This Porridge is Just Right

I have never subscribed fully to any political ideology. There has never been an "ism" that completely defined me, and I stay clear of labels for that very reason. I am a registered Independent, but if I had to give a name to my outlook on the world it would be Pragmatism. Regardless of the situation or controversy, I tend to find my personal solution somewhere in the middle of the spectrum. Whereas "conservative" answers typically look toward tradition and "liberal" arguments usually involve change, I tend to focus on what works and to hell with whether it's new or old.

I finding this especially true as I follow the epic saga of the Math Wars. As always, I find it only fair to mention that I am not yet a certified teacher and have no experience other that tutoring, so my opinions remain untested. But I do not think one needs to be a tenured educator to fully appreciate the state of math education in America. The situation is readily apparent. Americans, on average fear and despise math. It does not seem to be a recent phenomenon, as far as I can tell. I do not think it is something we can blame on TERC or Everday Math.

I will admit that people who learned math twenty or more years ago tend to be faster at arithmetic, both in their heads and on paper, though I suspect that cheap calculator technology is more at fault than any new age math reform. Nor can we say for sure whether this is a bad thing. The technology is too young for those kinds of evaluations. Farming, perhaps the greatest invention of mankind, did not immediately prove itself superior to the traditional hunter-gathering ways. Sure it was convenient and it's practitioners no longer had to follow their food supply, but there was a huge sacrifice in terms of overall nutrition. It wasn't until relatively recently that we have achieved the average nutrition of Stone Age diners. So I am reluctant to pass judgment too swiftly on the poor TI-89s and their ilk.

I remember Dan making a list once of all the skills that a great teacher needed to have (though I can't find the post I am thinking of right now.) I also remember him admitting that the list could probably added to ad infinitum and be no more comprehensive. It seems to me that teachers need as many weapons in their arsenal as possible, since there are exactly as many learning styles as there are students. It is because of this simple fact that I believe tradition and reform should not only coexist, but even cooperate. There is no "best" way to teach mathematics. What worked for one student may not work for the next. The very idea of a superlative runs counter to the reality of a multi-dimensional world. Let me describe it in terms of a fitness landscape. Competitors in a system ,whether life forms or educational theories are subject to a natural selection process that can be usefully modeled with a topographic relief map. Individual genes or memes attempt to climb in elevation, seeking relative maximums and thereby increasing their success or "fitness." This model, while helpful, can be deceptive. It masks two key facts about the real world. One, the real system is not static. The hills and valleys rise and fall with time. What reigned supreme in one era will be eaten alive in the next unless it continues to move and evolve. Two, the real system is not low-dimensional. If we consider each teaching style to be a point on the landscape, we must assign to that point all of the component elements of that style, which as Dan pointed out are quite numerous. This creates a multi-dimensional space that may not even have relative maxima in the way we are used to thinking.

So I say, when it comes to math education, the more the merrier. As a pragmatist, I go with what works here and now. I am not overly addicted to traditions, yet I am respectful of their proven track record. I am not mesmerized by the reforms for their newness alone, but I am excited by their search for something better. It is clear to me that the combatants in the Math Wars are passionate about what they do and that their first concerns are for their students. I just think everyone needs to take a deep breath. As with most arguments, the opposing sides probably have more in common than they think.