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

TL;DR

This paper provides evidence that experts integrate physical reasoning with mathematical reasoning when developing graphical models in physics, challenging the separation often taught in pre-college education.

Contribution

It characterizes how experts use physical context to guide mathematical reasoning in physics tasks, highlighting differences from student approaches and implications for instruction.

Findings

Experts use physical reasoning to guide mathematics in physics tasks

No evidence of context-free mathematical reasoning among experts

Differences in reasoning approaches may cause student-instructor mismatches

Abstract

Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a modeling cycle. In this paper, we present evidence that helps characterize how experts use mathematics in physics contexts while developing graphical models. An important finding is that there was essentially no evidence of experts reasoning in a context-free way with these tasks, but instead they used physical reasoning -- either grounded in the context of the task or from abstract physical models -- to guide their mathematics. The difference in approach of physics instructors and students may lead to a mismatch in expectations, and frustration, for both parties. This work contributes to the body of knowledge about how mathematical reasoning appears in physics, and can help researchers and instructors recognize the connections to the physical world in expert mathematical reasoning. This can help instructors and researchers be better equipped to develop materials and methods that can help students start building those connections as well.