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(Re)asserting a knowledge-building agenda in school mathematics

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Abstract

This paper makes a case for placing knowledge at the centre of the school mathematics curriculum, and for knowledge building and knowledge differentiation as critical for both equity and excellence, emphasising that knowledge is much more than a set of descriptions of content as might typically be found in a curriculum document or textbook. The paper commences by discussing the implications of the traditional epistemological view of knowledge as justified true belief for mathematics education and uses this to build a preliminary description of knowledge building. Ideas from critical realism are then used to show that it is not so much the content of knowledge that matters but the production of knowledge and to build an enhanced conception of knowledge building in school mathematics. A distinction is made between knowledge and knowing that provides a non-relativist yet fallible view of knowledge, recognising its emergent but directed nature through its production and legitimation within established fields. The importance of knowledge building as a democratic right is then discussed, highlighting the importance of specialised knowledge and arguing that knowledge differentiation provides a basis for a conception of school mathematics curriculum that is dynamic and empowering. The paper concludes by discussing a range of potential theoretical and empirical research projects arising from a focus on knowledge and knowledge building in school mathematics.

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Notes

  1. The term “knowledge building” is used in this paper as a generic phrase to describe the collective production and legitimation of knowledge, to be distinguished from specific realisations or technologies described, for example, by Scardamalia and Bereiter (2006).

  2. This paper does not take a position on fallibilist or absolutist philosophies, whether mathematics is “discovered” or “invented”, nor particular philosophies of mathematics such as Platonism, formalism, constructivism (in the mathematical sense) or social constructivism as described by Ernest (1998). Each contributes important perspectives to how we understand the nature of mathematical knowledge and its development and learning; however, debates favouring one position over another have arguably made little impact on the knowledge practices in school mathematics. The argument made in this paper is that critical realism cuts through these positionings and provides a productive way forward that honours both the distinctive truth warrants of mathematics and the epistemic relativism inherent in its development.

  3. Keno is a gambling game commonly played in hotels or clubs across Australia. Twenty numbers are drawn from a possible 80, with the numbers appearing on screens. Players mark up to 10 numbers that they predict might appear, and win varying amounts depending on how many numbers they choose and how many appear. The most and least commonly drawn numbers on any given day are frequently displayed on the screen.

  4. Moore (2013) distinguishes between social realism and its philosophical ancestor, critical realism. For simplicity, we do not make that distinction, as the fundamental tenets are the same. Social realism emphasises the existence, not only of physical objects but also of social structures and phenomena, independent of our conception or perception of them.

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Acknowledgements

The author acknowledges the support of colleagues Kristen Tripet, Ruqiyah Patel, Valerie Barker, Virginia Kinnear and Peter Galbraith as well as the anonymous reviewers who provided feedback on the first draft of this paper.

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  1. Charles Sturt University, Albury-Wodonga, Australia

    Steve Thornton

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Thornton, S. (Re)asserting a knowledge-building agenda in school mathematics. Math Ed Res J 34, 69–85 (2022). https://doi.org/10.1007/s13394-020-00322-1

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