2 - Math Concepts

Summary

If we desire to form individuals capable of inventive thought and of helping the society of tomorrow to achieve progress, then it is clear that an education which is an active discovery of reality is superior to one that consists merely in providing the young with ready-made wills to will with and ready-made truths to know with …

Jean Piaget (philosopher and natural scientist)

My familiarity with various software programs is part of my intelligence if I have access to those tools.

David Perkins (Professor of Education, Harvard)

[Mathematical maturity is] fearlessness in the face of symbols: the ability to read and understand notation, to introduce clear and useful notation when appropriate (and not otherwise!), and a general facility of expression in the terse—but crisp and exact— language that mathematicians use to communicate ideas.

Larry Denenberg (computer scientist)

I think mathematical maturity is about the confidence to follow abstract reasoning, and the ability to sustain abstract thinking over a long time span.

Hung-His Wu (mathematician)

I spent most of a lifetime trying to be a mathematician—and what did I learn? What does it take to be one? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.

Paul Halmos (mathematician)

Chapter Overview

God is in the details. What sorts of problems can be used to ferret out mathematical maturity? What aspects of the mathematics curriculum are essential to mathematical maturity?