Comments

Wow.

What a fantastic post.

And so rich -- this post opens up so many areas, like the profound oppportunity costs incurred in spending years of a child's young life learning multiple ways to do multiplication.

That one especially, the flagrant disregard for the value of a child's time, eats away at me.

Childhood is so short.

My oldest, Jimmy, is 18.

And my two youngest, Christopher and Andrew, are turning 11.

In just a moment, it's over.

Constructivists speak of time -- and I have seen this myself, in their prose -- as if it were infinite.

It's not.

The ideologues will have many more children to teach.

But this is your child's one and only childhood.

He won't have it to do over.

-- CatherineJohnson - 24 Jun 2005

My son, Daniel, is 12. He was in general ed classes for K-3. They used Everyday Math, but he was pulled out for Resource Room help during math. In his elementary school, they do not use EM for kids who need help. They use traditional math only. This is true in the special ed class that he was in for 4th and 5th grade too.

My daughter just finished second grade. She struggles with the EM curriculum. Our elementary school does not give grades. They give a sheet which shows whether your child has is beginning, developing, or secure in each EM topic. So if there is a topic that I think is inappropriate, I help her with the homework so that it is done, and I don't worry about the B,D or S on the report card. They don't worry about it either because they figure she will see it again.

I find the real problem with EM is when a topic is so far above their heads that they just tune out for the lesson. It is always hard to tune back in. For example, in second grade, they were teaching equivalent fractions. If the child does not understand it based on the picture that EM gives, their is no other way to explain it since they haven't had multiplication or division yet.

I have talked to my daugher many times about how some units in EM should not be taught yet. I tell her that it is not her fault that she doesn't understand it and that she will understand it later. What works best is when I tell her, "You'll learn that in 4th grade and then you will understand it." Intuitively, she knows that some of the stuff is supposed to be taught in higher grades.

-- AnneDwyer - 24 Jun 2005

I had no idea what was going on in the earlier grades in Everyday Math. Equivalent fractions in second grade!

I hate the idea that the kids are tuning out for class. That so easily becomes a trained-in response to lectures (and I oughta know).

One thing that bothered me about EM was the huge emphasis on statistics and data landmarks, They revisited that topic every single year, mostly recovering ground they had already covered. furthermore, they were unable to teach computation of the average because the kids hadn't learned to divide yet. Statistics at that level just isn't that deep; if they covered it thoroughly just once, in middle school, kids would know all that they need to know.

Your kids are so lucky to have you.

-- CarolynJohnston - 24 Jun 2005

"Secondly, in elementary school it doesn't matter what grades your kid gets; it doesn't impact his future until he gets to high school,..."

Catherine wrote about "phases" for her son in 5th/6th grades. I have only seen tracking (?) in math begin in 7th grade. Perhaps she can comment on what these phases are meant to do and whether they do influence what phase or track the child enters in high school. It would be one thing to hold a child back a year in school because they are not ready yet for the material (but still getting to algebra in 8th grade), but it's quite another to track them based on early ability into some permanent lower expectation track that they can't get out of without great effort.

I use Singapore Math with my son at home, but I expect him to do all of his Everyday Math schoolwork. He is going into 4th grade and I know that it's going to get worse. My son will have to hear me grumble and mutter a whole lot more.

"One thing that bothered me about EM was the huge emphasis on statistics and data landmarks,.."

I have seen this in a number of NCTM-type math programs. It starts in first grade. I remember one homework where my son had to ask us parents and brothers and sisters (none) what their favorite ice cream is. Data set is 2. Then he had to draw a picture of each type of ice cream cone and write the number under each picture. This is a school that doesn't force the mastery of adds and subtracts to 20 until the middle of third grade.

Actually, what I have seen is a lot of wasted time collecting data and the most they can do is find the median, mode, and range. This is all just fine, but what topics are they eliminating to do this? As you said, this could all be covered in a later grade in a more appropriate, efficient, and rigorous fashion.

Another type of problem that is common for NCTM-type math is the combination problem, such as - how many different ways can you arrange the letters in your name. This has to be done without ANY knowledge of combinations or permutations. It's a classic constructivist-type problem. Solve a problem where you don't have a clue as to how to solve it. Then, there are the probability problems when they don't know about fractions and decimals. Constructivism is neither necessary or sufficient, and it wastes a lot of time.

