kitchen table math, the sequel: how constructivists reject tracking

Saturday, May 26, 2007

how constructivists reject tracking

I reject tracking, too, btw.

I have now discovered the correct term for the form of grouping I support: "flexible ability grouping."

I assume flexible ability grouping is what Engelmann practices - though he's a touchy guy; he may not wish to use the same term Robert Slavin uses (I probably don't blame him ...)

The goal of flexible ability grouping is accelerated learning for all of the kids in all of the groups. That is the point: the fastest learners learn faster, the medium learners learn faster, and the slowest learners learn faster.

The other goal of flexible ability grouping is (I gather) to get rid of the lowest track - which appears to be entirely possible. I'm not sure how many groups you'd end up with in an ideal situation - I'm guessing you'd end up with 2 core groups once everyone has acquired a schema for the subject being studied. (And see: Engelmann on mastery as a leveler of individual differences, and Gentile on fast and slow learners). But I'm not sure. (I wonder if Ken knows.)

Then you'd have outliers: gifted kids on one end, developmentally disabled kids on the other.

So.... flexibile ability grouping. A good thing.

I'm just finishing Cheri Pierson Yecke's book The War on Excellence, and had been assuming that her account of the middle school movement's campaign against tracking & grouping summed up the standard objections. The arguments of Slavin & c. have been mostly focused on social equity, equality of outcomes, and so forth.

Turns out the constructivist take on tracking is even worse.

Tracking Criticized

When was the last time Tom Loveless worked in a public high school? His protracking bias in "Will Tracking Reform Promote Social Equity?" (April 1999) was all too evident. He just doesn't get it. Tracking simply doesn't belong in the school reform movement.

First, students in tracked classes are not necessarily the best and the brightest. Often, they are the "good" students who have exemplary behavior, text study and memorization skills, and parental involvement.

Second, data assembled in the early 1980s to support Loveless's tracking sympathies hardly reflect today's volatile, technology-savvy, and multicultural student populations. When teachers believe that all students can learn and be successful, challenges abound in every classroom.

Third, once the "good" students are removed from the untracked classes, their test scores may remain constant or rise slightly. But the remaining students, having lost the role models, standard-bearers, and high achievers, show declining scores. The schoolwide effect is a significant drop in test scores.

Fourth, what does it say about a school if its value and reputation rest on the high achievements of a select few students? I certainly wouldn't want to teach there.

Detracking is not a mistake, as Loveless claims. Rather, it is an imperative. Further, there is no point in conducting rigorous research on tracking in schools that are not employing authentic teaching and assessment practices that meet the needs and talents of all students. Tracking is a self-indulgent cop-out that caters to the convenience of a few at the expense of the inconvenience of the many. I hope that the schools of the future will have neither the time nor the inclination to track. They will be too busy focusing on high achievement for all students.

—Judith A. Gray, Science teacher, Henry M. Jackson High School, Everett, Washington


1. the smart kids aren't smart

This passage speaks to the issue of whether constructivism "positions" the ur-student as not very bright - an idea one of Paula's comments made me wonder about. Assuming I'm getting Paula's situation right, her kids (or at least one of her kids) tests gifted and is being perceived by the school as having learning problems. (If that's wrong, let me know. I'll revise.)

Here we have a constructivist position statement on tracking directly asserting that students in the top track aren't the brightest students. So.... there it is. This author isn't talking about a particular student she's encountered, but rather making a global assertion that kids who do well in school aren't the smartest kids.

You have to sit with that for a moment to realize how radical it is.

It's certainly true that placement in the top track has always left out a subset of the smartest kids. I suspect that a certain number of Asperger's kids probably get missed, for instance. Black and Hispanic kids with the ability to be in the top track probably get mulched -- or self-mulched -- all the time.

But I don't think it's ever been true that the top track in a school systematically includes kids who don't belong there while systematically excluding kids who do.

I don't think it's even possible.


