RUME 26
2024
Omaha, Nebraska
Isomorphism Across Courses: Students’ Metaphors in Discrete Math, Linear Algebra, and Abstract Algebra
Page: 1010
Isomorphism appears across many courses in mathematics, including discrete mathematics, linear algebra, and abstract algebra. However, examinations of student understandings of isomorphism have mostly focused on group isomorphism in abstract algebra. In this paper, we compare survey responses from 49 discrete math, 19 linear algebra, and 27 abstract algebra students who were prompted to explain the concept of isomorphism to a child. Results include a cross-course emphasis on types of sameness but variations in the types of language used to characterize isomorphism in each course. Implications include the need for care among instructors and researchers when referring the concept of “isomorphism” without a context as well as the need for further work in understandings of graph theory.