3 - Teaching Techniques

Summary

Proofs should be communicated only by consenting adults in private.

Victor Klee (mathematician)

I was of course flabbergasted by the variety of generalisations that have blossomed in that particular garden!

Bryan Birch (mathematician)

Computers are incredibly fast, accurate, and stupid. Human beings are incredibly slow, inaccurate, and brilliant. Together they are powerful beyond imagination.

Leo Cherne (economist)

An individual understands a concept, skill, theory, or domain of knowledge to the extent that he or she can apply it appropriately in a new situation.

Howard Gardner (developmental psychologist)

To be mature means to face, and not evade, every fresh crisis that comes.

Fritz Kunkel (psychiatrist)

The stone age did not end because we ran out of stones.

anon.

Chapter Overview

It is natural to wonder which teaching techniques will contribute to mathematical maturity. Do the tenets of teaching reform have something to show us about the matter? What about OnLine learning?

These days capstone experiences are in vogue. At the end of a four-year undergraduate education, the capstone experience helps the student draw together material from different courses, and to see connections that were previously unnoticed. It seems likely that such a project could help to push the student along the maturity path.

There are many new approaches to math teaching, from those of Uri Treisman to those developed at Harvard as part of the reform movement. They are all worth considering as we work to help our students move ahead in the mathematical maturity cycle.