Identifying and supporting teachers’ robust understanding of proportional reasoning

Abstract This case study uses the Framework for Teachers’ Robust Understanding of Proportional Reasoning for Teaching (Weiland et al., 2020) to characterize how 51 mathematics teachers solved a comparison proportional problem. We found 50 of the 51 teachers productively drew upon four knowledge resources: (1) proportional situation, (2) ratios as part: part or part: whole, (3) unit rates, and (4) ratio as measure. This study details these and teachers’ less commonly used knowledge resources, as well as counterproductive statements related to the knowledge resources. We analyze the structure of the comparison proportion problem and suggest why teachers drew on particular knowledge resources. Lastly, we highlight how counterproductive statements highlight areas of focus for mathematics teacher educators and extends the operationalizing of the robust proportional reasoning framework for mathematics education researchers.