PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Inverse, Composition, and Identity: The Case of Function and Linear Transformation
Page: 1-46
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 that all the students said the result of composition of a function and its inverse is 1. 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 used what we termed “do-nothing function” ideas. This analysis highlights several implications for classroom practice, including 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.