Original Research

The merits of teaching mathematics with variation

Michael Mhlolo
Pythagoras | Vol 34, No 2 | a233 | DOI: https://doi.org/10.4102/pythagoras.v34i2.233 | © 2013 Michael Mhlolo | This work is licensed under CC Attribution 4.0
Submitted: 13 June 2013 | Published: 29 November 2013

About the author(s)

Michael Mhlolo, Faculty of Humanities, Central University of Technology, South Africa


There is a general perception that the South African curriculum statements for mathematics create polarity between the ‘old’ and the ‘new’, which does not benefit both the teachers and the learners. The new curricula demand a radical shift from the traditional teacher-led approaches that teachers are familiar with, yet does not provide a model of what it might mean to teach for conceptual understanding. This article aims to provide such a model by examining the potential of teaching with variation, which is viewed as an important mathematics teaching and learning style. Proponents of the theory of variation claim that how teachers make available the object of learning to their students has been neglected yet it has a critical influence on learners’ learning. This is important for educators as they struggle to make sense of the seemingly contradictory requirements of the new curriculum. In this article a discernment unit comprising four variation patterns is used as a tool to analyse a seemingly rich teacher-led approach to teaching that was observed in one South African Grade 11 mathematics classroom. The results of the analysis and implications for theory and practice are then discussed.


procedural variation; paradox; procedural teaching


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