Snapshots of sameness: Characterizations of mathematical sameness across student groups

Sameness is foundational to mathematics but has only recently become an area of focus in mathematics education research. In this paper, we describe characterizations of sameness generated by four student groups: discrete mathematics students, linear algebra students, abstract algebra students, and graduate students. Based on qualitative analysis of open response surveys, we compare these groups’ characterizations of sameness; note the subcomponents discussed and variation within each dimension; and highlight experiences influential to students’ perceptions of sameness. Findings include interpretability of sameness as a big idea, nascent development of thematic connections across courses, emphases on current course material rather than connections to prior courses for students solicited from a particular course, greater reflectiveness from the graduate student group, and abstract algebra as an impactful course. Implications include a need for thoughtful examinations of how “big ideas” develop among students and what experiences might support such development. •Graduate students made connections across and within multiple contexts.•Undergraduates mostly commented on equality or course-based sameness concepts.•Sameness influences were mostly from current courses or abstract algebra.•More research is needed on graduate students’ understandings outside proof.•More research should explore snapshots of understandings at different times.