Preservice Teachers’ Exploration of Model Breaking Points

This study is an investigation of elementary preservice teachers’ (PSTs’) exploration of model breaking points in fractions. Eighty-three PSTs at two universities in the Midwestern and Southwestern regions of the USA were asked to explore the area model of fraction addition through a series of tasks and explain their reasoning in determining its affordances and constraints. The PSTs presented their critical mathematical ideas on modeling fraction addition and area models’ breaking points when used to add two fractions, as well as suggestions for alternative models to overcome model breaking points. An inductive content analysis showed that most PSTs represented fraction addition well with simple fractions but had difficulty representing fraction addition with improper fractions or fractions with unlike and relatively large denominators and tended to use algorithm-based thinking. Also, the area models drawn by several PSTs revealed various misconceptions, suggesting the impact of their content knowledge on their understanding of area models. Based on the findings from this study, we provide some implications for teacher educators.