An Activity Structure for Supporting Students' Coordination of Computer Algebra Systems and Paper-and-Pencil across Phases of Curriculum

In this study I examine the issue of how to support students' coordination of computer algebra systems (CAS) and paper-and-pencil in solving mathematics problems. Together with a classroom teacher I designed and conducted a collaborative teaching experiment in a ninth-grade algebra classroom to understand how to support students' coordination of tools. I introduce a predict-act-reflect-reconcile activity structure for coordinating CAS and paper-and-pencil in solving problems involving linear expressions and equations and adopt this as an analytic lens to examine the role of curriculum materials on impacting students' learning. Findings suggest the activity structure of predict-act-reflect-reconcile is a potentially fruitful starting point for coordinating CAS and paper-and-pencil in classroom activity, but not sufficient on its own as a task design principle without focused classroom discussion and support during the enacted curriculum. This research points to the importance of teaching students how to communicate about their process of using multiple tools while solving problems, especially the mathematical thinking that students engage in while reconciling differences across tool-based representations.