RUME 27
2025
Alexandria, Virginia
Students’ Connections About Equivalence Across Contexts: Substitution and Known vs. Own Equivalences
Page: 562
The concept of equivalence is fundamental to problem-solving in mathematics. Particularly, an oft-utilized feature of equivalence is substitution, in which the mathematics doer replaces one object with an equivalent object. Equivalence in general, and substitution in particular, have been identified as common threads that can tie together different areas of mathematics, but do students notice these connections in their own mathematics? In this paper, I report on task-based clinical interviews with students exploring the commonalities they identify among tasks implicitly involving equivalence relations. In particular, I discuss themes that students explicitly identified as relevant when answering the interview tasks: (1) substitution equivalence and (2) a distinction between students using a known equivalence for substitution or introducing their own equivalence.