Entries from EverydayMath

Welcome Independent George!

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

I received an email today from Joanne Cobasko of Save Our Children from Mediocre Math (SOCMM). She drew my attention to a couple of articles, describing the improvement in California test scores after the new California standards were adopted.

I looked at the attachment and skimmed the second article. It's not a research study (i.e., it would not meet the WWC's standards of evidence for a well-designed study); but it is definitely one situation where Saxon went head-to-head with fuzzy math, and won.

Here's the letter (thanks, Joanne!):

Hi Carolyn:

Both these studies show fantastic classroom results achieved in CA classrooms which are attributed to Saxon Math. I believe Bishop & Hook down play the Saxon Math connection in favor of the "CA Key standards" so as not to promote any particular curriculum over another, they choose to promote the math standards employed.

You will find references to the curriculum in their write ups though.

http://www.nychold.com/talk-hook-040404.pdf
http://www.nychold.com/report-wbwh-040619.pdf

There is also a great district comparison of standardized test results from Manhattan Beach, CA and Palos Verdes, both well to do communities (the comparison was provided to me by Martha Swartz from Mathematically Correct). [Note: Joanne points out that Manhattan Beach uses Saxon Math, and Palos Verdes uses Everyday Math. -- Carolyn]

Palos Verdes has the edge with a 26% Asian population, and one Kumon or other type tutoring facility for every 429 grade 2 - 6 elementary age student (the tutoring info was my informal review of the school population per the state testing info and a print out from the Kumon & other centers indicating their locations within a 5.22 mi radius).

Manhattan Beach, with a 7% Asian population and only 1 KUMON facility in town for 2,1113 grade 2-6 students, outscores Palos Verdes on the 2004 test scores.

Jo Anne Cobasko
Save Our Children from Mediocre Math (SOCMM).

And I've read enough about other countries' curricula to believe this observation:

"The middle school is the crux of the whole problem and really the point where we begin to lose it," says William H. Schmidt, a professor of education at Michigan State University and the U.S. research coordinator for TIMSS. "In math and science, the middle grades are an intellectual wasteland."

Still, I'm not persuaded middle schools are entirely to blame for the middle school slump, necessarily.

Everyday Math in Schaumburg, IL

I'd been meaning to write about this for awhile now.

I met two retired teachers, a married couple, from Schaumberg, IL at the airport on my first trip to Chicago this summer.

I was working on problems from my Russian Math book, so we got to talking about school & about math, and the wife, who had been a first grade teacher, told me that Schaumberg has been using Everyday Math for 15 years.

They were one of the first districts to try it out, and their students' scores promptly went up by 3 times. So they adopted Everyday Math, and have been using it ever since.

The grade school teachers apparently love E-Math, and the parents don't seem to mind. There was a Schaumberg district mom sitting next to me, who said she couldn't help her daughter with any of her math homework because she didn't understand it. This wasn't a problem; she seemed to think it was natural not to understand anything your 4th grader is doing in math, and not to be able to help with homework. No complaints.

The middle school teachers were another story.

When I asked how the middle school kids were scoring, both grimaced & said, 'Their scores are terrible.'

Then the wife gave me the story on the middle school teachers. 'They don't want to change,' she said. 'They want to keep doing things the same way they've been doing them for 20 years.' Her husband nodded.

They were sure that if the middle school also changed curricula, those students would have high scores, too.

I started to say kids need to know fractions & long division to do algebra, but had to stop when the wife grew visibly alarmed, thrust out both her arms at me hands first, and said emphatically, 'I teach first grade. I don't know anything about that.'


Schaumberg, I learned from my brother-in-law, is the 2nd largest school district in the Chicago area, after Chicago itself.

update

THE STUDENT SHOULD BE THE UNIT OF ANALYSIS!

Tomorrow I'm reading up on Cargo Cults.

update update

parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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ClocksWithoutHands 12 Sep 2005 - 02:02 CarolynJohnston


This just in from Lamprey River, New Hampshire: kids will be learning a new way to tell time this year! This is a news article that parodies itself. From the article:

RAYMOND - Students at Lamprey River Elementary School will learn a new way to tell time this year, thanks to a math program called Everyday Math.

They will be learning to tell time from clocks that have no hands. At least the first time they spiral through telling time.

The research-based and classroom-tested program (which is also recommended by No Child Left Behind) will break with the traditional worksheet-centered approach and embrace a more hands-on strategy.

Except that the hands will actually be off. The clocks. At least to start.

Principal Jane Lacasse says that rather than teaching children basic computation facts, Everyday Math emphasizes concepts and making sure children understand why. The program is centered on a "spiraling curriculum," which means that instead of moving on to a new topic after the old topic has been completed, classroom teachers will keep coming back to topics that had already been studied and expanding on them.

