Cognitive Framework for Blended Mathematical Sensemaking in Science

Abstract: Blended mathematical sensemaking in science (blended MSS) involves deep conceptual understanding of quantitative relationships describing phenomena in science and has been studies in various disciplines. However, no unified characterization of blended MSS exists. We developed a theoretical cognitive model fro blended MSS grounded in prior work. The model contains three broad levels representing increasingly sophisticated ways of engaging in blended MSS: 1) deriving qualitative relationships among relevant variables describing a phenomenon (qualitative level, 2) deriving mathematical relationships among these variables (quantitative level), 3) explaining how the mathematical operations used in the formula relate to the phenomenon (conceptual levels). Each level contains three sub-levels. We used PhET simulations to design dynamic assessment scenarios in various disciplines to test the model. We used these assessments to interview undergraduate students with a wide range of math skills. Interview analysis provided validity evidence for the cognitive model. It also revealed that students tend to perform at the same level across different disciplinary contexts, suggesting that blended MSS is a distinct cognitive construct, independent of specific disciplinary context. This paper presents a first-ever published validated cognitive model for blended MSS which can guide instruction, curriculum, and assessment development.