George Polya

In 1957 a Hungarian mathematician called George Polya wrote a book called "How to Solve it". In this book he delineated the strategies that mathematicians use. They don't just wade into the problem, they first spend time trying to understand what the problem is. What is involved in this problem? What are the questions to be answered? In trying to understand the problem they may well sketch it, draw a diagram, make a chart or draw a graph to help them, all the time considering what is a likely path to a solution. This is something that less proficient persons tend not to do. Such people, generally, take a quick look at the problem and classify it according to which routine they think will provide them with a solution, then they apply that mathematical method to the problem. Whereas this approach may work with simple problems given in a school classroom to illustrate a mathematical routine, it is not appropriate to solving more difficult problems with more than one layer of reasoning for which different techniques might be required.