EJMT Abstract

Linear algebra is a conceptually rich and challenging subject, demanding that students reason flexibly about abstract mathematical objects such as matrices, vectors, and eigen-structures. To support this learning, we have developed digital interactive figures that allow students to explore linear algebraic relationships without the cognitive burden of routine computation. In this paper, we present a Markov chain assignment integrating two such digital figures alongside conceptual and proof-based problems, scaffolding students’ exploration toward conjectures about the spectral properties of stochastic matrices and long-term behavior of the Markov chain. We discuss the pedagogical principles underlying our design, revisions following task-based student interviews, and implications for teaching linear algebra with technology-integrated materials.