## 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.

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## Notes

- 1.
Racial classifications such as “black”/“African”, “coloured” and “white” are still used to report educational performance in South Africa, despite a growing recognition of how this construct works with others in constituting “educational disadvantage”.

- 2.
More recently, the university has recognised limitations in what both the regular and foundation first year courses offer in supporting the transition to advanced mathematics by requiring that all potential mathematics majors complete an additional first year level course.

- 3.
Our description of mathematical objects in this article draws on Fairclough’s critical realist distinction between

*real*objects, the*actual*and the*empirical*(Chouliaraki & Fairclough, 1999). We acknowledge broader debates in the philosophy of mathematics and mathematics education regarding the nature of mathematical objects; debates that are not the focus of this article. - 4.
See le Roux & Adler (2012) for our re-description of this activity from a socio-political practice perspective, i.e., our shift from the psychological notions of operational and structural “conceptions” used extensively in undergraduate mathematics education research.

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## 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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le Roux, K., Adler, J. A critical discourse analysis of practical problems in a foundation mathematics course at a South African university.
*Educ Stud Math* **91, **227–246 (2016). https://doi.org/10.1007/s10649-015-9656-5

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### Keywords

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