The new AP Physics exams: Integrating qualitative and quantitative reasoning

When physics instructors and education researchers emphasize the importance of integrating qualitative and quantitative reasoning in problem solving, they usually mean using those types of reasoning serially and separately: first students should analyze the physical situation qualitatively/conceptually to figure out the relevant equations, then they should process those equations quantitatively to generate a solution, and finally they should use qualitative reasoning to check that answer for plausibility (Heller, Keith, {\&} Anderson, 1992). The new AP Physics 1 and 2 exams will, of course, reward this approach to problem solving. But one kind of free response question will demand and reward a further integration of qualitative and quantitative reasoning, namely mathematical modeling and sense-making--- inventing new equations to capture a physical situation and focusing on proportionalities, inverse proportionalities, and other functional relations to infer what the equation ``says'' about the physical world. In this talk, I discuss examples of these \textit{qualitative-quantitative translation} questions, highlighting how they differ from both standard quantitative and standard qualitative questions. I then discuss the kinds of modeling activities that can help AP and college students develop these skills and habits of mind.