2. chaos means challenge for all

The smart-kids-aren't-smart theme is pretty bad, but the notion that a constructivist classroom is so seething with activity that at any given moment there are dozens of challenges being offered to students particularly horrifies me.

Good God.


4. gotta keep those scores up

I think we all must appreciate an avowed constructivist making an appeal to Schoolwide Test Scores to justify heterogeneous grouping.


5. on the other hand ...

On the other hand, standardized test scores tell us nothing, so forget the research.


What a mess.

Nevertheless, I am now wondering whether there is an aggressive strain in constructivism, a wish to take these little memorizers down a peg or two or three.

After all, as this science teacher (science teacher!) points out, who are the kids typically considered the brightest in any school setting?

They are the fast learners, which means the fast rememberers.

The memorizers.

The memorizers with the good behavior and the parental involvement. Don't like 'em.

We've heard quite a lot of this rhetoric around here. A lot. That was one of the reasons given for de-tracking math in K-5. The kids who were tracked into Phase 4 were "just" good at memorizing. Then when they got to 4th grade and had to understand math (apparently understanding math used to begin in 4th grade) they couldn't do it. So they and their parents were terribly disappointed because here everyone thought they were good at math but they really weren't.

etc.

I've had a bad feeling about constructivists and constructivism for a long time -- bad beyond the dread that we won't manage to escape K-12 before it is completely submerged in the constructivist tsunami that is bearing down upon us. I always get the feeling that I'm looking at masked aggression -- a feeling I never get with Engelmann, to pull a random non-constructivist name out of a hat. Engelmann is a wild man with a horrible mouth on him, but reading his stuff I feel, always, that what you see is what you get.

You don't get a lot of masked aggression with Siegfried Engelmann. Let me put it that way.

With constructivists, often enough, you do.


constructivism as masked aggression
the 80% rule

13 comments:

SteveH said...

I don't like the term tracking because it means different things to different people. Perhaps the problem with tracking is that it sounds so permanent. This is wrong in the early grades, but it's what happens in high school.

The problem in the lower grades is that any sort of non-flexible (non-changeable?) grouping tends to be permanent. We talked about this before. You want a slower pace, not a different curriculum. You don't want it across the board, but subject-by-subject.

The traditional model for elementary school (K-6) is just one track (no tracks?) with specific grade-level expectations. Everyone (for the most part) is treated equally. If you don't meet expectations, you get held back or you have to go to summer school. If the expectations are high enough, waiting until 7th grade to separate by ability is a reasonable thing to do. Many schools still do this.

What has changed since I was growing up is full-inclusion and the idea that schools can have both very mixed-ability groupings (for social reasons) and high expectations. The only way they can do this is to change the definition of education (and intelligence) in the lower grades, K-4 especially.

Education is changed so that content and mastery are minimized; that memorization is not important.


"Nevertheless, I am now wondering whether there is an aggressive strain in constructivism, a wish to take these little memorizers down a peg or two or three."

I don't know if it's constructivism. I think it has to do with the mixed versus homogeneous grouping of kids. They want very mixed-ability groups. They can't do that if they accept the idea that fast learners (memorizers) are smarter. This is exactly why my son's first grade teacher said to us that: "Yes, he has a lot of superficial knowledge." when we said (in first grade) that he could find any country in the world. That is why she talked about looking for "voice" in the kids' writings instead of whether they spelled correctly of if the writings made any sense at all.

"The memorizers with the good behavior and the parental involvement. Don't like 'em."

This is my son. His memory borders on scary. I never got the feeling that the teachers didn't like him. He isn't weird about his skill, but teachers seem to go out of their way to tell us that (in effect) there is a lot more to education. Unfortunately, the "lot more" tends to dominate the the classroom agenda.

Maybe this is a chicken-and-egg problem, but my view is that constructivism allows them to treat all kids as intellectual equals. If they emphasize the content and skills portion of education, then they have no basis for keeping kids in mixed-ability groups. Constructivism doesn't come first, tracking by age comes first.

