Toward a framework for the natures of proportional reasoning in introductory physics

We present a set of modes of reasoning about ratio and proportion as a means of operationalizing expert practice in physics. These modes, or natures of proportional reasoning, stem from consideration of how physicists reason in context and are informed by prior work in physics and mathematics education. We frame the natures as the core of an emerging framework for proportional reasoning in introductory physics, that will categorize the uses of proportional reasoning in introductory physics contexts, and provide guidance for the development of reliable assessments. We share results from preliminary assessment items indicating that university physics students have difficulty interpreting and applying ratios in context.