Using math in physics: 5. Functional dependence

TL;DR

This paper emphasizes the importance of teaching the concept of functional dependence in physics education to help students understand how variables relate and change together within equations, which is often overlooked in math classes.

Contribution

It highlights the need to explicitly teach functional dependence in physics to improve students' understanding of mathematical relationships in science.

Findings

Students often lack understanding of variable relationships in equations.

Explicit instruction on functional dependence can enhance conceptual understanding.

Bridging math and physics concepts improves scientific reasoning.

Abstract

When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation: their functional dependence. Understanding this sort of relationship is rarely taught in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the relevance and power of this idea. We need to explicitly teach functional dependence as part of our effort to help students to learn to use math productively in science.