March 13, 2009

Ladies and gentlemen:

This is an open letter from a mathematician and citizen who has been a math teacher to the people who have to make the decisions about mathematics education for our state. All of you know a lot more about politics than I do, but I know it when I see it, and there has been a lot of it in our state's recent discussions and decisions about K-12 mathematics.

Consider “mathematical soundness.”

Reading dozens of textbooks carefully would be cruel and unusual work. But asking the math chairs at our six public four year colleges and universities to each read through the K-12 benchmarks would have meant at most a day's work for each, work quite relevant to their roles as mathematics education leaders in our state. Independent letters from these six individuals would have produced all information needed to decide whether or not the proposed benchmarks were mathematically sound..

Instead, we spent money outside of state for a review by one highly partisan though entirely honorable and qualified individual. The decision to hire an outside reviewer appears to me to have been almost purely political.

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If the reference here is to the mathematical soundness of Math texts at the high school level, then the fact is two mathematicians were hired Dr. Wilson from Johns Hopkins and Dr. Harel from California.

If the reference here is to the mathematical soundness of Math texts at the high school level, then the fact is two mathematicians were hired Dr. Wilson from Johns Hopkins and Dr. Harel from California.

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Consider the recent textbook and materials reviews.

I participated in two. I was struck by the integrity of the process, by how careful those running the review were and how hard we all worked to be fair and objective. But we were limited by a kind of self-inflicted intentional ignorance.

For example, I had to mark Algebra II textbooks down if they did not include “coverage” of quadratic inequalities.

I don't recall ever being taught about them or ever using them, though I suppose I have. They are of monumental insignificance compared to either quadratic equations or linear inequalities. We know what they are, just from the words. Any student who knows the two other topics well can figure out, when and if they have to, all they need to know about quadratic inequalities.

But the way our decision was structured, I was forced to rank a text that was merely adequate on quadratic equations and linear inequalities and covered quadratic inequalities as superior to a text that treated quadratic equations and linear inequalities superbly but didn't mention quadratic inequalities. Our students will suffer because of such self inflicted stupidity.

Traditionalists in our state often denigrate pedagogy and push versions of content as a way to get their views accepted. The decisions about the structure of these textbook assessments were partly political.

Consider the National Mathematics Advisory Panel.

Yes, Virginia, there is politics in mathematics education in the other Washington, too. And, again, one aspect of it is a self inflicted ignorance of material that is material to decisions about our children's education in mathematics.

The course I took in psychology as an undergraduate fifty years ago was wall to wall behaviorism. The view presented of what was scientific in psychology would have precluded the kinds of evidence that George Miller, Jerome Bruner, and countless others later used to carry out a “cognitive revolution” in that field. Noam Chomsky similarly expanded the kinds of evidence and ideas considered in linguistics. The social sciences and what came to be called the cognitive sciences advanced by getting over what some had characterized as physics envy. The NMAP appears to me to have suffered from medical science envy.

The problems studied in education seem to me much more like those studied in sociology and psychology and maybe even comparative literature than those studied in biology and medicine. Throwing out most research that didn't fit into a clinical trials template seems stupid to me.

I hope that those of you making decisions about mathematics education for our state will, in addition to considering the ideas and opinions of the NMAP carefully, also consider those of the AERA. { AERA link http://www.aera.net/ }

Sincerely,

Bill Marsh, Ph.D.

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