Author ORCID Identifier

Document Type


Publication Title

The Journal of Mathematical Behavior


Group isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight class periods, this paper examines the language used to discuss isomorphism and homomorphism. Language used by instructors in interviews and classroom settings are identified and classified into four main categories: formal definition, mapping, sameness, and combinations of sameness and mapping language. How the two instructors drew on language classified into those four categories in the interview and instruction settings are examined for isomorphism and homomorphism. Similarities and differences between the interview and instruction contexts reveal the wide variety of ways of understanding isomorphism and homomorphism as well as a research need to examine mathematicians’ content knowledge in more than one context.


Publication Date


Original Citation

Rupnow, R. (2021). Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching. Journal of Mathematical Behavior, 62(2), 100867.


Center for the Interdisciplinary Study of Language and Literature| Department of Mathematical Sciences



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