Math Texts: The Horrors, The Horrors

Everybody complains about Common Core. Before that, the New New Math. Before that, the New Math.

Parents seem to sense that “The textbooks in my day were not too bad, but these new ones are just off-the-charts horrific.” I’d say they’re only half-right. For generations, textbooks have been really bad. Here is an article about Dr. Feynman’s experiences in 1964 – about 50 years ago: Judging Books By Their Covers. Feynman is funny, acerbic, and observant. In his words:

[T]he 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. […]

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!

Not being an economist, Dr. Feynman found the causes difficult to perceive. I’d point to at least two reasons. First, the problem of concentrated special interests. Textbook publishing is a special interest; nowadays, it is estimated that K-12 textbooks are an $8 billion business in the USA.

Second, the entire business of K-12 education in America is dominated by governments; between 80-90% of American children attend government schools. This leads to the Economic Calculation Problem: the inability to effectively calculate what parents, children, and teachers want, nor how to provide it efficiently. Decisions are made for political reasons, not economic reasons. Worse than this – even in a time when there were many small school districts, and enough freedom for the Democratic process to sort of work, many important decisions – such as textbooks – were made at the State level by a few people, whom the textbook publishers could lobby – see Feynman’s article, above.

I [Dan Greenberg] had been involved in developing the “new math,” and had come to hate it. Back then when we were working on it — young academicians of the Kennedy post-sputnik era — we had few doubts. We were filled with the beauty of abstract logic, set theory, number theory, and all the other exotic games mathematicians had played for millennia. I think that if we had set out to design an agricultural course for working farmers, we would have begun with organic chemistry, genetics, and microbiology. Lucky for the world’s hungry people that we weren’t asked.

I had come to hate the pretensions and abstruseness of the “new math.” Not one in a hundred math teachers knew what it was about, not one in a thousand pupils. People need arithmetic for reckoning; they want to know how to use the tools. That’s what my students wanted now.

I found a book in our library, perfectly suited to the job at hand. It was a math primer written in 1898. Small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and swiftly.

I love math, aced all sorts of courses – including AP Calculus – but I agree with Greenberg’s assessment. So would Feynman, as you can find in his Judging Books By Their Covers excerpt. I have been unable to locate the 1898 math primer used by Greenberg, but have seen others of that era; they do not strive to turn every student into a professional mathematician, but into one who is competent with ordinary arithmetic calculation. For most people, this is a perfectly adequate stopping point. Truth is, about half of all high school graduates don’t even learn that much. They learn confusion and despair; they do not learn how to compute sales tax or a tip. These skills are not rocket science; Greenberg relates how his students easily learned 6 years worth of arithmetic with just 20 hours of classroom instruction.

By trying to accomplish too much, we’re doing it wrong. We include bits which simultaneously tantalize the brighter students, and offend them by being so utterly wrong, to a discerning mind, and confuse other students, by being beyond their powers of abstraction. In this way, we shortchange almost all students; their retention of important math concepts declines, and we are seldom informed enough about politics and economics to understand why the political allocation of resources to education must be inherently flawed.

If it can be done at all, it would be best done by appointing a competent and benevolent dictator, such as Feynman – but the political question is insurmountable – how shall we determine who should be dictator?

In a market-organized system, many parents and teachers make interdependent decisions, sifting through information, trying this or that, and rejecting inferior alternatives. Each decision-maker is, for a small domain, a “benevolent dictator” – and each has skin in the game, something to lose if the decision is wrong. Government-controlled systems don’t work that way; they respond to political, not economic pressures. Some of those political pressures have very little to do with the interests of parents, teachers, and students.

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