Communities in university mathematics

Abstract

This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of Communities of Practice. From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form their identity through engagement, imagination and alignment. In addition, when inquiry is considered as a fundamental mode of participation, through critical alignment, the community becomes a Community of Inquiry. We discuss these theoretical underpinnings with examples of their application in research in university mathematics education and, in more detail, in two Research Cases which focus on mathematics students' and teachers' perspectives on proof and on engineering students' conceptual understanding of mathematics. The paper concludes with a critical reflection on the theorising of the role of communities in university level teaching and learning and a consideration of ways forward for future research.

Keywords:

• Community of Practice
• Community of Inquiry
• identity
• critical alignment
• university mathematics education

Acknowledgement

The ESUM project (Engineering Students Understanding Mathematics) reported in the Research Case 2 was supported by the UK HE STEM programme via The Royal Academy of Engineering.

Notes

1. We use ‘(university) teacher’ to describe all those involved in the teaching of mathematics at university level. We describe other identities with specific characterisations, such as research mathematician, or mathematics educator, when necessary.

2. All the excerpts presented in Research Case 1 are translated from the Swedish.