Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis

Abstract

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories – explanation, motivation and question posing routines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines include known mathematical facts, summary and repetition, different representations, everyday language, and concretization and metaphor; the motivation routines include reference to utility, the nature of mathematics, humour and result focus; and the question posing routines include control questions, asking for facts, enquiries and rhetorical questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics.

Keywords:

• mathematics
• university education
• commognitive framework
• function
• discourse
• teaching

Acknowledgements

I wish to thank the anonymous reviewers for their valuable comments on the first draft of this paper. Also, I am very grateful to the university mathematics teachers who kindly agreed to participate in this study.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. The graph of cos(x).

2. On the unit circle.

3. The first lecture on linear transformations, that is. The lecture is actually positioned fairly late in the course, so it is reasonable to expect that the exam will be on students’ minds.