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Pre-college mathematics modeling instruction often frames mathematics asbeing separated from reasoning about the real world -- and commonly treatsreasoning mathematically and reasoning about the real-world context as separatestages of a modeling cycle. In this paper, we present evidence that helpscharacterize how experts use mathematics in physics contexts while developinggraphical models. An important finding is that there was essentially noevidence of experts reasoning in a context-free way with these tasks, butinstead they used physical reasoning -- either grounded in the context of thetask or from abstract physical models -- to guide their mathematics. Thedifference in approach of physics instructors and students may lead to amismatch in expectations, and frustration, for both parties. This workcontributes to the body of knowledge about how mathematical reasoning appearsin physics, and can help researchers and instructors recognize the connectionsto the physical world in expert mathematical reasoning. This can helpinstructors and researchers be better equipped to develop materials and methodsthat can help students start building those connections as well.

Empirical evidence of the inseparability of mathematics and physics in expert reasoning about novel graphing tasks