RUME 28
2026
Alexandria, Virginia
Indifference as a Key Aspect of a Global Perspective on Equivalence Relations
Page: 1044
Equivalence is a central concept of mathematics and is a fixture in the K-16 curriculum. Though equivalence has been very well-studied overall, very little is known about how students reason with formal equivalence relations in advanced mathematics. Recent research has demonstrated that one component of productive reasoning about equivalence relations entails the ability to flexibly move between viewing equivalence from both an elementwise (local) perspective and a set-oriented (global) perspective. Building on this work, we report on a pilot study intended to aid the development of a conceptual analysis of equivalence in advanced mathematics - in which we seek to refine the notion of a global perspective on equivalence. In this preliminary report, by showcasing excerpts from task-based clinical interviews with two advanced mathematics students, we propose ‘indifference’ as a beneficial way of reasoning about equivalence from a global perspective.