Blending Mathematical and Physical Negative-ness.

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.