How Physics Textbooks Embed Meaning in the Equals Sign

TL;DR

This paper analyzes how physics textbooks assign different conceptual meanings to the equal sign, revealing five categories and their varying usage across educational levels, which influences understanding of physics concepts.

Contribution

It identifies and operationally defines five distinct meanings of the equal sign in physics textbooks, highlighting their role in linking mathematics to physical concepts.

Findings

Five categories of equal sign meanings identified

Significant differences in usage between textbook levels

Operational definitions help distinguish different meanings

Abstract

Physics as a discipline embeds conceptual meaning about the physical world in mathematical formalism. The meaning associated with mathematical symbols depends on context, and physicists can shift conceptual meaning by manipulating those symbols. We present an analysis of the different physical meanings associated with the equal sign "=" that can be inferred from introductory and upper--level physics textbooks. Five distinct meanings/categories are identified: causality, balancing, definitional, assignment, and calculation, each with operational definitions that help identify their presence. The different uses can be seen to link mathematical equations to intuitive conceptual ideas, and significant differences in the frequency with which these are used exist between textbooks of different levels.