PEDAGOGICAL PERSPECTIVE ONILL-DEFINED MATHEMATICAL PROBLEMS
PEDAGOGICAL PERSPECTIVE ONILL-DEFINED MATHEMATICAL PROBLEMS

Summary/Abstract: Traditionally teaching mathematics in schools is based primarily on well-posed problems. Intuitively, there is a clear difference between them and ill-defined problems. Research in the field of problem-solving is often based on the analysis of procedures for solving incompletely posed problems (i.e. ill-defined problems) because they are expected to provide a deeper insight into mathematical abilities as well as the ability of critical and creative thinking of respondents. However, ill-defined problems are scarcely explored as a main subject of interest. This paper aims to investigate the place of those types of problems in teaching mathematics. As a context of the investigation, we consider various classifications of math problems. Three classifications of mathematical problems with a "pedagogical perspective" are elected to be analyzed using the theoretical epistemological method of comparative analysis. All three classifications consider the position of participants in problem-solving, teacher and students. As a result of the analysis, we create a comparison of the spectrums of problems, particularly paying attention to ill-defined problems in them. The discussion finishes addressing the place and purpose of using ill-defined problems in mathematics instructions.

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