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Abstract

National curriculum statements continue to espouse the ability to solve problems arising in everyday life, society, and the workplace as a major goal of mathematics education. But support for such high sounding rhetoric is typically weakened (or absent) when the specifics of curricula are elaborated. The epistemic fallacy relates to the conflating of ontology and epistemology – confusing the nature of an underlying reality with knowledge of it. Here the underlying reality concerns mathematical modelling as real world problem solving. It is argued that manifestations of the fallacy occur in critiques of modelling theory, in debates about the authenticity of models and approaches, and in considering whether issues concerning practice are most fundamentally a curriculum or a pedagogical matter.

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Notes

  1. 1.

    International Community for the Teaching of Mathematical Modelling and Applications.

References

  • ACARA. (2010). Australian Curriculum, Assessment and Reporting Authority. Mathematics: Draft consultation version 1.1.0 Australian Curriculum. Formerly available from www.australiancurriculum.edu.au/Documents/Mathematicscurriculum.pdf

  • ACARA. (2013). Australian Curriculum, Assessment and Reporting Authority. D12/3780: Draft Senior Secondary Curriculum – Mathematical Methods Curriculum May 2012. http://www.acara.edu.au/default.asp?id=site_search&query=mathematical+methods

  • Bhaskar, R. (1975). A realist theory of science. Brighton: Harvester.

    Google Scholar 

  • Blum, W., et al. (2002). ICMI study 14: Applications and modelling in mathematics education – Discussion document. Educational Studies in Mathematics, 51(1–2), 149–171.

    Article  Google Scholar 

  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86–95.

    Article  Google Scholar 

  • Bryant, L. R. (2011). The democracy of objects. Ann Arbor: Open Humanities Press.

    Book  Google Scholar 

  • Burkhardt, H. (1981). The real world and mathematics. Glasgow: Blackie-Birkhauser.

    Google Scholar 

  • Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38(2), 178–195.

    Article  Google Scholar 

  • CCSSI. (2012). Mathematics: Standards for mathematical practice – Model with Mathematics. Retrieved March 16, 2013 from http://www.corestandards.org/Math/Practice/MP4

  • Galbraith, P. (2013). From conference to community: An ICTMA journey – The Ken Houston inaugural lecture. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 27–45). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 503–510). New York: Springer.

    Chapter  Google Scholar 

  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, M. Niss, & H.-W. Henn (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3–32). New York: Springer.

    Chapter  Google Scholar 

  • Perrenet, J., & Zwanefeld, B. (2012). The many faces of the mathematical modelling cycle. Journal of Mathematical Modelling and Application, 1(6), 3–21.

    Google Scholar 

  • Pollak, H. O. (1969). How can we teach applications of mathematics? Educational Studies in Mathematics, 2(2/3), 393–404.

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, MA: Cambridge University Press.

    Book  Google Scholar 

  • Valsiner, J. (1997). Culture and the development of children’s action: A theory of human development (2nd ed.). New York: Wiley.

    Google Scholar 

  • Zbiek, R., & Connor, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89–112.

    Article  Google Scholar 

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Correspondence to Peter Galbraith .

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Galbraith, P. (2015). Modelling, Education, and the Epistemic Fallacy. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_28

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