Categorizing mathematical sense making and an example of how physics understanding can support mathematical understanding

For both instructors and researchers there is interest in student "sense making" and specifically on mathematical sense making Here, we introduce a framework that distinguishes between the object of the sense making (mathematical or physical) and the tool used for sense making (formal mathematics or conceptual physics), thus foregrounding focus and mechanism in student problem solving. We situate this framework in both a general discussion of sense making and of mathematical sense making in particular, and then apply it to data from a focus group. This analysis highlights a particular mode of sense making, where a conceptual understanding of a physical system is used as a tool to understand a mathematical object. While we begin to demonstrate its utility in describing the individual moves that students make, as well as the coordination and sequencing of these moves, when engaged in a larger mathematical sense making activity, we anticipate that the framework will also provide a guide for the design and development of curricula that support these sense making moves.