Hence, we'll start in first grade with handless clocks, then add the hour hand, then the minute hand, then the second hand, and in fifth grade we'll take up money, starting with pennies.

For example, Lacasse said, in first grade, children might learn to tell time to the hour, while in second grade, when time-telling is revisited, they will learn to unravel the mystery of the clock to the quarter hour or to the minute.

"The mystery of the clock" used to be taught outright in first grade, didn't it? Never to be spiraled back to again? Why not just ditch the clock completely, send it the way of the slide rule? Telling time is so 20th century.

The school purchased Everyday Math from the McGraw-Hill Publishing Company, investing in new textbooks and workbooks (although assistant principal Dan LeGallo is quick to point out that "this is not a textbook program").

I'll bet they spent real money on those non-textbooks.

The school also had to retrain its personnel.

I'll bet they did! They had to train them to tell time from the handless clocks. Perhaps they told them that there were hands on the clocks that only the most virtuous people could see.

What on earth does it mean to be "recommended by No Child Left Behind"?

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EverydayMathLongDivision 13 Sep 2005 - 15:06 CatherineJohnson


Thanks to NYC HOLD I have a graphic of Everyday Math's substitute division algorithm. TRAILBLAZERS teaches the same approach, which it calls 'forgiving division.'

...instead of teaching long division, students are taught to divide numbers using the partial products method, a technique where children guess how many times a number goes into another and keep subtracting the guesses until they come up with the answer (see box). This method works, but it takes more time and doesn't allow the student to divide past the decimal point.

[snip]

Isaacs and others defend the alternative algorithms by explaining that they teach students how math works. The partial product method of division, for example, is a lot more transparent to students than the long division method.

I'm sure he's wrong about this. I found partial product division quite confusing myself when I used it.

otoh, I think partial product division might work as a teaching tool when used on simple demonstration problems. (I tried it on a complicated division problem and got completely lost mid-stream.) I might use a problem like 16 divided by 2 to show that division is repeated subtraction, analogous to multiplication being repeated addition.

I haven't tried it with any children just learning long division, but if I ever get a chance to, I'll take notes.

the honeymoon

Some parents like the program as well. "It's sort of incredible," said Susan Pottinger, whose son Theo attends kindergarten at P.S. 261 in the Cobble Hill section of Brooklyn. "For him it's great fun. He's fascinated by numbers. He sees patterns everywhere," she said. "He'll put shoes away and alternate shoes with sneakers and say, 'See I'm making a pattern with my shoes.' "

We parents (well, some of us) spend those early elementary school years in a wonderland. Then the you-know-what hits the fan in 5th grade.

source:
Weighing the Factors Does the City's Standardized Math Curriculum Measure Up? By Amy Sara Clark

update

Lone Ranger supplies this link to lattice multiplication, the method Everyday Math teaches children when they cover multiplication. Carolyn points out that lattice multiplication is distinctly opaque; it obscures rather than reveals the fact that multiplication depends on the distributive property.

Here's another link to lattice multiplication at Math Forum Carolyn posted awhile back.


why long division?

Milgram & Klein links:

• Why Long Division? speech by James Milgram, Stanford University
  
• The Role of Long Division in the K-12 Curriculum
  by David Klein, Department of Mathematics California State University, Northridge and R. James Milgram, Department of Mathematics, Stanford University
  

Everyday Math's alternative division algorithm
forgiving division
forgiving division, part 2
try this with forgiving division
who says long division is hard?
advice from Canada
Everyday Math division algorithm fighting innumeracy at CO
conceptual understanding vs numbers

keywords: Columbiajournalismstudent EverdayMatharticle

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WhatIsConstructivism 14 May 2006 - 17:18 CarolynJohnston


AndyJoy asked on this thread: Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithm for a problem or make children memorize facts?

The short answer is yes, but for the record, here is a fuller explanation. I think the best quick introduction to constructivism and its recent history in U.S. educational practice is Barry Garelick's An A-maze-ing Approach To Math, which appeared in Education Next this year. I'll excerpt a little piece of it to answer Andy's question, entirely without Barry's permission (but hopefully with his blessing).

Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering (and taking ownership of) the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.

Texts that are based on NCTM's standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches "mathematical thinking" rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without first teaching him to swim.

The Standards were revised in 2000, due in large part to the complaints and criticisms expressed about them. Mathematicians felt that the revised standards, called The Principles and Standards for School Mathematics (PSSM 2000), were an improvement over the 1989 version, but they had reservations. The revised standards still emphasize learning strategies over mathematical facts, for example, and discovery over drill and kill.

