In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and…

We explore ways that university students handle proving statements that have the overall structure of a conditional implies a conditional, i.e., (p [right arrow] q) [implies] (r [right arrow] s). We structure our analysis using the theory of conceptual blending. We find conceptual blending useful for describing the creation of powerful new ideas…

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate…