kitchen table math, the sequel: 2nd exposure

Friday, February 9, 2007

2nd exposure

Yesterday Ms. K taught a lesson on dimensional analysis.

The last time she taught a lesson on dimensional analysis was March 10, 2006.

Today is February 9, 2007.

According to the math department an 11-month gap between a first exposure and a second exposure is fine.

It's more than fine, actually.

If a student has been exposed to a topic for one week in 6th grade, and then again for another week in 7th grade, he should be ready and able to take a test.

And not just any test, either. He should be ready and able to take a complicated test filled with multi-step first-applications of the topic or skill.

I'm not surmising this, by the way.

Ed and I were directly told this by the math chair, who was defending Ms. K's latest test which half the kids had hosed, and which we had no interest in discussing in any event no matter how many kids hosed it. We've given up on Ms. K's tests. We've given up on Ms. K! We'd come to discuss curriculum and pedagogy; the math chair had come to defend the test. Under no cricumstances, she said, would she discuss curriculum and pedagogy with a parent. Any parent.

So she discussed the test and we discussed curriculum and pedagogy.

That's how we know the chair of the math department thinks 11 months between exposures is fine and the kids should be ready to take a test.

This is the kind of thing that gets me even more revved than I already am.

I'm handing this one off to Mr. Engelmann:

Typically about 60 school days pass before any topic is revisited. Stated differently, the spiral curriculum is exposure, not teaching. You don't "teach" something and put it back on the shelf for 60 days. It doesn't have a shelf-life of more than a few days. It would be outrageous enough to do that with one topic-- let alone all of them.

...Don't they know that if something is just taught, it will atrophy the fast way if it is not reinforced, kindled, and used? Don't they know that the suggested "revisiting of topics" requires putting stuff that has been recently taught on the shelf where it will shrivel up? Don't they know that the constant "reteaching" and "relearning" of topics that have gone stale from three months of disuse is so inefficient and impratical that it will lead not to "teaching" but to mere exposure? And don't they know that when the "teaching" becomes mere exposure, kids will understandably figure out that they are not expected to learn and that they'll develop adaptive attitudes like, "We're doing this ugly geometry again, but don't worry. It'll soon go away and we won't see it for a long time"?

The Underachieving Curriculum judged the problem with the spiral curriculum is that is lacks both intensity and focus. "Perhaps the greatest irony is that a curricular construct conceived to prevent the postponing of teaching many important subjects on the grounds that they are too difficult has resulted in a treatment of mathematics that has postponed, often indefinitely, the attainment of much substantive content at all."

War Against the Schools' Academic Child Abuse, pp. 108-9

The good news is, I spent the past week having Christopher do dimensional analysis problems.


I've been teaching Christopher how to use unit multipliers off and on since January 24, 2006. It's been more off than on, extremely sloppy teaching.

But it's been "on" enough that he always has some residual memory when I wake up one day and remember I haven't given him any practice on unit multipliers in a great long while.

I desperately need an afterschooling drill-and-kill book.

I need a book that has pages and pages of dimensional analysis problems of all kinds, along with pages and pages of various multi-step complex problems using algebra, geometry, baby statistics & probability, stem and leaf charts, etc. - I need it all.

In one book.

Anyway, about a week ago I started having Christopher do dimensional analysis problems every day. Five or six of them. My goal this time, and I'm sticking with it until it happens, is for Christopher not only to be able to do dimensional analysis problems, but to do them fast.

We're going to carry on doing dimensional analysis problems until the state test in March; then I'm going to write on my calendar the next date he should do some more of them.


when is that date?

how long am I supposed to wait?

how long can I wait?

I bet Engelmann knows.

One of these days I'll get around to reading his book.

After Christopher gains speed and accuracy I am going to carry on having him do dimensional analysis for the next 2 years so he'll remember unit multipliers for the rest of his life.


Oh, fine.

I can no longer find the Dan Willingham article I was positive said that if you study the same thing 3 years in a row you remember it forever.


The good news is that because I just spent a week having Christopher do dimensional analysis problems he was able to do Ms. K's overly-complicated homework (multi-step dimensional analysis word problems) with ease.

In fact, multi-step dimensional analysis word problems were exactly what he needed.

I hope this is evidence I'm beginning to channel the mind of Ms. K.

Life would be a lot easier around here if that were the case.

rules for installing a new curricula


Instructivist said...

"Anyway, about a week ago I started having Christopher do dimensional analysis problems every day. Five or six of them. My goal this time, and I'm sticking with it until it happens, is for Christopher not only to be able to do dimensional analysis problems, but to do them fast."

Where do you see the major stumbling blocks?

When I was teaching DI to 8th graders some of the hurdles were understanding that conversion factors like 1 ft/12 in mean one and that we are taking advantage of the identity element for multiplication. Another hurdle was to figure out which unit of the CF should be in the numerator and vice-versa. I thought I had developed crystal-clear strategies for a foolproof approach, even though the approach didn't sink in easily.

I always insisted on writing out each step and wrote the direction of the conversion on top of the problem with an arrow to minimize confusion, e.g. sec --> hours. Not all students were converts to my approach to conversion.

Catherine Johnson said...

Just re-read this post: 6.5.2009

C.'s last day of school was yesterday. His freshman year! Over already.

Maybe I'll see if he can solve a problem using dimensional analysis sometime today...

heh heh

Catherine Johnson said...

I re-read the article after reading Andy Isaacs' comment on Everyday Math & distributed practice.