Multi-variable narratives in qualitative research on mathematical problem posing

Abstract

We substantiate the following claim: multi-variable narrative in qualitative research on problem posing bears promise for a better understanding of causality relationships between ways in which problem-posing activities are organized on the one hand, and characteristics of processes, products, and effects of problem posing on the other hand. Our notion of multi-variable narrative is first introduced by means of a hypothetical scenario. We then discuss relationships between different types of variables while adapting the terminology developed in mediation analysis literature to problem-posing situations and suggest heuristics for choosing problem-posing variables in research that aspires to inform practice. This is followed by an illustration in the context of a problem-posing activity by mathematics teachers. The illustration shows how features of the posed problems can be related to the problem-posing task organization, and how these relations may be mediated or moderated by particular features of the problem-posers, and by choices they make.