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 try to be rigorous, but they would use examples (like automobiles in the street for "sets") which were almost OK, but in which there were always some subtleties. The definitions weren't accurate. Everything was a little bit ambiguous -- they weren't smart enough 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 every child 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 an utterly useless thing. If you can do it, maybe it's entertaining; if you can't do it, forget it. There's no point to 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 vaguely right -- 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't quite understand what they're talking about, I cannot understand. 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.