Student reasoning and justification for the invertible matrix theorem: an analysis using adjacency matrices

Title from first page of PDF file (viewed November 19, 2010)Includes bibliographical references (p. 34-35)Central goals of most any linear algebra course are to ensure that students develop relational understanding of concepts, become proficient at various techniques, and develop personal justifications for relationships between concepts. This thesis addresses the latter goal, linear algebra students' personal justifications for relationships through the analysis of end of the semester problem solving interviews. In particular, the interview question analyzed in this thesis prompted students to consider, given an invertible matrix A, whether five different claims are true or false. These claims are formally part of what many texts refer to as the Invertible Matrix Theorem (e.g., Lay, 2003). This report addresses student responses by highlighting the justifications students provided for relating invertibility, linear independence, determinant, span in R??, null space and pivots. The analysis also contributes to the development of an innovative method using adjacency matrices to analyze students' understandings of concepts and the connections students make between concepts