# A critical discourse analysis of practical problems in a foundation mathematics course at a South African university

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## Abstract

Mathematical problems that make links to the everyday and to disciplines other than mathematics—variously referred to as practical, realistic, real-world or applied problems in the literature—feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this article, we present a micro- and macro-analysis of a prototypical practical problem in an undergraduate mathematics course at a South African university. This course offers an alternative route to a mathematics major for students considered disadvantaged by enduring educational inequalities in South Africa. Using a socio-political practice perspective on mathematics and critical discourse analysis—drawn from Norman Fairclough’s critical linguists—we describe what mathematics and mathematical identities practical problems make available to students and compare this to what is valued in school mathematics and other university mathematics courses. Our analysis shows that these practical problems draw in complex ways on sometimes contradictory practices in the wider context, requiring the student to work flexibly with the movement of meaning within and across texts. We raise for further consideration the possible consequences of this complexity and offer suggestions for practice that take into account issues of power.

## Keywords

Access Advanced mathematics Calculus reform Critical discourse analysis Equity Practical problems Socio-political practice perspective## Notes

### Acknowledgments

We thank Lucia Thesen for her insightful comments, and reviewers whose feedback has enhanced the clarity. This study has been supported by the National Research Foundation in South Africa under Grant number TTK2006040500009. Any opinion, findings and conclusions or recommendations expressed in this article are those of the authors, and the National Research Foundation does not accept any liability in regard thereto.

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