-- SteveH - 24 Jun 2005

Here is something that happened to my daughter in first grade in EM. I regret to say that I did not address this with the teacher.

EM loves the rule boxes. The rule box (I'm not sure if that is the official EM name) is when there are input numbers, a rule box and output numbers. So, the rule box may be add 2. Then the student has to add 2 to every input and put it in the output chart. Sometimes, the input and output were given and you had to find the rule. Such was the case with this one particular problem. After doing a full page of rule boxes with add and subtract a constant, there was one particular problem I couldn't solve. So I sent her back to school with a blank problem. The answer came back that we were supposed to double the input!!! So now, we change the definition for rule boxes for the first grade: instead of add or subtract a constant, we are now asking them to add a variable!! I couldn't believe it. I really think that the teacher should have left that problem out. It did not at all match the other problems and completely violated its own rules!!! I sometimes think that we should send complicated mathematical proofs back for these teachers showing them why certain problems are not mathematically correct.

-- AnneDwyer - 25 Jun 2005

I remember the rule boxes; they do those all the way through 5th grade.

EM routinely throws curve balls like this without warning through all the grades.

-- CarolynJohnston - 25 Jun 2005

"EM loves the rule boxes."

AAAAARRRRRRRGGGGGHHH! Rule Boxes are stupid, stupid, stupid, stupid. My son has heard words to this effect when I look at his homework. It's almost as if they really don't want to jump right in and do real math. They have to find anything, ANYTHING, else that is different (with vague or ambiguous function rules), just to be different. Lattice Method anyone? Can anyone explain what it is about the Lattice Method that leads to more understanding than the traditional algorithm? EM - different because the same doesn't sell.

-- SteveH - 26 Jun 2005

You could really be right about that -- that EM simply strives to be different; anything goes as long as it's different.

I think they're also smitten by the new tricks they teach -- things like the lattice method, pan-balance problems, and those little diagrams they use to teach multiplication of fractions.

-- CarolynJohnston - 26 Jun 2005

We had TONS of rule boxes in SRA Math, which is not an NSF-funded curriculum.

What were they called?

They were called 'machines'--function machines?

I can't remember.

I wasn't horrified by them, and I don't remember suddenly being given a function machine with a brand new rule (though I do remember, last fall, having to do one that I couldn't for the life of me figure out using real algebra... That was an interesting moment for me, because it turned out I needed to use the distributive property and I couldn't see it. I spent hours wrestling with the problem, and finally my brother in law said, 'use the distributive property. It was a classic experience of what Willingham calls 'inflexible' knowledge. I knew the distributive property perfectly well, could recite it in my sleep, could do 'mental math' distributive property problems in a flash. But I didn't recognize it once I was using variables.

-- CatherineJohnson - 26 Jun 2005

Catherine wrote about "phases" for her son in 5th/6th grades. I have only seen tracking (?) in math begin in 7th grade. Perhaps she can comment on what these phases are meant to do and whether they do influence what phase or track the child enters in high school. It would be one thing to hold a child back a year in school because they are not ready yet for the material (but still getting to algebra in 8th grade), but it's quite another to track them based on early ability into some permanent lower expectation track that they can't get out of without great effort.

I'm going to write a post about this, because it's very interesting.

The 4-track 'phase' system here in Irvington seems to have 'evolved' accidentally, by which I mean that no one in the school ever intended, going in, to have a 4-track system starting in 3rd grade.

Steve is right that the 4-track system slotted kids--and this happened to Christopher--into a slow-track math at the age of 8 that took phenomenal effort to get out of.

Last summer we were doing two Saxon Math lessons a day. Two. These are heavy-duty lessons in terms of the amount of work involved, though not in terms of the amount of material covered, which is always 'bite-sized.'

Once school began we were still doing 1 complete Saxon lesson a day, along with his SRA Math homework from school.

We did Saxon lessons on both days of the weekends, too.

