Half the base or half the height?: Exploring a student’s justification of ½ × base × height

Abstract

ABSTRACTThe purpose of this work was to explore how elementary pre-service teachers responded to a novel strategy for justifying the triangle area formula. We conducted interviews with 24 pre-service teachers, asking them to evaluate and respond to a hypothetical student strategy for the triangle area. Findings highlighted several interesting struggles our pre-service teacher experienced when assessing the mathematical content of the strategy, as well as differences in pedagogical responses depending on content knowledge. In many cases, pre-service teachers leveraged their understanding towards productive responses, while also grappling with a generalization of the strategy to other contexts. Recommendations for supporting pre-service teachers in navigating the intersection between content and pedagogical knowledge are discussed.