They just redefine education and intelligence. They've done it in math.

Instructivist said...

"I always get the feeling that I'm looking at masked aggression..."

The quote below from Eclectic Educator cites TERC's view of math before the advent of fuzzy math. When I read such views expressed by the fuzzies I get the feeling that I am looking at a slew of highly undesirable characteristics. Not only aggression, but also ignorance or deliberate misrepresentation (dishonesty, disingenuousness, lying), insults and bullying to gain an undeserved advantage.

Here EE:

[The literature of reform math has changed history, painting a dichotomy wherein its proponents state that all former math teaching required memorization of algorithms without understanding and that students had to "check their brain at the door" before math class.

I didn’t invent that expression. The official TERC Investigations web site reads, "otherwise intelligent and curious children who check their brain at the door as math time begins." That’s how they characterize "math before TERC."]

PaulaV said...

Catherine,

You have it right about my third grader.

It is hard to tell exactly how the principal and vice principal group the students at my son's school. This has been my concern this year.

Is it tracking or flexible grouping? I am not opposed to grouping by ability as long as the work is the same and the kids are placed correctly. However, what startled me at the beginning of the year, was when I compared the level of work being done in three different classrooms, there were major differences.

For instance, one class was doing first grade math work. I copied the worksheet my son brought home and googled to see the publisher. It was from a first grade workbook. I then compared the work my neighbors kids were bringing home. So one group was below grade level, one at grade level and one above.

If my child is doing below grade level work in math, I need to know why. Only after my son was placed in the low-level class did I go to the principal and ask what happened. It is then I learned he had a disconnect when it came to math and he couldn't follow three step directions. There were no interventions in second grade. The report card did not indicate there was a problem. When I checked his school record, he met all the math objectives for that year. There was no mention of not being able to follow directions.

I felt vindicated when I received the ITBS scores. In math on the ITBS, he was in the 80th percentile, 60th in problem solving and data interpretation. He was not tested in math computation because the county did not test this.

He took the ITBS when he in the low level class. I cannot imagine him having to sit there the whole year doing first grade work.

The principal, by the way, was totally against moving him. Although two other parents had moved their children and they landed in the upper level classes. I think this was based on the parents status at the school.

Anyway, I just would like my son to placed where he can learn. That is all I have ever wanted.

Catherine Johnson said...

"The memorizers with the good behavior and the parental involvement. Don't like 'em."

This is my son. His memory borders on scary. I never got the feeling that the teachers didn't like him.


I should clarify.

A few individual teachers have always disliked a few individual kids. That goes with the territory.

I've never felt that any of the teachers here, apart from she-who-cannot-be-named disliked C.

Exactly the opposite.

I have had other parents tell me that certain teachers dislike their kids - but this isn't a chronic issue.

I'm talking about a kind of global, overriding attitude running through a lot of these articles and letters to the editor.

Catherine Johnson said...

This is my son. His memory borders on scary. I never got the feeling that the teachers didn't like him. He isn't weird about his skill, but teachers seem to go out of their way to tell us that (in effect) there is a lot more to education. Unfortunately, the "lot more" tends to dominate the the classroom agenda.

Again, I think they're probably dead wrong about this.

Don't the "smart kids" tend to have good memories??

I had a fantastic memory when I was a kid; I have a pretty fantastic memory for a middle-aged adult whose memory peaked lo these many years ago.

AND.... I'm reasonably intelligent - I'm definitely a "lifelong learner" and a creative problem-solver. You can't write nonfiction books without being a lifelong learner and creative problem solver. That's almost the nature of the job.

If you look at the smart people you know, you're probably going to see a lot of people with very good memories.

I don't think that correlation can be an accident.

Catherine Johnson said...

I would say that Christopher has an excellent memory. I've always been amazed by his memory. When he was little I could be reading a nonfiction book out loud to him, he would seem as if he was paying no attention, and when I asked him what I'd read he could recite it back to me instantly in full detail.

