abstractmath.org 2.0
help with abstract math

Produced by Charles Wells     Revised 2016-10-04
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Mathematics is not a spectator sport. --David Tall


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


To do math includes all the following activities and others:

Understanding and doing

This chapter is a companion to the chapter on Understanding Math.  But the distinction between understanding and doing math is not fundamental.

You can’t understand math without doing it.
You can’t do math without understanding 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 at math by doing math

You get better at math by (for example) doing the things on the blue list above.

Physical activity too

You might think that succeeding at math doesn't require physical activity, but in fact physical activity helps a lot. 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 or run around or do other active things.

Occasional breaks for physical activity
help when you math.

Useful and dysfunctional

This chapter has two parts.

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. You may also have dysfunctional attitudes that hinder your progress.

The discussions in these two parts are drawn from the math education research literature and from my own observations.

Useful behaviors


Zooming and chunking

Rewrite according to the definitions

Think of examples

Trial and error


Dysfunctional attitudes and behaviors


Boundary values of definitions




Existential bigamy

False symmetry

Jump the fence



Method addiction

Proof by Example


Reading variable names as labels

The representation is the object


Unnecessarily weak assertions


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