So how does this fine-sounding idea play out in the classroom? Kids tend to spend too much deriving everything from first principles. What gets sacrificed is time spent learning advanced skills, as Barry shows:

Concept still trumps memorization. Textbooks often make sure students understand what multiplication means rather than offering exercises for learning multiplication facts. Some texts ask students to write down the addition that a problem like 4 x 3 represents. Most students do not have a difficult time understanding what multiplication means. But the necessity of memorizing the facts is still there. Rather than drill the facts, the texts have the students drill the concepts, and the student misses out on the basics of what she must ultimately know in order to do the problems. I've seen 4th and 5th graders, when stumped by a multiplication fact such as 8 x 7, actually sum up 8, 7 times. Constructivists would likely point to a student's going back to first principles as an indication that the student truly understood the concept. Mathematicians tend to see that as a waste of time.

Another case in point was illustrated in an article that appeared last fall in the New York Times. It described a 4th-grade class in Ossining, New York, that used a constructivist approach to teaching math and spent one entire class period circling the even numbers on a sheet containing the numbers 1 to 100. When a boy who had transferred from a Catholic school told the teacher that he knew his multiplication tables, she quizzed him by asking him what 23 x 16 equaled. Using the old-fashioned method (one that is held in disdain because it uses rote memorization and is not discovered by the student) the boy delivered the correct answer. He knew how to multiply while the rest of the class was still discovering what multiples of 2 were.

Now, consider the constructivists' argument for allowing this lack of 'domain knowledge' to persist -- kids develop deeper understanding, 21st century skills, bla bla bla -- after having read KDeRosa's "Terminator essay" on math education.

That essay just puts this nonsense to death, don't you think?

p.s. from Catherine

I found the smart constructivism post.

Here are the 2 best passages.

Smart constructivism says:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**

Radical constructivism says:

It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.

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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!

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AnimatedLatticeMultiplication 18 Nov 2005 - 15:34 CatherineJohnson

extended problem

What ironclad rule have I just violated?

(I'm betting on Doug for this one.)

time's up

The answer is here.

OK, I should have read the Comments first

As predicted, Doug takes this one:

"To say that the animation was distracting to these users would be an understatement. It was downright irritating. ...

"... During at least one of our tests, while trying to answer a question about the lowest fares to England, an animated ad appeared with the text of "Lowest Fares To London." Not only did the user not click on the ad, he swore he never saw it. Somehow, the user had "masked" out the animation."

The language here is interesting: 'the user had masked out the animation.

My understanding of frontal lobe function—and I'm not entirely confident of this, so take it with a grain of salt—is that it requires energy to block out distractions.

'Ignoring' something is an action.

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LatticeMultiplicationWithCarrying 22 Oct 2005 - 16:31 CatherineJohnson






This explanation at Math Forum is the clearest I've seen. Perfect.


I'm too tired to think it through right now, but I'm not so sure the final point is right.....

'Doctor Mason,' at Math Forum, says:

Multiplication really takes three steps: multiply, carry, add. The method we typically use does the multiply and carry steps together. The lattice method does all three steps separately, so it's really easier! Centuries ago, the Germans had a method for doing all three steps at once. That method takes a lot of concentration!

But I think the method I left in one of the Comments threads also separates the 3 steps.

Doesn't it?


I'm going to keep an eye out for Dr. Mason.

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EverydayMathFramesAndArrows 23 Oct 2005 - 00:00 CatherineJohnson






from Anne Dwyer:

In a frame and arrow problem, the idea is to either use a rule to fill in the blank boxes or to use the data already in the boxes to get the rule. The trick is that two boxes have to be filled in next to each other so that the students can add or subtract to get the rule.

The problem should have looked like this:

9 ---- 16 ---- ? ------30.

The the students could have subtracted 9 from 16 and get the rule +7. Then they could have added 7 to 16 to fill in the next empty box.

By leaving two boxes in a row empty, the problem took away the students only known way of solving the problem. Adding letters to make it more clear:

9 ---- a ----- b ----- 30.

Since the arrows stand for addding a constant, the problem becomes:

9+c = a
a+c = b
b+c = 30

[T]he actual solution required the construction of and solution to three simultaneous equations. The only other way to do it is, you guessed it, guess and check.

Everyday Math to the rescue

Although TIMSS and other studies (e.g. Fuson, Stigler, & Bartsch, 1988) suggest that U.S. school mathematics lags behind Japanese and German curricula by a year or more, EM lessons are generally a year or more ahead of topics in other U.S. programs. Where traditional mathematics programs are slow and repetitive, Everyday Mathematics picks up the instructional pace, increasing both the depth and the breadth of the mathematics taught.

source:
An Analysis of Everyday Mathematics in Light of the Third International Mathematics and Science Study, by William Carroll UCSMP Elementary Component (pdf file)

OK, I have the answer to this one.

