Volume 7 · Number 2 · Pages 104–111
On the Role of Constructivism in Mathematical Epistemology

Andreas Quale

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Abstract

Context: the position of pure and applied mathematics in the epistemic conflict between realism and relativism. Problem: To investigate the change in the status of mathematical knowledge over historical time: specifically, the shift from a realist epistemology to a relativist epistemology. Method: Two examples are discussed: geometry and number theory. It is demonstrated how the initially realist epistemic framework – with mathematics situated in a platonic ideal reality from where it governs our physical world – became untenable, with the advent of non-Euclidean geometry and the increasing abstraction of the number concept. Results: Radical constructivism offers an alternative relativist epistemology, where mathematical knowledge is constructed by the individual knower in a context of an axiomatic base and subject items chosen at her discretion, for the purpose of modelling some part of her personal experiential world. Thus it can be expedient to view the practice of mathematics as a game, played by mathematicians according to agreed-upon rules. Constructivist content: The role played by constructivism in the formulation of mathematics is discussed. This is illustrated by the historical transition from a classical (platonic) view of mathematics, as having an objective existence of its own in the “realm of ideal forms,” to the now widely accepted modern view where one has a wide freedom to construct mathematical theories to model various parts of one’s experiential world.

Key words: knowledge construction, noncognitive knowledge, realism, relativism, platonic world, physical world, non-Euclidean geometry

Citation

Quale A. (2012) On the role of constructivism in mathematical epistemology. Constructivist Foundations 7(2): 104–111. http://constructivist.info/7/2/104

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References

Geelan D. (1997) Epistemological anarchy and the many forms of constructivism. Science & Education 6(1–2): 15–28. ▸︎ Google︎ Scholar
Glasersfeld E. von (1981) The concepts of adaptation and viability in a radical constructivist theory of knowledge. In: Siegel I. E., Brodzinsky D. M. & Golinkoff R. M. (eds.) New directions in Piagetian theory and practice. Lawrence Erlbaum, Hillsdale NJ: 87–95. http://www.vonglasersfeld.com/067
Glasersfeld E. von (1984) An introduction to radical constructivism. In: Watzlawick P. (ed.) The invented reality. Norton, New York: 17–40. http://www.vonglasersfeld.com/070.1
Glasersfeld E. von (1989) Cognition, construction of knowledge and teaching. Synthese 80: 121–140. http://www.vonglasersfeld.com/118
Glasersfeld E. von (1995) Radical constructivism: A way of knowing and learning. The Falmer Press, London. ▸︎ Google︎ Scholar
Glasersfeld E. von (2000) Problems of Constructivism. In: Steffe L. P. & Thompson P. W. (eds.) Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld. Routledge, London: 3–9. http://www.vonglasersfeld.com/233
Glasersfeld E. von (ed.) (1991) Radical constructivism in mathematics education. Kluwer Academic Publishers, Dordrecht. ▸︎ Google︎ Scholar
Pickering A (1986) Constructing quarks: A sociological history of particle physics. Barnes & Noble, London. ▸︎ Google︎ Scholar
Quale A. (2008) Radical constructivism: A relativist epistemic approach to science education. Sense, Rotterdam. ▸︎ Google︎ Scholar
Weinberg S. (1993) Dreams of a final theory. Random House, New York. ▸︎ Google︎ Scholar
Wigner E. (1960) The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics 13(1) http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

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