Non-routine Mathematical Problems Research Articles

Development of a Framework for Analysing Mathematical Problem Solving Behaviours

Abstract The taxonomy described in this paper was developed to investigate the process of mathematical problem solving in terms of definable behaviours. It was also used as an instrument to classify and encode behaviours in their sequence of observed occurrence during the process of mathematical problem solving. It is a behavioural analysis framework formulated to examine the “thinking-aloud” protocols of individuals for comprehensive information about the problem solving process itself, the individual differences in the behaviours of subjects and the strategies applied by each in dealing with non-routine mathematical problems.

Measures of Problem-Solving Performance and of Problem-Solving Instruction

This article presents and discusses three paper-and-pencil tests of students' performance on nonroutine mathematics problems at the college level. These tests assess the following: 1. the frequency with which students apply various problem-solving heuristics, and how far and with what success they pursue them; 2. students' subjective assessments of their own problem-solving behavior; and 3. transfer of heuristic behavior on problems related in various degrees to ones that students have studied. These measures were used to assess students' performance before and after a month-long intensive problem-solving course. They provide evidence that such a course can produce strong changes in students' problem-solving behavior.