Meet Hans Freudenthal

I finally did get my book, though I must confess I haven't made it very far yet. Great first sentence, though: "Men die, systems last."

Okay, I have made it further than that. Anyway . . .

Freudenthal's thinking about mathematics education is interesting to me for two reasons: (1) it seems to deliberately avoid (or perhaps be unconscious of) what I have been thinking of lately as "didactic maternalism" and "didactic paternalism."

With apologies to women and men everywhere for such a gross generalization, I would link the former with the sanctification of error, an obsession with "behavior," and an unhealthy animosity to uncomfortable change; the latter (which will be much more familiar with "edusphere" readers) with stoic arrogance, intimidation, and an unhealthy obsession with individuality at the expense of everyone else (i.e., parochialism); (2) it seems to recognize the complexity of the subject of mathematics education, which is pretty rare on both of the made-up sides of our education debate in the U.S.

Here's a nice quote I wanted to share:

In order to write a phenomenology of mathematical structures, a knowledge of mathematics and its applications suffices; a didactical phenomenology asks in addition for a knowledge of instruction; a genetic phenomenology is a piece of psychology.

All the psychological investigations of this kind which I know about suffer from one fundamental deficiency: investigations on mathematical acquisitions (at certain ages) have involved the related mathematical structures in a naive way—that is, they lack any preceding phenomenological analysis—and as a consequence, are full of superficial and even wrong interpretations. The lack of a preceding didactical phenomenology, on the other hand, is the reason why such investigations are designed in almost all cases as isolated snapshots rather than as stages in a developmental process.