This is the top page of the chapter on doing math.

Contents

Introduction. 1

Useful behaviors. 2

Dysfunctional attitudes and behaviors. 2

Introduction

To do math includes all the following activities and others:

¨ Carry out an algebraic calculation

¨ Solve a problem

¨ Think through math statements you read

¨ Work through example to understand a concept

¨ Think of a statement that might be a theorem

¨ Come up with the proof of a theorem

¨ Write up your results

There is a separate chapter on understanding math.  However, the distinction between understanding and doing math is not fundamental. 

¨ You cannot learn to play a musical instrument by (only) reading about how to do it. 

¨ You cannot learn to play tennis by (only) reading about it. 

The same principle applies to math.  Learning to play an instrument or tennis involves physical changes in your brain and in your muscles.  To learn some math involves changes in your brain in the same way.  You get better only by exercising the part of your brain that does math by (for example) doing the things on the blue list above.

Physical activity seems to help doing math, too.  I can speak both from personal experience and from the reported experience of many other mathematicians that if you are stuck on a concept or a problem, it really does help to get up and walk around, including taking a longish walk.

Useful and dysfunctional

When you do math you may engage in useful behavior, that enables you to make progress.  You may also engage in dysfunctional behavior:  behavior which is counterproductive, such as repeatedly making the same algebraic mistake, or repeatedly trying a single approach to a proof over and over instead of considering other lines of attack.   You may also have dysfunctional attitudes that hinder your progress.  These are the subjects of these webpages:

Useful behaviors

This chapter describes some behavior patterns that successful mathematicians are known to use.  They are drawn from the math education research literature and from my own observations.

Self-monitoring

Zooming and chunking

More useful behaviors

Useful behaviors for proofs

Dysfunctional attitudes and behaviors