Analyzing Errors in Preservice Middle‐Grade Mathematics Teachers' Proof Writing

ABSTRACT Reasoning and proof play an important role in mathematics and mathematics education. Despite its importance, gaps and challenges exist in middle‐grade students' and teachers' learning and teaching of reasoning and proof. By examining preservice middle‐grade mathematics teachers' (PMMTs) proof writing in a college geometry content course, this study aims to identify common errors in PMMTs' proof construction and to discuss the nature and types of these errors through a theoretical lens, connections to current literature, and our own teaching expertise. Overall, the errors fell into three main categories: errors with respect to organizing the given/proved conditions and applicable theorems/axioms/definitions within one deductive step, errors with respect to linking deductive steps into a proof, and errors in the rigor of mathematical writing. Through our discussion, we hope to provide insights into PMMTs' understanding of deductive reasoning and formal proof, and to suggest instructional strategies that can support teacher educators in enhancing the preparation of PMMTs' geometry content knowledge.