2021 Research in Undergraduate Mathematics Education Reports
2021
N/A
Student Understandings of Properties of Linear Transformations
Page: 316
Student understanding of linear algebra concepts is a growing research area. This study explores students’ conceptualization of linear transformations and the various ways in which they use such conceptualization to reason through linear transformation problems after they have completed a linear algebra course. Three students participated in a task-based interview. Through analyzing interview data using a grounded theory approach, emerging themes were found indicating that students’ exposure to linear transformations in other courses and the nature of these experiences impacts how they further conceptualize linear transformations. Notably, the way that the participants were engaged with linear transformations within their other courses for their major seemed to influence their use of geometry, algebra, and proofs in determining whether a given transformation is linear. One implication of this study is a need to engage students with more real-life applications of linear transformations in linear algebra courses.