  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.
