Critique-mediated lesson redesign as a perspective on emerging pedagogical reasoning: Preservice mathematics teachers teaching the equal sign
چکیده
Background: Preservice teachers may solve equality tasks correctly while still explaining them procedurally, suggesting that correct performance does not necessarily reflect a relational understanding of the equal sign. When planning lessons, they must translate their mathematical understanding into instructional decisions, making lesson redesign a useful context for examining developing pedagogical reasoning. Aim: This study explored what critique-mediated lesson redesign revealed about preservice mathematics teachers’ emerging pedagogical reasoning when planning Grade 7 lessons on the equal sign. Setting: The study took place in a mathematics methodology course at a South African university. Methods: A qualitative multiple-case artefact-analysis design was used. Three group lesson redesigns were compared using lesson plans, written rationales and lecturer critique. The Knowledge Structures of Teaching in Emerging Practice (K-STEP) framework was used to interpret how the groups’ reasoning developed during redesign. Results: Redesign prompted greater attention to relational meanings of the equal sign, conceptual sequencing and learner understanding, although procedural routines and limited responses to anticipated learner thinking persisted. Conclusion: Critique-mediated lesson redesign made visible the uneven nature of developing pedagogical reasoning. The groups began to move towards more relational and learner-responsive lesson designs, although this development remained incomplete. Contribution: The study shows how lesson redesign can be used not only to improve planning but also to explore how preservice teachers interpret, revise and justify instructional decisions.