Student understanding of linear independence of functions
Résumé
We present findings regarding student understanding of linear independence of vector-valued functions, a concept common in linear algebra and differential equations. Data were collected from written homework questionnaires and a paired interview, prior to any formal instruction about the definition of linear independence of functions. Grounded theory was used to categorize student approaches, resulting in five main categories: Function Combination, Focus on t Values, Focus on Graphs, Focus on Scalars, and Previous Rule. Results suggest that students' transition from linear independence of vectors in Euclidean space to linear independence of functions in function space is not trivial and that fostering an object view of function may facilitate students more readily operating with functions as elements of a vector space.
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