The role of sign in students' modeling of scalar equations

TL;DR

This paper investigates how students revise physics equations to match physical situations, often violating laws, and how their reasoning about variables can inform teaching strategies.

Contribution

It reveals students' reasoning processes when revising equations and highlights the context-dependent nature of their understanding, informing instructional approaches.

Findings

Many students rewrite F = -ma to match coordinate directions.

Students' variable reasoning is context-dependent and can be leveraged in teaching.

Students' equation revisions often violate physical laws but serve a purpose in understanding.

Abstract

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.