Analysis of Teacher Shaping Practices in Elementary Mathematics Classrooms: Focusing on the Recursive Process based on Task Characteristics

This study explores how teachers capture student thinking and coordinate interactions in complex classroom situations from the perspectives of ‘shaping’ and ‘self-scaffolding’. To this end, a micro-analysis was conducted on two contrasting episodes—a convergent task (multiplication operation) and a divergent task (finding rules)—in a fourth-grade elementary mathematics classroom. The results revealed that teacher shaping practices operate through different recursive pathways depending on the characteristics of the task. In the convergent task, where the goal was clear, the teacher utilized an ‘information reduction’ strategy, filtering out errors or irrelevant information to converge the focus onto core principles. Conversely, in the divergent task aimed at generalization, the teacher employed an ‘information generation’ strategy, identifying ambiguous explanations or unexpected ideas as resources and expanding them to structure the discussion. Despite these differences, both cases shared a commonality: they functioned as a ‘self-scaffolding’ mechanism where the teacher autonomously regulated the information environment to control uncertainty without external support. This study is theoretically significant in that it identifies teacher noticing not merely as a passive cognitive process but as an active design practice and an adaptive practical mechanism. Furthermore, it suggests that teacher education should emphasize adaptive information structuring competencies tailored to task characteristics.