Other countries, when they introduce topics earlier than we do, see to it the students actually learn them.

8th grade algebra in New York state

On the face of it, the new Grade 8 content guidelines for New York state require that algebra be taught in the 8th grade. I know, because I asked Caroline to look them over for me last year. Here's what she had to say:

It's a fairly standard algebra 1 course, I think.

I was excited when I read that, because I thought it meant that even if I didn't manage to get Christopher into Phase 4, he'd be taking algebra in 8th grade anyway, because state standards now required algebra in 8th grade.

I was wrong.

The department chair told us that, yes, they would be teaching 'algebraic concepts' to all 8th graders. (I think she used the word concepts. Something like that.)

But none of the regular-track 8th graders would be prepared to pass Regents A, which tests algebra, after 8th grade. Only the Phase 4 kids would be prepared to take the Regents after 8th grade.

What would the regular track kids do in 9th grade, after being exposed to algebraic concepts in 8th grade?

They would take algebra.

That's the plan.

spiraling is a waste of time

The idea that introducing advanced concepts before students are ready is a good thing is ludicrous on the face of it.

Singapore Math doesn't it.

Saxon Math doesn't do it.

Russian Math doesn't do it.

A good curriculum introduces a new topic at precisely the moment a student is ready to learn it, then makes sure the student does learn it.

That's the secret to high TIMSS scores.

Not dabbling in frames & arrows problems that require a 3-simultaneous equation solution in 3rd grade.

bonus quote

Caroline also said, in the same email:

What the heck does item 8.A.5 mean? I have no clue.

Beats me.

8.A.5 Use physical models to perform operations with polynomials

Guess I'm gonna have to find out before Christopher hits 8th grade.

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LatticeMultiplicationAtIllinoisLoop 08 Dec 2005 - 15:06 CatherineJohnson



Becky C reminded me that Illinois Loop has a scathing review of TRAILBLAZERS posted (I've read it at least twice & am due for another go at it).

When I clicked over to the site I found this:

"Yes, New-Math is multiplying, but I am sorry to report that too many children are not learning to multiply with New-Math. ... Multiplication is not all that difficult if one learns the multiplication tables and the logical, precise algorithm for the process. One day I was teaching traditional multiplication when one of the special education students wanted to show me the process she had been taught. Her problem even shocked me, and luckily I had my camera with me.

source:
New Math Multiples by Linda Schrock Taylor



For some reason I've come to love images of lattice multiplication. I'm forming a collection. Any minute now I'll be bugging J.D., Doug, Dan, and perhaps Carolyn, too, to make me one of my very own!

(Just kidding. I do love looking at them, though.)

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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

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SheddingTearsOverEverydayMath 06 Dec 2005 - 21:02 CatherineJohnson



from Joanne Cobasko of SOCCM:

The email below came from a CVUSD parent. Names and sexual identities have been changed to protect the innocent and guilty.





Another Everyday Math Crying Story - Discovery method strikes out again

Working with my 2nd grader on her math homework - she becomes frustrated because she isn't being taught the algorithms that are needed to solve the problem. She sometimes gets so frustrated she cries. (name of curriculum director) should be fired for installing this crappy math curriculum. The one problem she cried on was:


91 — unknown = 45.


The teacher didn't instruct her to put the numbers in a column and subtract:

  91
 -45
  __
  46

How are the kids supposed to know how to do this without being taught? How is a kid supposed to solve the problem? My daughter's classmate wanted to construct a number grid writing all the numbers between 45 and 91 to try to solve it, her mother said. These poor kids whose parents are not helping them with math at home are going to be lost.

Heresay at (School using Everyday Math) is that the teachers aren't making the kids do the ridiculous algorithms EM teaches.

Supposedly a kid in Mrs B's 5th grade class who was a straight A student in math is now getting D's because Mrs. B isn't explaining the EM method well enough. What a shame these kids have to suffer through EM.

You know the kids will say they like the program because they just play games and don't memorize the math facts.

If you follow the logic of EM, why then should the kids have to memorize spelling words if they can just use spell check on the computer?

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ChangingDeckChairsOnTheTitanic 10 Jan 2006 - 16:21 CatherineJohnson


from Illinois Loop comes word that &mdash:

At one point, Oak Park District 97 used the merely mediocre Scott Foresman Addison Wesley "Math" series.

Then the district jumped into that land of fuzzy math with both feet by adopting Math Trailblazers.

In May 2005, a parent reported to us that D97 "is leaving Trailblazers behind in Fall 2005 to go to Everyday Math for grades 1-6."

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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 result