Blending Mathematical and Physical Negative-ness

TL;DR

This paper investigates how students interpret and manipulate negative signs in algebraic physics problems using Conceptual Blending theory, revealing insights into their understanding of algebraic symbolism.

Contribution

It applies Conceptual Blending theory to analyze students' meaning-making of negative signs in physics algebra, a novel approach in physics education research.

Findings

Students' understanding of negative signs varies with context.

Students often struggle with multiple negative signs in expressions.

The study highlights the importance of conceptual understanding in algebraic manipulation.

Abstract

Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate them becomes a challenging task for students, especially when more than two elements in the mathematical expression could carry a negative sign. We use Conceptual Blending theory to investigate how students attribute emergent meaning to the signs and how they articulate different signs in their algebraic symbolization. The data for this research is drawn from oral exams of students enrolled in upper-division physics. The results shed light on students' understanding of algebraic symbols and their competence in formulating and manipulating them.