**An Analysis of a Solution**

**Derek HOLTON**

#### Melbourne Graduate School of Education

University of Melbourne

Australia

Published in The Mathematician Educator, 2020, Vol 1, No. 2, pp 62-74.

### Abstract

How do mathematicians solve problems? In what follows we look at the Tower of Hanoi problem that is accessible to secondary students and show how a mathematician might tackle it. This ‘showing’ involves more than the final written solutions. It considers how the mathematician might be thinking and the body of mathematics that might have been used in the process. Now we have avoided taking a real mathematician’s work on a research problem, simply because that would require the reader to know a large amount of mathematics relevant to that problem. Instead we will take an imaginary mathematician working on a problem that is easy to explain and does not rely on mathematics that is beyond the experience of secondary students. By doing this we hope that the reader is able to understand what happens while the fictitious mathematician is working on the problem. In the Discussion section, we will consider some of the things that a mathematician does on problems they are trying to solve.

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