PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
A Hypothetical Learning Trajectory for Conceptualizing Matrices as Linear Transformations
Page: 2-251
In this presentation we articulate a hypothetical learning trajectory (HLT) designed to support students’ development and elaboration of a transformation view of matrix multiplication. The major learning goals of this HLT are (a) interpreting a matrix as a mathematical object that transforms input vectors to output vectors, (b) interpreting matrix multiplication as the composition of linear transformations, (c) developing the imagery of an inverse as “undoing” the original transformation, and (d) reasoning about matrices as objects that geometrically transform a space. Within this HLT, we extend students' conceptualization of the “matrix acting on a vector” view to a more global view of a matrix transforming an entire space, as opposed to the localized view wherein matrices are interpreted as transforming one vector at a time.