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Pedagogical Reflections on the Role of Modelling in Mathematics Instruction

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Teaching Mathematical Modelling: Connecting to Research and Practice

Abstract

From a broad perspective, there are two categories of pedagogical aims of modelling. The first is where modelling itself is treated as an objective. The second is mathematical knowledge construction, where modelling is treated as a means to an end. For the first aim three key questions are considered: (1) How can the teacher set an appropriate situation so that students realise the necessity of solving a real-world problem? (2) How can the teacher assist students’ abstraction processes? (3) How can the teacher show students the necessity of controlling various assumptions? For the second aim, three principles are suggested: (1) expanding and clarifying real-world situations satisfying a developed original model, (2) expanding and integrating mathematical knowledge by setting up a concrete situation so that students can consider it, and (3) refining and clarifying the developed mathematical methods by treating instances of the same contexts repeatedly.

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References

  • Blomhøj, M. (2009). Different perspectives in research on the teaching and learning of mathematical modelling – Categorising the TSG21 papers. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics (IMFUFA tekst nr.461, pp. 1–18). Roskilde: Roskilde University, Department of Science, Systems and Models.

    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 

  • Dewey, J. (2007). How we think. Stilwell: Digireads.com Publishing.

    Google Scholar 

  • Galbraith, P. (2007). Authenticity and goals – Overview. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 181–184). New York: Springer.

    Chapter  Google Scholar 

  • Hesse, M. B. (1966). Models and analogies in science. Notre Dame: University of Notre Dame Press.

    Google Scholar 

  • Ikeda, T., & Stephens, M. (1998). The influence of problem format on students’ approaches to mathematical modelling. In P. Galbraith, W. Blum, G. Booker, & I. D. Huntley (Eds.), Mathematical modelling – Teaching and assessment in a technology-rich world (pp. 223–232). Chichester: Horwood Publishing.

    Google Scholar 

  • Ikeda, T., & Stephens, M. (2010). Three teaching principles for fostering students’ thinking about modelling: An experimental teaching program for ninth grade students in Japan. Journal of Mathematical Modelling and Applications, 2(1), 49–59.

    Google Scholar 

  • Iyanaga, S. (2008). How to learn mathematics. Tokyo: Chikumasyobou Pubilisher (in Japanese).

    Google Scholar 

  • Matsumoto, S. (2000). Activities that expand mathematical world through making mathematical models – Considering length of mirrors that whole body can be reflected. Journal of Japan Society of Mathematical Education, Mathematical Education, 82(1), 10–17 (in Japanese).

    Google Scholar 

  • Niss, M. (2008). Perspectives on the balance between applications and modelling and ‘pure’ mathematics in the teaching and learning of mathematics. In M. Menghini, F. Furinghetti, L. Giancardi, & F. Arzarello (Eds.), The first century of the International Commission on Mathematical Instruction (1908–2008) (pp. 69–84). Roma: Instituto DELLA, Enciclopedia Italiana, Fondata da Giovanni Treccani.

    Google Scholar 

  • Osawa, H. (2004). Development of applications and modelling by action research in Japanese secondary school. In H.-W. Henn & W. Blum (Eds.), ICMI Study 14: Applications and modelling in mathematics education. Pre-conference volume (pp. 199–204). Dortmund: University of Dortmund.

    Google Scholar 

  • Programme for International Student Assessment – PISA. (2009). PISA 2009 assessment framework – Key competencies in reading, mathematics and science. Paris: OECD.

    Google Scholar 

  • Shimada, S. (1990). Collected problems for teachers. Tokyo: Kyouritsu Publisher (In Japanese).

    Google Scholar 

  • Tyuto Gakko Kyokasho Kabushiki Kaisya. (1943). Mathematics 1–3 (Textbooks at grade 7–9) Dai Ichirui and Nirui. Tokyo: Sanseido (in Japanese).

    Google Scholar 

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Correspondence to Toshikazu Ikeda .

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Ikeda, T. (2013). Pedagogical Reflections on the Role of Modelling in Mathematics Instruction. In: Stillman, G., Kaiser, G., Blum, W., Brown, J. (eds) Teaching Mathematical Modelling: Connecting to Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6540-5_22

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