PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
A Hypothetical Collective Progression for Conceptualizing Matrices as Linear Transformations
Page: 1-465
In this paper we develop the notion of a hypothetical collective progression (HCP). We offer this construct as an alternative to the construct of hypothetical learning trajectory in order to (a) foreground the mathematical development of the collective rather than that of individuals, and (b) highlight the integral role of the teacher within this development. We offer an abbreviated example of an HCP from introductory linear algebra based on the “Italicizing N” task sequence, in which students work to generate and combine matrices that correspond to geometric transformations specified within the problem context. In particular, we describe the ways in which the HCP supports students in developing and extending local “matrix acting on a vector” views of matrix multiplication (focused on individual mappings of input vectors to output vectors) to more global views in which matrices are conceptualized in terms of how they transform a space in a coordinated way.