Equivalence, the idea that two objects can be considered the same in some way, is one of the most important concepts in mathematics.
Learners from elementary through graduate school encounter equivalence in many ways across many mathematical topics. However, despite its prevalence and importance, undergraduate students can be challenged to understand instances of equivalence, especially if similar concepts are introduced in a disconnected way. Moreover, characterizations of equivalence in research are often implicit or domain-specific, speaking to the need for cognitive models that might prove useful within and across mathematical disciplines.
This project aims to develop a crosscutting theory of equivalence that could be applied in multiple contexts. Focusing on the domains of combinatorics and abstract algebra, the project’s primary research questions are:
What is entailed in undergraduate students’ ways of thinking about equivalence within the domains of abstract algebra and combinatorics?
What is entailed in undergraduate students’ ways of thinking about equivalence across these domains?
This project is funded by the EHR Core Research (ECR) program of the United States National Science Foundation (NSF), which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.