PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Operational and Structural Reasoning with Linear Transformations
Page: 2-413
In this report we detail linear algebra students’ interpretations of linear transformations. Data for this analysis comes from mid semester, semi-structured problem solving interviews with 13 undergraduate students in linear algebra. We identified two main categories for student reasoning students in completing three tasks: 1) students who used structural reasoning with entries of the matrix, columns of the matrix, and orientation of the shape and 2) students who used operational reasoning through matrix and vector multiplication. We examine the patterns that emerged from student strategies, and discuss possible explanations for these patterns.