We were working 7 days a week to try to get him onto the accelerated track. (The accelerated track is the only group of kids who take and master algebra in the 8th grade. I say 'take and master' because the new plan is to have the kids 'take' algebra in 8th grade, but not master it. They will not be able to pass the Regents Exam at the end of 8th grade, but will re-take algebra in 9th.)

Hmm.

I see I'm writing a full post anyway ... I think I'll break off and wait 'til I have time to do a real post.

In any case, the district did not plan to have a 4-phase system starting in 4th grade; the original intent, I believe, was to pull out a few obviously gifted kids for enrichment.

But then, according to school lore (and I have heard this from administrators, teachers, aides, and other parents) 'pushy parents' insisted that their kids should also be in the advanced group.

Administrators and teachers bent before the onslaught of parents (and we parents can be pretty onslaughty--I'm sure this part of the oral history is true) and pretty soon Phase 4 was oversubscribed.

This year 40% of the 5th graders were in the fast track class.

Interestingly, the teachers seemed to universally believe that 50% of the class was in Phase 4.

You get into the folk psychology of numbers once you hit 50%: I have heard teacher after teacher say, 'Come on. Fifty percent of Irvington kids can't possibly belong in advanced math.'

Well, it wasn't 50%!

It was 40%!

(It's true, of course, that if you're defining 'advanced' in terms of a bell curve, then 40% of the kids wouldn't belong in advanced math, either.)

Eventually we came to a pass where the school had decided to rectify the situation, end tracking in the early grades, and, by the by, bring in fuzzy math.

The Phase 4 parents--300 of them--fought a battle over tracking, and lost.

I didn't oppose them, but I didn't join them, either.

I didn't know the research on tracking (and didn't trust that the research would be any good in any case) -- and tracking didn't seem to be good for Christopher, who was defining himself as a '3' not a '4.'

When I taught my Singapore Math class in the after-school program the kids constantly talked about whether they were 3s or 4s. The 4 tracks, as far as I could tell, were definitely having a detrimental effect on kids' confidence, self-esteem, liking for math, etc. I didn't necessarily think that should rule them out, but I needed some very good evidence that our kids were benefitting from an off-setting gain.

Unfortunately, the tracking fight ended up being a case of misdirection.

I had no idea that doing away with tracking meant bringing in TRAILBLAZERS.

If I had, I would have been on the front lines.

-- CatherineJohnson - 26 Jun 2005

Our school had two different tracks, and they weren't as clique-ish as the Irvington tracks. The idea was that the tracks would be fluid -- they were teaching Everyday Math, and giving those pre-tests that they give, and trying to place kids in either a regular or advanced group based on the results of the pre-test. It didn't work out very well, though, and in the second half of this year they gave up tracking completely.

That would be my only concern about simply dumping the fuzzy curriculum in favor of a supplementary curriculum -- having the child tracked into a slower curriculum. I don't know how realistic this is, though. The only data point we have is Christopher, who moved up in the tracks when he had good supplementation.

-- CarolynJohnston - 26 Jun 2005

The school seemed to have done their homework, and apparently 'no one' (I know this includes Singapore) tracks kids in grade school.

Singapore goes to a two track system that sounds fantastic in...8th grade?

I'm not sure; I'll look it up.

I'd put money on it that the reason for all the tracking woes in Irvington is the fact that American math curricula are too slow for everyone.

In other words, an accelerated track in America isn't really accelerated.

So all the parents who were intuiting that their not-brilliant child nevertheless belonged in fast-track math were correct.

That's what happened to me once I read MATH COACH.

I took Christopher's placement for granted; it never crossed my mind that he should be 'advanced' or 'accelerated.'

He doesn't seem like a natural-born 'mathhead.'

But when I read Wickelgren saying that average kids in other countries take algebra in 8th grade, my point of view changed completely.

My big concern, now, with eliminating tracking is that everyone is going to be on a sub-par track, whereas before the kids who managed to make it into 4 at least managed to be on the same schedule as the rest of the world.

Trailblazers, unfortunately is sub-sub, since all the fuzzy curricula go slower than the non-fuzzy American curricula, which are already slow.

-- CatherineJohnson - 27 Jun 2005