PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Utilizing Types of Mathematical Activities to Facilitate Characterizing Student Understanding of Span and Linear Independence
Page: 2-277
The purpose of this study is to investigate students’ concept images of span and linear (in)dependence and to utilize the mathematical activities of defining, example generating, problem solving, proving, and relating to provide insight into these concept images. The data under consideration are portions of individual interviews with linear algebra students. Grounded analysis revealed a wide range of student conceptions of span and/or linear (in)dependence. The authors organized these conceptions into four categories: travel, geometric, vector algebraic, and matrix algebraic. To further illuminate participants’ conceptions of span and linear (in)dependence, the authors developed a framework to classify the participants’ engagement into five types of mathematical activity: defining, proving, relating, example generating, and problem solving. This framework could prove useful in providing finer-grained analyses of students’ conceptions and the potential value and/or limitations of such conceptions in certain contexts.