Moving Between the Embodied, Symbolic and Formal Worlds of Mathematical Thinking with Specific Linear Algebra Tasks

Abstract

Linear algebra is made out of many languages and representations. Instructors and text books often move between these languages and modes fluently, not allowing students time to discuss and interpret their validities as they assume that students will pick up their understandings along the way. In reality, most students do not have the cognitive framework to perform the move that is available to the expert. In this chapter, employing Tall's three-world model, we present specific linear algebra tasks that are designed to encourage students to move between the embodied, symbolic and formal worlds of mathematical thinking. Our working hypothesize is that by creating opportunities to move between the worlds we will encourage students to think in multiple modes of thinking which result in richer conceptual understanding.