PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Students Reconciling Notions of One-to-One Across Two Contexts
Page: 2-297
As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. Analysis of these data led to a classification of student responses into properties, computations and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this classification to analyze students’ written and verbal responses to questions regarding one-to-one in the context of function from high school algebra and in the context of linear transformation from their study of linear algebra. We found that students’ ability to construe sameness across the two contexts is related to their reliance on properties versus metaphors. We conjecture that this phenomenon is likely to occur for other mathematical constructs as well.