A Twisted Phrase

The image I have in front of my mind’s eye, the image of schooling, especially from middle school on, is not of a deep, wide ocean of knowledge and skill but of a series of high, bland walls. Whitewashed. Unnecessary Artifacts.

It’s an image I build when I think about the phrase, “get your math requirements out of the way.” If learning or playing with mathematics is something we are supposed to “get out of the way,” then something has gone wrong. Our middle schools, high schools, and undergraduate programs have turned learning mathematics into a series of standard obstacles, “mathematics requirements,” that are nearly the same for nearly everyone.

Formal, coercive schooling has twisted many areas of intellectual life from sources of growth, maturity, character development, and pleasure, and from realms of intrinsic value, into obstacles to clamber over. At least that’s how these realms will seem in the experience of many if not most students, especially when, as is too often the case – though fortunately, with more creative teachers, not always – engagement with them is mediated by worksheets, short answers to standardized questions, tedious, formal problem sets, reports with assigned topics, and, worst of all, constant evaluation and judgement in the form of simplistic letter grades.

Recently, a student of mine who is quite young, barely a so-called “teenager,” asked to learn probability theory. As I teach him and aid him in learning, he learns many other things. He develops his skill in working with fractions since calculating probabilities involves operations with fractions (all probabilities lie between zero and one, inclusive). He learns some set theory and basic operations with sets, since the foundations of probability involve working with finite sets. He learns combinatorics (permutations and combinations) since calculating probabilities often involves determining the sizes of large sets. We play with coins, dice, and especially cards: we discuss different kinds of poker: Five Card Draw, Seven-Card Stud, Razz, and so on. And it works, he stays engaged, because his motivation doesn’t come from external, ad-hoc authority, but from within.

Once again, constructive reform lies in the direction of self-directed education.