Abstract
The concept of “heuristics” or “heuristic strategies” is central to (mathematical) problem solving and related research; however, there is no generally accepted definition of this term. Trying to clarify the concept might help avoiding misunderstandings and difficulties in dealing with studies that use different terms meaning the same concepts or that use the same terms meaning different concepts. Therefore, the research presented in this paper aims at a clarification of the term “heuristics” and suggestions for the use of it in future research. Building on previous work from last year’s ProMath conference, the consequences of using different characterizations of “heuristics” on vignettes (= short, completed scenes) of problem solving attempts are investigated. The conceptualization of “heuristics” has a significant influence on the types and numbers of perceived heuristics, which in turn affects empirical studies that identify and analyze heuristic strategies.
Highlights
Problem solving is an integral part of both mathematics – Halmos (1980) even calls it the “heart of mathematics” – and of mathematics education and mathematics in school respectively
The results show that the students’ mean scores in a test of mathematical abilities (SAT) increased significantly as well as the average number of heuristics used in the problem solving interviews
Applying different characterizations to the same vignettes leads to explicitly different outcomes
Summary
Problem solving is an integral part of both mathematics – Halmos (1980) even calls it the “heart of mathematics” – and of mathematics education (cf. Schoenfeld 1992) and mathematics in school (cf. NCTM 2000) respectively. When actively engaging in and researching on (mathematical) problem solving, heuristics play a central role (cf Schoenfeld 1985). This article theoretically deals with research on problem solving with a focus on heuristics. Different conceptualizations of the term “heuristics” will be compared and discussed referring to vignettes (= a short description of a process) of problem solving attempts. It will be shown that different conceptualizations could lead to different interpretations of empirical data and, to different results
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