Developing a formative assessment framework for supporting students’ reasoning during problem solving

Abstract When students solve problems by means of their own reasoning, they develop mathematical competencies and retain knowledge better than if they imitate given solutions. However, when the challenges are too great students require support. Supporting students’ own mathematical reasoning is difficult; it has been repeatedly shown that opportunities for reasoning are often removed by teachers telling the students how to solve the problem. Researchers have developed categories for what teachers do when trying to support students’ reasoning and for feedback with different potential for supporting students’ reasoning. However, these categorisations are based on limited data and lack either support for interpreting students’ reasoning or for selecting feedback based on such interpretations. The aim of this study was to develop a comprehensive formative assessment framework that is functional for aiding teachers in supporting students creative mathematical reasoning during problem solving. We describe how we reached this aim by building on a previously developed diagnostic framework and devising iterations of design experiments to test and develop feedback that supports students’ creative mathematical reasoning. The data comprises 334 student–teacher interactions from 109 lessons in 38 classes in Grades 1–12, related to 77 mathematical problems. The Supporting Creative Mathematical Reasoning (S-CMR) framework includes feedback with properties adapted to the main specific reasoning difficulties students may encounter during problem solving. Feedback with diagnosis-adapted properties was found to be substantially more likely to support students’ reasoning than other suggestions. The framework therefore has the potential to aid teachers in supporting their students’ creative mathematical reasoning.