PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Inverse, Composition, and Identity: The Case of Function and Linear Transformation
Page: 2-341
In this report we examine linear algebra students’ conceptions of inverse and invertibility. In the course of examining data from semi-structured clinical interviews with 10 undergraduate students in a linear algebra class, we noted a proclivity for students to identify 1 as the result of the composition of a function and its inverse. We propose that this may stem from the several meanings of the word “inverse” or the influence of notation from linear algebra. In addition, we examined how students attempted to reconcile their initial incorrect predictions with their later computational results, and found that students who succeeded in this reconciliation made heavy use of what we termed “do-nothing function” ideas. The implications of this work for classroom practice include a possible method to help students develop object conceptions of function, as well as the need to pay more explicit attention to often-backgrounded notational issues.