PEDAGOGICAL PERSPECTIVE ONILL-DEFINED MATHEMATICAL PROBLEMS

doi>10.24250/jpe/2/2021/JM/IR

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. illdefined
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.