PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Developing an open-ended linear algebra assessment: Initial findings from clinical interviews
Page: 828
The primary goal of this study was to design and validate a conceptual assessment in an undergraduate linear algebra course. We work toward this goal by conducting semi-structured clinical interviews with 8 undergraduate students who were currently enrolled or had previously taken linear algebra. We try to identify the variety of ways students reasoned about the items with the intent of identifying ways in which the assessment measured or failed to measure students’ understanding of the intended topics. Students were interviewed while they completed the assessment and interview data was analyzed by using an analytical tool of concept image and concept definition of Tall and Vinner (1981). We identified two themes in students’ reasoning: the first theme involves students reasoning about span in terms of linear combinations of vectors, and the second one involves students struggling to resolve the number of vectors given with the number of entries in each vector.