PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Stages of development for the concept of inverse in abstract algebra
Page: 520
In this study, we conducted a teaching experiment with two students to investigate the development of a generalized concept of inverse in abstract algebra. In particular, we document the stages through which the students’ reasoning progressed, initiating with an understanding of the additive inverse of an element as the result of a procedure applied to that element, and concluding with a generalized understanding of inverse that was broad enough to identify instances of inverses in various and unfamiliar algebraic structures. Of critical importance was the development of and coordination with a corresponding concept of identity.