My Educational Philosophy

The hiring season has begun: schools in New Jersey have started posting open positions for high school math teachers for the 2012-2013 school year. In preparation, I dusted off a draft of "My Educational Philosophy" that I wrote for Larry at Traders-to-Teachers and cleaned it up for use on applications. I still consider it a working document, but it does express what I think are key points:

• Learning is neurologically based: education must be based on a sound theory of cognition. This is the old cognitive scientist coming out in me.
• There is an inherent tension between the needs of society and the needs of an individual, and a good teacher in the classroom does not avoid this tension.
• I teach for understanding, and my definition of "understanding" owes a lot to Howard Gardner. 

OK, here it is:

Errol Morris on Pythagoras, Incommensurability, and Whiggish History

In March 2011 Errol Morris, an award-winning documentary filmmaker and director of TV commercials, published a series of five opinion pieces in the New York Times with the collective title "The Ashtray". Those who know about Morris through his films and ads may not be aware of his philosophical writings about the nature of truth, knowledge, and history. If those topics put you off from reading Morris, perhaps it would help to know that the series title comes from the object thrown at the author by Thomas Kuhn, author of "The Structure of Scientific Revolutions", when Morris was a graduate student under Kuhn at Princeton. (If that's still not enough, then see his description of a Dan-Brownish library encounter, below.) The series as a whole is a critique of Kuhn's notion of "incommensurability" of scientific paradigms, but the part that appealed to me particularly is the third in the series, on the origin of the term "incommensurable" in mathematics and the legends surrounding the Pythagorean proof that the square root of two is irrational.

An ending and a beginning

Classes ended today, but fieldwork continues. While waiting for my ride, I began to realize that I need to have a working definition of mathematics, something I can hold in mind and use to frame my planning and teaching.

Thus: number / form / pattern. These are the objects of study in mathematics.

Numbers are used to distinguish, to arrange, to count, to measure.

Forms describe shapes or structures and the way parts fit together into a whole.


Patterns describe the way things repeat and change.