PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Presentation of Matrix Multiplication in Introductory Linear Algebra Textbooks
Page: 518
We conducted an analysis of 17 modern, introductory linear algebra textbooks to investigate presentations of matrix multiplication. Using Harel’s (1987) textbook analysis framework, we examined the sequencing of matrix multiplication and its accompanying rationale. We found two principal sequences: one which first defines the operation as a linear combination of column vectors before introducing the dot product method (LC to DP), and another which invokes the dot product method before linear combinations (DP to LC). The rationale for these two trajectories varied in interesting ways. LC to DP demonstrates that solving a system of linear equations is equivalent to solving its corresponding matrix equation Ax=b. The rationale for DP to LC was less focused, opting in several cases to postpone the explanation until linear transformations are covered. We hope to initiate a discussion about the effectiveness of and pedagogical implications for these two contrasting approaches.