PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Student Understanding of Linear Independence of Functions
Page: 992
In this study, we present preliminary findings regarding student understanding of linear independence of vector-valued functions. Students were given a series of homework questionnaires and participated in individual and paired interviews. The researchers used grounded theory to categorize student approaches for determining linear (in)dependence of functions. In order to gain insight into students’ intuitive notions, data were collected before any formal instruction about the definition of linear independence of functions. The researchers describe initial analyses of student approaches, conjecturing their treatment of vector-valued functions at specific t-values or for varying t as a potentially beneficial lens of analysis. Students who evaluated specific t-values determined the linear independence of a set of vectors in 2 rather than the linear independence of the set of functions, themselves elements of a function space. The analytical construct of process/object pairs (Sfard, 1991) could be a useful lens to explore this distinction.