Analysing the Competency of Mathematical Modelling in Physics

TL;DR

This paper examines how developing mathematical modeling skills in physics involves integrating physical meaning into mathematical representations, highlighting challenges in teaching students to effectively use math in physics.

Contribution

It analyzes the unique nature of mathematical modeling in physics and emphasizes the importance of blending physical meaning with mathematical symbols for effective learning.

Findings

Mathematical modeling in physics requires understanding physical meaning beyond mathematical procedures.

Students often struggle to connect mathematical symbols with physical concepts.

Effective physics education should focus on integrating physical meaning into mathematical representations.

Abstract

A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on the learning of both physics and math, the problem of how to successfully teach most of our students to use maths in physics effectively remains unsolved. A fundamental issue is that in physics, we don't just use maths, we think about the physical world with it. As a result, we make meaning with math-ematical symbology in a different way than mathematicians do. In this talk we analyze how developing the competency of mathematical modeling is more than just "learning to do math" but requires learning to blend physical meaning into mathematical representations and use that physical meaning in solving problems. Examples are drawn from across the curriculum.