Problem Solving in Mathematics and the Role of the Mathematical Puzzle

Abstract

The aim of this research was to investigate problem solving and whether there is role in this for the mathematical puzzle. The research undertaken involved a survey of the literature on both problem solving and mathematical puzzles, and the administration of a questionnaire to secondary teachers. From the literature ten attributes of a problem deemed to be effective in problem solving were found and 19 attributes of a mathematical puzzle, of which twelve might be regarded as recreational in nature but the remaining seven could genuinely be claimed to be linked to problem solving. Responses to the questionnaire were received from 59 secondary school teachers throughout New Zealand. The results show that teachers have a largely favourable attitude to puzzles and support some of the recreational attributes such as their ability to enliven the lesson; to motivate; to exercise the brain; and to show mathematical concepts in novel ways. They said they would choose to give a puzzle to the class for these reasons, even if it could not be tied directly to the topic they were teaching. Two attributes that received strong support were the ability of puzzles to stimulate mathematical thinking and to develop problem-solving skills. For a problem to be effective in teaching problem solving it should require the use of a number of problem-solving heuristics, but this survey has shown that teachers are aware of only a small number of potential heuristics. Teachers recognise the need for professional development on problem solving and using puzzles and it is recommended that this could cover further heuristics, explanations of how to use them and problems and puzzles to use them on. Teachers see the merits of using puzzles that are relevant to the curriculum and hence there is a need for this kind of material to be produced. At present it appears that there is a difficulty finding suitable puzzles because of the sheer volume of puzzles available and the time it would take to investigate them all.