He picks things up - gets them into longterm memory - amazingly fast.

That's what's gotten him through the Phase 4 class: very, very fast ability to memorize.

The school can talk all it wants about "understanding." The kids making it through the class are memorizing at top speed.

Watching Christopher it's crystal clear that Carolyn was right: you can memorize first, understand later.

Christopher carries on developing -- constructing?? -- understanding.

But first he memorizes.

If the course were taught differently, he might not have to memorize huge quantities of stuff every day. The development of conceptual understanding might go along with the development of longterm memory for math.

But it's not.

Catherine Johnson said...

John Lithgow was a friend of ours back in L.A. (his wife, Mary, was one of Ed's colleagues at UCLA).

John is extremely intelligent; went to Harvard; just super smart.

We went to watch one of the tapings for THIRD ROCK FROM THE SUN & watching him deliver a long intricate comic monologue perfectly and "by heart" was pretty astounding.

I've always had a good memory; I could easily memorize passages of prose to recite.... but I don't know if I could do what John was doing at the age he was doing it.

Again: brilliant guy, brilliant memory.

What does "brilliant memory" mean?

It means fast learner.

Which as far as I can tell means smart.

Catherine Johnson said...

Yes, "tracking" is taken to mean a permanent TRACK.

That's what was done to Christopher here in 3rd grade.

He was tracked out of calculus AND we weren't told.

Of course, the school is still attempting to keep as many kids out of calculus as possible.

Apparently "no one" takes Calculus BC because they teacher it in a shorter time frame than other schools do....

Catherine Johnson said...

I get the feeling that I am looking at a slew of highly undesirable characteristics. Not only aggression, but also ignorance or deliberate misrepresentation (dishonesty, disingenuousness, lying), insults and bullying to gain an undeserved advantage.

That's exactly the way I feel.

I'm sure I sound just as obnoxious to TERCites as they do to me.

And, in fact, at this point I am as obnoxious: this really is a math war.

The difference is that I am perfectly happy for them to teach TERC to their own kids and to the kids of parents who freely choose TERC.

Live and let live.

The reform math folks are not in the live and let live business.

Any time I see groups of people who are intent upon imposing their view on others by fiat I see aggression.

I'm pretty sure I'm right about that.

Tracy W said...

First, students in tracked classes are not necessarily the best and the brightest. Often, they are the "good" students who have exemplary behavior, text study and memorization skills, and parental involvement.

I'm puzzling over this one. Surely, due to the nature of the bell curve, a school will only have something like one to three kids who are the best and the brightest? After that, surely the remainder of the kids, no matter how smart and adept they may be, are not going to be the best and the brightest, just very good and very bright? I attended a high school with 180 in my year. One girl was the best and the brightest (it was a single-sex school), but there were quite a few others who were pretty darn smart. Does Ms Gray really think that there are any problems with providing say the top twenty at a school with an education that extends them? Was Kate really the only person in my year at my school who deserved a good education?

And if exemplary behaviour, text study, memorisation skills and parental involvement means a kid can learn more than they could be relying on pure natural ability, then what's wrong with teaching them more?

PaulaV said...

My son's memory is great. He remembers things in first grade like where he sat and particular questions and how he answered. He says he remembers everything as if it were yesterday.
Yet, his principal, commented he needed a "fire lit under him".

SteveH said...

"I don't think that correlation can be an accident."

I consider it to be (at least one type of) 'g' factor. I know that some claim that it can't be, but when I look at my son, I see his memorization ability linked to so many things. It's not a rote process. There is a big connection with understanding. I said years ago that he was a sponge for knowledge and that the school was feeding him with a teaspoon.

SteveH said...

"Any time I see groups of people who are intent upon imposing their view on others by fiat I see aggression."

Academic turf. If they admit that it's just opinion (and not "best practices"), then they have nothing left. Aggression is their way of defending their turf.

Preemptive parental strikes.

Helicopter parent stories.