Critical stance within a community of inquiry in an advanced mathematics course for pre-service teachers

Simon Goodchild,Chris Rasmussen,Brian Katz,Naneh Apkarian

doi:10.1007/s10857-020-09456-2

Abstract

This paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor’s degree in mathematics to be followed by a year-long teacher education credential program. The analysis of students’ end of course presentations and written portfolios is framed with community of practice theory, complemented with analytic categories from community of inquiry, including notions of inquiry stance and critical alignment. Our social theorization of university mathematics education adds a complementary perspective to the more conventional cognitive and discursive analyses and is necessitated by the very nature of inquiry approaches to education. The analysis of students’ presentations and writing leads to exploring their development of the notion of critical stance, which the students are seen to take toward the mathematics, their learning, and approaches to teaching mathematics. We find that the notion of critical stance can be distilled into three components: awareness, self-evaluation, and agency.

Highlights

In this paper, we use community of practice theory (CPT) as an overarching framework to explore the mathematics education of university students who intend to become secondary school mathematics teachers
The three conditions for taking a critical stance outlined in this paragraph go beyond “inquiry stance” and “critical alignment” and go some way toward answering these questions; further we claim that in this report we demonstrate how these conditions can be met within a mathematics course for pre-service teachers
Concurrent engagement with the literature applying CPT to educational settings led the team to reflect on the substantive question: what are the grounds for claiming that the class had developed into a community of inquiry? At this point, the theorization provided by Biza et al (2014) became the key to our interpretation as we looked for evidence of critical alignment

Summary

Introduction

We use community of practice theory (CPT) as an overarching framework to explore the mathematics education of university students who intend to become secondary school mathematics teachers. The conventional approach adopted by many university mathematics teachers who perceive their purpose is to model authentic mathematics through lecture (London Mathematical Society 2010) From such a perspective, it is of little interest to examine issues of teaching and learning within a social practice theoretical framework. There has been considerable endorsement of such strategies by professional organizations (e.g., Conference Board of the Mathematical Sciences 2016; Mathematical Association of America 2017; Saxe and Braddy 2015), challenging the dominant paradigm of modeling by lecture. All this precipitates a need to develop the social theorization of university mathematics education.

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Results

Conclusion