Leading students towards the formal world of mathematical thinking: a mathematician’s reflections on teaching eigentheory

ABSTRACT

In this study, we analysed a mathematician’s teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall’s [How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press] three-world model of embodied, symbolic and formal as a framework for understanding the mathematician and teacher’s pedagogical reflections as he led the class to the formal world. In order to reach the formal world, he used a sequence of tasks that emphasized embodied and symbolic, as well as formal thinking. The analysis of the journals showed that the mathematician faced challenges in leading the class towards the formal world. The study also revealed that the mathematician strived to build a concept image, that, while perhaps mirroring his own, did not resonate with the students.

KEYWORDS:

• Concept images
• IOLA
• reflections
• eigenvalues and eigenvectors
• formal world

Acknowledgements

We would like to thank David McKnight, for his tremendous contributions to this project.

Disclosure statement

No potential conflict of interest was reported by the authors.