PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Using student reasoning to inform assessment development in linear algebra
Page: 163
The primary goal of this study was to design and validate an assessment of student reasoning in undergraduate linear algebra. We worked toward this goal by conducting semi-structured clinical interviews with 8 undergraduate students who were currently enrolled or had previously taken linear algebra. We identified the variety of ways students reasoned about the items in order to determine the extent to which the assessment measured or failed to measure students’ reasoning about the intended topics. Students were interviewed using a think-aloud protocol while they completed the assessment, and interview data was analyzed by using the theoretical framing of concept image and concept definition (Tall & Vinner, 1981). In this paper, we describe how students’ reasoning on items relating to span and linear independence informed adjustments to our assessment.