare her step-by-step explanation of the solution to the non-explanation of this Extended Response problem Christopher was given early this year:






challenge? or teach?

Virtually all of the problems Christopher has been given this year have been 'Challenge' problems. That's what the Assistant Superintendent in charge of curriculum told me about the Extended Response problems: "These students need to be challenged." (Christopher brought home a whole batch of challenge problems last night; I'll post some of them tomorrow.)

Virtually none of the problems Christopher has been given this year have been Teaching problems.

There is a vast difference between challenging a student and teaching a student.



keyword: actionmath


-- CatherineJohnson - 10 Mar 2006

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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

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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

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KtmGuestOnKelleyWingate 11 Mar 2006 - 01:50 CatherineJohnson



KTM Guest left this comment about the Kelley Wingate Pre-Algebra workbook I've been using with Christopher:

The Kelley-Wingate is ok. I use it for reinforcing some concepts in a HS Algebra class. Many of our students arrive in HS with little knowledge of Middle School math. Just be careful, every 5 sheets or so I've found a typo or error in one problem on the sheet.

I'm very curious to learn what teachers do - or try - to teach unprepared kids the subject they're contractually bound to teach them.

Are there 'work-arounds' for lack of foundational skills? (Dumb question, I know, but I'm asking.)

Are there shortcuts?

Are there ways to recruit some parents or parent-volunteers to oversee remediation at home for their own kids, or in Homework Help classes as parent-volunteers?

Are there ways to pare the list of topics way down to give you time to teach what hasn't been learned thus far without 'Alerting the Authorities'?

Is student motivation and/or anxiety a big problem?

Are their particular foundational skills that are more important to remediate at once than others?

Are there work-arounds and shortcuts that definitely don't work?

and more.....

When any of you currrent and former teachers & tutors have time to leave thoughts and experiences, I'm eager to hear.






resources for practicing pre-algebra skills

-- CatherineJohnson - 11 Mar 2006

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UpRising 13 Mar 2006 - 01:50 CatherineJohnson



The other shoe dropped this week.

Christopher came home from school Tuesday and said that 6 kids had gone en masse to the guidance counselor to protest Mrs. R's treatment of them in class. When he got wind of the plan, Christopher talked his way in, so that made 7.

The tennis mom filled me in the next day. Her daughter was one of the six.

Apparently Mrs. R was much nicer for a time after Christopher was moved out of her class (we'd heard this from numerous sources, including the tennis mom). But then she reverted to form.

We've stayed away from the situation, partly because the principal took such good care of Christopher, and partly because until this week there wasn't any situation as far as we knew. Last I heard, Mrs. R. was acting much, much nicer to all of the kids. Christopher was hearing this on a daily basis.

'Mrs. R is so much nicer now that you're gone!

Mrs. R is so much happier now that you're gone!' etc.

I managed not to get bent out of shape over the countless expressions of Joy Across The Land Now That Christopher Has Gone. He's been in middle school long enough by now for me to know that if his friends aren't reporting that Mrs. R. is thrilled to see the last of him they're going to be telling him he's a) fat or b) dumb or c) God-knows-what. If I can deal with 'Bocy,' I can deal with Mrs. R is so happy you're gone, especially since I'm sure she is happy he's gone. Also seeing as how Christopher gives as good as he gets. (Was he calling his closest friends in the world 'anorexic midgets' last fall? Yes, he was.)

At the time, Ed said that Scott, the principal, had handled the situation perfectly.

I said something skeptical about the likelihood that everything was now going to be Fine, and Ed said, 'Here's what an administrator will do' [Ed being an administrator and all]. 'He'll have a serious talk with Mrs. R., then he'll hope everything is resolved. Then when it's not resolved, he'll deal with it. That's what I would do.'

He said, 'That's what I would do' in a particular way.

He said it like Having a serious talk with a person you're overseeing and then hoping everything is resolved never works.

There's always another shoe.



update

So today (3-13) all the kids were telling Christopher Mrs. R is great, they love her, he's crazy.

Gaslight.

I'm at least half-serious about that. This teacher is far too present in these children's thoughts. Middle-schoolers are obsessed with other middle-schoolers; they're only dimly aware that adults, including teachers, exist. If one teacher is commanding this much 11-year old attention, there's a problem.


-- CatherineJohnson - 12 Mar 2006

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TheFilmstripsOfThe1990s 22 Mar 2006 - 00:21 CatherineJohnson



The Filmstrips of the 1990s....that would be computers in the classroom.

source:
The Atlantic Monthly
July 1997
The Computer Delusion Volume 280, No. 1 pages 45-62



news from nowhere

I'm going to go out on a limb and say that someone, somewhere in the Irvington administration wants to buy lots more technology.

Why do I say this?

1. 'Technology' was a line item on the PTSA Forum wish list. This list, I believe, (NOT FACT-CHECKED) was created by the school board.

2. Irvington is holding its first ever 'Technology Expo,' an event at which teachers from all four schools will show how they use technology to teach. Students will "share digital portfolios, computer programming, and multimedia presentations." Vendors will be present! Call me cynical, but that sounds like a dog and pony show to me.



I'm against it

No more technology.

Please.

Teachers don't like it, as far as I can tell.....at least, judging by the relative non-use of edline thus far.

Back in the fall Raina Kor told parents that many teachers feel 'uncomfortable' with technology. That's why it was going to take awhile for teachers to start using edline; they were uncomfortable.

Well, I say: GOOD FOR THEM.

What is all this technology doing for us? The one skill I have seen a 6th grader use from his 'Technology' class this year is to download soft porn from funbay. I'm serious. His mom asked him where he learned how to pull pictures from the web and put them in his 'Picture File,' and he said, 'I learned it in Technology.'

I don't want any more technology.

I certainly don't want to pay for any more technology.



what do teachers want?

from Computer Delusions by Todd Oppenheimer:

If history really is repeating itself, the schools are in serious trouble. In Teachers and Machines: The Classroom Use of Technology Since 1920 (1986), Larry Cuban, a professor of education at Stanford University and a former school superintendent, observed that as successive rounds of new technology failed their promoters' expectations, a pattern emerged. The cycle began with big promises backed by the technology developers' research. In the classroom, however, teachers never really embraced the new tools, and no significant academic improvement occurred. This provoked consistent responses: the problem was money, spokespeople argued, or teacher resistance, or the paralyzing school bureaucracy. Meanwhile, few people questioned the technology advocates' claims. As results continued to lag, the blame was finally laid on the machin