Making Meaning with Math in Physics: A semantic analysis

TL;DR

This paper explores how cognitive semantics can help improve understanding of the complex relationship between mathematical symbols and physical meaning in physics education.

Contribution

It proposes applying cognitive semantics to facilitate unpacking the meaning of mathematical language in physics for better teaching and learning.

Findings

Highlights the integration of math and physical meaning in physics expertise

Identifies difficulties novices face in understanding mathematical physics

Suggests cognitive semantics as a tool for improving physics education

Abstract

Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But because of the way the cognitive system builds expertise through binding, experts may have difficulty in unpacking their well established knowledge in order to understand the difficulties novice students have in learning their subject. This is particularly evident in subjects in which the students are learning to use mathematics to which they have previously been exposed in math classes in complex new ways. In this paper, we propose that some of this unpacking can be facilitated by adopting ideas and methods developed in the field of cognitive semantics, a sub-branch of linguistics devoted to understanding how meaning is associated with language.