Author ORCID Identifier

https://orcid.org/0000-0001-6022-9630

Document Type

Article

Publication Title

The Journal of Mathematical Behavior

Abstract

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.

DOI

https://doi.org/10.1016/j.jmathb.2021.100867

Publication Date

3-15-2021

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. https://doi.org/10.1016/j.jmathb.2021.100867

Department

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

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.