Monday, July 16, 2012

Exeter and Park Curricula: HS Moore Method?

In my blogging binge, I have repeatedly come across posts about the Exeter and Park Curricula and many discussions about their differences, similarities and foundation.

My first impression is that they are similar to the Moore Method with a crucial distinction. For the unfamiliar, the Moore Method is a teaching style which emphasizes having students prove theorems from a given set of axioms and present and presenting their results in class. The Exeter and Park Curricula seem to differ in that they don't propose any axioms or framework for the students to operate in. Instead, they seem to "front load" the conceptual work by having the students propose a "framework" in which to work (with gentle prodding and guidance from the teacher?). My guess is this is meant to avoid issues students have with axioms, new concepts, etc.--justifying and understanding why they are using the axioms or concepts since the student has already done that by proposing them! That seems to be the idea anyway.

Moore Method:

The way the course is conducted varies from instructor to instructor, but the content of the course is usually presented in whole or in part by the students themselves. Instead of using a textbook, the students are given a list of definitions and theorems which they are to prove and present in class, leading them through the subject material.
More Moore Method:
I do not consider it important in using the Moore method whether one lectures a lot, a little or none at all. It is important that there be regular interaction with the students so that the instructor knows how well the students understand the material. It is also important that they be given challenging problems, be motivated to work on them and to want to report their progress.
My undergraduate topology course was more or less a Moore class. It was an interesting opportunity to learn about something mathematically useless while developing real mathematical skills proving theorems and formulating conjectures. The course developed a topology on sequences using a modified lexicographical order for containment of sets and truncation and concatenation for set operations. Lesson learned: while the content might not have been "mathematically" worthy the experience and process itself justified the approach.

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