Anyway, here's an excerpt and the whole chapter is here:

I can tell you from personal knowledge that California textbooks haven't improved.... much.... I do like the algebra book that Kieron is using. I understand that California is trying to standardize introduction of algebra in 8th grade. I see how they are doing it, because this book isn't really high school algebra. It moves at half speed from Jacob's which is what I used with the other kids. So one day Kieron learns to "transform" equations with a variable using addition.The reason was that the books were so lousy. They were false. They were hurried. They would

tryto be rigorous, but they would use examples (like automobiles in the street for "sets") which werealmostOK, but in which there were always some subtleties. The definitions weren't accurate. Everything was a little bit ambiguous -- they weren'tsmartenough to understand what was meant by "rigor." They were faking it. They were teaching something they didn't understand, and which was, in fact,useless,at that time, for the child.I understood what they were trying to do. Many [Americans] thought we were behind the Russians after Sputnik, and some mathematicians were asked to give advice on how to teach math by using some of the rather interesting modern concepts of mathematics. The purpose was to enhance mathematics for the children who found it dull.

I'll give you an example: They would talk about different bases of numbers -- five, six, and so on -- to show the possibilities. That would be interesting for a kid who could understand base ten -- something to entertain his mind. But what they turned it into, in these books, was that

everychild had to learn another base! And then the usual horror would come: "Translate these numbers, which are written in base seven, to base five." Translating from one base to another is anutterly uselessthing. If youcando it, maybe it's entertaining; if youcan'tdo it, forget it. There's nopointto it.Anyhow, I'm looking at all these books, all these books, and none of them has said anything about using arithmetic in science. If there are any examples on the use of arithmetic at all (most of the time it's this abstract new modern nonsense), they are about things like buying stamps.

Finally I come to a book that says, "Mathematics is used in science in many ways. We will give you an example from astronomy, which is the science of stars." I turn the page, and it says, "Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees . . ." -- so far, so good. It continues: "Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of . . . (some big number)." There are no green or violet stars, but the figures for the others are roughly correct. It's

vaguelyright -- but already, trouble! That's the way everything was: Everything was written by somebody who didn't know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don'tquiteunderstand what they're talking about, Icannotunderstand. I don't know why, but the books are lousy; UNIVERSALLY LOUSY!

x + 8 = 2

Then the next day he learns to transform using subtraction:

X - 8 = 2

A day later he learns how to manage multiplication and division:

2x - 8 = 2

Well, I'm exaggerating a bit but not much. This is what we used to call "pre-algebra".

I was worried upon hearing that he would have to take algebra this year in the charter, because I'd been following MEP which doesn't do traditional US pre-algebra and so I was afraid he'd be lost, but I needn't have worried.

It's good though. I'm not in a hurry with him. And as a pre-Algebra textbook, which is what it seems to me to be, it doesn't appear to be too bad.

I've always enjoyed these Feynman books too (except for the philandering, that is). His explanations of science are some of the most entertaining around. I think his description of textbooks gets at something important: The ideas imparted always seem to come to the students third or fourth hand, so the resulting lesson may not bear any relation to the original intent.

ReplyDeleteI got a typical hodge-podge 1970s education. I never knew what to expect from one year to the next, because it really ran the gamut. But I do remember enjoying the one alternative base activity we got.

I'm still fascinated with your algebra comparisons. Honestly, CZ and I took a break between Singapore math and Jacobs. There really didn't seem to be any new material in any of the books we looked at, and it gave her some time to read and learn music theory. Oh, we refreshed and practiced a bit, but perhaps the reason no one can seem to write a suitable textbook for middle school is because there really *aren't* a lot of new concepts appropriate for these years. (I could be wrong, but that was what I noticed.)

One more question: With your kids in the K-12 program this year, do you feel more like an administrator than a teacher? Perhaps not, since you still have young ones to shepherd along. But I do, and I confess the role makes me feel strangely idle and yet busy at the same time, and I'm looking for ways to make the role feel more natural. (Come to think of it, "idle and yet busy" sounds like Pieper's definition of acedia.)

One tiny point of clarification: We're not doing K-12, but just have a lot of outside classes, so I'm not as hands on.

ReplyDeleteI have changed roles Laura but I still seem to do a lot of direct teaching. With Kieron it's partly because this is his first year with the program -- it assumes a lot of skills and knowledge that he hasn't gotten. So I do a lot of filling-in gaps. Just as a recent example, they will assign a five paragraph history research report to be written over 2 days. He doesn't have that background. So I talk him through it.

ReplyDeletePlus, if he's going to do lit ana, he's going to do it RIGHT ;-) -- I try to interact with him to get him thinking about the reading, not just saying what he thinks they want to hear, or sitting there with a blank mind wondering WHAT they want.

I know a lot of other people who get where you are now, though; it's a little like I am with Sean my sophomore who is going to school. I still try to pay attention, but most of it is just him. There's still stuff to do, but it's different.

I went to school in the 80s, and I have no clear concept of how 'new math' is different from old math, or really why. I have only the blurriest memories of school math in general, except for grade 10 geometry, which was pragmatically spatial, and problem-solving, and I loved it.

ReplyDeleteGood thing, too. It's useful for sewing!