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Last
edited 12 May 2009
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DOING
MATH
This is the
top page of the chapter on doing math.
Contents
Dysfunctional
attitudes and behaviors
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 examples
to understand a concept
¨
Think of a statement
that might be a theorem
¨
Find counterexamples to
a statement
¨
Come up with the proof
of a statement
¨ Write up your results
This chapter is a companion to the chapter on understanding math. But 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 at math by doing math.
You get better at math by (for example) doing the things on the blue list above.
Occasional breaks for physical activity help when you math.
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.
Zooming and chunking
Look at examples