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Monday, September 18, 2006
I Joined the Math Wars

Here's the text of a letter I sent last week to the principal and teachers at my children's elementary school.

I heard that the District had asked principals not to distribute any letters from Oak Norton on the math curriculum, so I decided to write my own letter and e-mail it to the principal and teachers at my children's elementary school, Barratt Elementary in American Fork. Here it is, with the initial paragraph deleted, because that was specific to Barratt and not, therefore, of general interest.

I chose the salutation, "Dear Colleague," because -- as I explained in the e-mail messages in which I sent the letter -- (1) I have some experience in the teaching profession, (2) I view the education of children as a shared effort among teachers and parents, and (3) "Dear Teacher/Administrator" seemed unbearably awkward.

September 15, 2006

Re: Math Curriculum

Dear Colleague:

I am and long have been concerned about math instruction. This concern actually precedes the ongoing district-wide backlash over the current curriculum.

The short version of my longer discussion (which follows) is this:

As the Alpine School District makes good on its promise to allow schools some flexibility in choosing their math curricula, I urge you to use your influence to help Barratt Elementary choose something that actually will produce students who understand and can do math well, using proven methods to get correct answers reliably -- because in the real world the wrong answers are useless, sometimes even dangerous. The curriculum which preceded Investigations was inadequate; Investigations itself is worse in some ways and should be replaced.

Allow me to explain.

As a student, I had fairly solid credentials as a math geek (a term of endearment at my house), but my professional teaching experience is in other fields. So it was a particular treat a few years ago when an opportunity arose to volunteer for a few months at Barratt, teaching introductory algebra to a particularly able group of sixth graders in the Advanced Learning Laboratory (ALL). They displayed a happy combination of intelligence, eagerness to learn, and willingness to work.

This was just long ago that they had come through the previous math curriculum. Their capacity to think about a problem and discuss possible solutions was well developed, and the confidence and self-esteem with which they approached math seemed quite robust. But their ability actually to solve even basic, pre-algebraic problems proved surprisingly limited.

These ALL students were arguably as fine a group of sixth grade math students as one could assemble even in our very large district. I found myself wondering how other students could succeed in the same program, if even the best were conspicuously deficient. In any case, this struck me as mostly the result of a lack of practice, so we practiced a lot -- drilled, if I may use what has somehow become a dirty word. They made rapid progress.

By this time earlier grades were moving to Investigations, so I immediately began to observe its style and effects also, as I monitored my own children's homework and sometimes tutored others' children. I'm all for teaching children (and anyone else) to understand how math works, not just to solve problems. But it was clear to me then, as it is now, that if in the long term there is insufficient practice solving actual problems with the methods that have proven most efficient, most robust, and most reliable, conceptual understanding alone merely creates the dangerous illusion of having skills one actually does not possess.

The move to Investigations did not swing the pendulum in the other direction, which would have been helpful. It has proved to be a significant additional move in the same unfortunate direction. This, combined with the Alpine School District's period of well-documented hostility to the use of any other methods to supplement Investigations, including multiplication tables, has seriously impeded the math education of many students.

More than math itself is at stake here. Employers increasingly need employees with good basic math, problem-solving, and logical skills. Locally, however, the supply of workers with solid junior high- or high school-level skills in these areas seems to be dwindling. Meanwhile, the percentage of college students requiring remedial math training is soaring. Clearly, something is not working as we need it to -- not just in the Alpine School District, of course.

As I indicated, I hope that the Alpine School District actually makes good on its promise to allow schools to choose between a more traditional curriculum and what I have called elsewhere "The Emperor's New Math" (meaning Investigations and other warm, fuzzy approaches). If and when this happens, I urge you to use your influence to help Barratt Elementary choose something that actually will produce students who understand and can do math well and use proven methods to get correct answers reliably -- because in the real world the wrong answers are useless and sometimes dangerous. Saxon is widely reputed to be an excellent choice -- or Singapore Math, if a school is confident in the quality of its current and future math teachers. No doubt there are other excellent programs -- to which Investigations might be a valuable supplement, if the other programs swing the pendulum too far in the other direction.

I firmly believe in the importance of learning how to learn and understand, and of trying new things, not just memorizing facts. There are many fascinating things to discover along the way through a traditional math curriculum, for students with teachers who know and love mathematics. But most of those discoveries rely on solid mastery of the traditional tools of mathematics.

The simple fact of this matter is that it took the likes of Archimedes, Euclid, Fibonacci, Descartes, Newton, Gauss, and many others millennia to discover and refine the mathematics which an average high school student should master by about age 18, if he or she is to function well in democratic society, a modern economy, or an institution of higher learning. This seems to suggest that the proper mix in a math curriculum should include some discovery, but lots of learning and practicing what others have discovered. The current approach inverts this: lots of discovery and a minimum of rigor.

Let's look at this for a moment in terms of student self-esteem, which I fear is the educational lingua franca of our age. It's a simplification, and it does not account for the many dedicated teachers who are determined to teach math well no matter what the District says -- many of us are very grateful to them -- but it seems to me that traditional math, well taught, yields good, useful skills and resultant self-esteem. With "The Emperor's New Math" students get self-esteem and inadequate skills. Either way they get the self-esteem. So why not get it with solid skills -- based on something real?

Finally, as fond as education theorists are of discovery curricula, mathematicians -- who do and in many cases also teach math for a living -- overwhelmingly condemn them in favor of more traditional curricula. A growing body of research suggests that the mathematicians are right, if our goal is to produce functional mathematical literacy in students. I would be happy to supply upon request some links to related materials which are readily available on the World Wide Web. For the moment, I offer only this link to a front-page Wall Street Journal article this week:


Thank you for your attention to this matter. If I can help in some way, please let me know.

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