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Abstract

This chapter deals with a distinction between two kinds of mathematical modelling purposes and related modelling endeavours, descriptive modelling and prescriptive modelling. Whilst descriptive modelling is usually the focus of attention of practice, research and development in mathematics education, prescriptive modelling – in which the aim is to design, organise or structure certain aspects of extra-mathematical domains – is hardly noticed, let alone investigated in mathematics education. After having presented three concrete examples of prescriptive modelling, this chapter makes a plea for paying attention to its cultivation and investigation in mathematics education contexts. It does so by analysing prescriptive modelling in relation to the so-called modelling cycle and finishes by outlining challenges and opportunities for such an endeavour.

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Notes

  1. 1.

    In Blum and Niss (1991, p. 39), the authors spoke about descriptive models rather than descriptive modelling, and also about normative models (not prescriptive models). Thus, the terms proposed in the present chapter represent a move from focusing on the product (the model) to focusing on the modelling purposes, whilst replacing ‘normative’ with ‘prescriptive’, following Davis (1991).

References

  • Amit, M., & Jan, I. (2010). Eliciting environments as “nurseries” for modeling probabilistic situations. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 155–166). New York: Springer.

    Chapter  Google Scholar 

  • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.

    Article  Google Scholar 

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

    Google Scholar 

  • Davis, P. J. (1991). Applied mathematics as a social instrument. In M. Niss, W. Blum, & I. Huntley (Eds.), Teaching of mathematical modelling and applications (pp. 1–9). Chichester: Ellis Horwood.

    Google Scholar 

  • Gini, C. (1912). Variabilità e mutabilità. Bologna: C. Cuppini.

    Google Scholar 

  • Gravemeijer, K. (2007). Emergent modelling as a precursor to mathematical modelling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 137–144). New York: Springer.

    Chapter  Google Scholar 

  • Lesh, R. A., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching. Mahwah: Erlbaum.

    Google Scholar 

  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 43–59). New York: Springer.

    Chapter  Google Scholar 

  • Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 385–398). New York: Springer.

    Chapter  Google Scholar 

  • Wikipedia a. www.wikipedia.org/wiki/Body_mass_index. Accessed 14 Nov 2013.

  • Wikipedia b. www.wikipedia.org/wiki/Gini_coefficient. Accessed 14 Nov 2013.

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Correspondence to Mogens Niss .

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Niss, M. (2015). Prescriptive Modelling – Challenges and Opportunities. 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_5

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