# A framework for the natures of negativity in introductory physics

## TL;DR

This paper introduces a framework to categorize the various meanings of negative signs in physics, aiming to improve students' understanding of signed quantities and support better mathematical reasoning in physics education.

## Contribution

It develops a novel framework inspired by algebra education research to analyze the different interpretations of negative signs in physics contexts.

## Key findings

- Framework categorizes meanings of negative signs in physics
- Supports instructional innovation for better conceptual understanding
- Addresses student struggles with signed quantities in physics

## Abstract

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebra contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond.