Students’ Reflective Concepts when Reflecting on Statistical Measures—A Design Research Study

Abstract

The normative conceptualization of mathematical literacy comprises a mathematizing side (addressing the ability to use mathematical concepts for structuring phenomena in the social and natural world) as well as a reflective side (addressing the ability to reflect and evaluate the role mathematics plays in the society). But whereas decades of research contributed to thoroughly specifying the mathematizing side of mathematical literacy in theoretical as well as in empirical terms, the reflective side remains empirically underdeveloped. In light of the existing empirical gap of the reflective side of mathematical literacy, the article presents results of a design research study to establish reflective learning situations and to empirically describe students’ reflective learning processes. For this, the construct of reflective concepts is introduced. A reflective teaching-learning arrangement for the exemplary topic of statistical measures is designed, and seventh graders’ reflection processes in design experiments are investigated. Central outcomes are empirically refined reflective concepts that can serve as starting points for designing reflective learning trajectories, as well as the insight that their consolidation will require further learning opportunities.