Math Wars

The math wars are heating up again. On one side we have the National Council of Teachers of Mathematics (NCTM) and on the other, distressed parents, social conservatives, and people who actually know some math - a motley crew indeed. At issue is the latest fashion in math education, promoted by the NCTM and variously known as "constructive math," "math investigations," and "whole math." A look at the NCTM's web page on statement of beliefs reveals a certain amount of motherhood and apple pie plus the following:

Students use diverse strategies and different algorithms to solve problems, and teachers must recognize and take advantage of these alternative approaches to help students develop a better understanding of mathematics.

This seems pretty inoffensive too, but in practice it means that students are encouraged/forced to invent their own algorithms and strategies rather than being taught those refined over the centuries. There is a strong hostility in the program to any kind of memorization or rote learning. The idea is that instead, the students will learn problem solving skills and critical thinking.

Who could object to this? Put me down for one. I don't think that one can learn problem solving skills or critical thinking without a command of the facts - the essential substrate upon which thought acts.

Today's New York Times has this story by Samuel G. Freedman. The opening paragraphs set the theme:

LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician.

So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.

Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problem-solving formulas that constructivist math denigrates as mindless memorization.

As Freedman's story makes clear, this is not an isolated case. Superintendants and teachers mouth the official NCTM propaganda. Parents complain because they don't understand the new math pedagogy. Learning the multiplication tables is unacceptable "drill and kill."

This is all very familiar to those who were involved the reading wars of past years. The same denigration of conventional ideas, the same claims to something new and better, and the same catastrophic results when students fail to learn. I don't know where the NCTM gets its ideas or theories, but I have a dark suspicion. There are two powerful and interlocked interest groups who have a huge stake in education remaining a fashion industry: textbook publishers and education professors. The publishers need new ideas to justify new textbooks, and the ed profs write the new books and teach the new methods to baffled classroom teachers. No matter if the new methods don't work, in fact so much the better - that just proves that we need a whole new set of remedial textbooks and trained teachers.

I don't think that math should be taught exactly the way it was 40 years ago. Calculators and computers can provide insights that just weren't available back then. The aversion to facts and memorization, though, seems wholly misguided to me. Kids are very good at memorization and most of them like it. Once they have a command of the basic facts, it becomes possible to do some reasoning and problem solving. Anyone who learns any advanced math knows what a complex hierarchy of knowledge is needed for that learning.

I occasionally volunteer in elementary school classrooms, mostly recently to teach some math ideas and techniques. Some students invariably are excited by the mathematical ideas presented and others find them very difficult. Most commonly those who have trouble haven't mastered multiplication and addition facts. If they are still trying to add and multiply on their fingers, they don't have enough mental processing space left to look at more advanced ideas.

Finally, I think the emphasis on problem solving skills and so-called critical thinking at the expense of facts is exactly backwards. Our brains are naturally equipped with problem solving and critical thinking algorithms - they were as essential to our survival when we were hunter-gatherers as they are now. Math facts were not, and we have no innate grasp of them.