Symbolic Manipulators Affect Mathematical Mindsets

TL;DR

This paper explores how symbolic calculators like Mathematica influence upper-level physics students' mathematical reasoning, often narrowing their thinking and affecting their problem-solving approaches.

Contribution

It provides a model of how symbolic manipulators impact students' framing and focus during mathematical reasoning in physics education.

Findings

Students engage in powerful reasoning but are drawn into local calculation attractors.

Mathematica influences students' framing and focus during problem-solving.

Students struggle with narrowed thinking due to reliance on calculation schemes.

Abstract

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.