Gina's mathematics: Thinking, tricks, or 'teaching'?

摘要

Students with learning disabilities display a diverse array of factors that interplay with their mathematical understanding. Our aim in this paper is to discuss the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions. We present analysis and results from multiple sessions conducted during a teaching experiment cast as one-on-one intervention. Results of a multi-phase qualitative analysis reveal two themes evident in the child's thinking structures across the sessions: (a) Gina's accommodations over time versus traditional progressions, and (b) Persistent factors that interacted with the child's reasoning. Throughout the analysis, we raise questions about the child's reasoning and what the child's apparent knowing and learning was relying upon. When wellintentioned researchers or educators provide children interventions that promote procedures and replication of teacher-taught strategies, not only are they not serving their children's mathematics learning needs, they may be preventing them from engaging in, reflecting upon, and coordinating actions that support the children to accommodate their thinking structures and advance their learning. Discussion and implications are shared.