Compromises between required and preferred features of mathematical definitions in mathematics education

Abstract

The mathematics education literature distinguishes between the preferred and the required features of mathematical definitions. However, it is unclear whether and how this distinction differs between mathematical and didactical contexts. Here, we address the didactical context in which the purpose of the definition is to help students learn and understand the meaning of a new concept. We administered a comparative judgement study to assess how 12 mathematics teacher educators value the relative importance of required and preferred features of mathematical definitions. We found that the educators did not value the required features as more important than the preferred features of mathematical definitions. Furthermore, we found that the educators valued some required features more than others. These results suggest that, in a didactical context, the categorization into preferred and required features of mathematical definitions may not be as clear cut as indicated in the mathematics education literature and depends on the context or purpose of the definition.