Blending embodied, symbolic, and formal thinking in linear algebra: The experiences of a mathematician and his students
Sepideh Stewart
University of Oklahoma
Joint Work with Jonathan Epstein, Jonathan Troup and Aidan Powers.
A deep understanding of linear algebra concepts requires recognizing and grasping many different representations of the concepts. Mathematicians often move fluently between various representations and modes of thinking while solving problems or explaining ideas. Employing Tall’s (2008; 2013) three-world model of the embodied, symbolic, and formal worlds of mathematical thinking, as both a theoretical perspective and a pedagogical tool and the notion of blending (Fauconnier & Turner, 2002), we studied a mathematician (instructor and co-researcher) and his linear algebra students over a semester. The results of this study are based on the analysis of the mathematician’s teaching journals, two student surveys, and a student interview. Our working hypothesis is that blending the embodied, symbolic, and formal worlds encourage a richer conceptual understanding of linear algebra. Our study revealed the instructor, and his students valued the unique advantages each world gives; however, only the mathematician strategically utilized blends of the various worlds.
