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Dual Modelling Cycle Framework for Responding to the Diversities of Modellers

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Book cover Teaching Mathematical Modelling: Connecting to Research and Practice

Abstract

The modelling cycle (e.g., Blum and Leiß How do students and teachers deal with modelling problems? In: Haines C, Galbraith P, Blum W, Khan S (eds) Mathematical modelling (ICTMA12): education, engineering and economics. Horwood, Chichester, pp 222–231, 2007) contains the repeated processes that modellers are asked for in deepening their thinking. When we investigate the modelling cycle of modellers, we have to consider the diversities of various modellers in their modelling progress (Blum and Borromeo Ferri J Math Model Appl 1(1):45–58, 2009). In addition, problems or tasks can be changed from the initial real situation and problem with the aim of meeting the need of modellers. In this chapter, we make two modelling cycles parallel and focus on interactions between cycles, and call it the dual modelling cycle. We show three types of modelling cycles based on the dual modelling cycle framework through the example of one modelling cycle based on an Oil Tank Task, and another modelling cycle based on a Toilet Paper Tube Task.

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References

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Acknowledgement 

Mr. Kurokawa Hiroshi (Tokushima office, Nisshinbo Holdings Inc.) allowed us to measure a heavy oil tank and introduced the staff concerned. Mr. Kurebayashi Yutaka (Tokai Seishi Kogyo Co., LTD.) gave us a factory tour and explained the process of making the toilet paper tube. Mr. Kainuma Kenji (Anan office, Asahi Synchrotech Corporation) provided important plan data of the heavy oil tank. Thanks to all concerned.

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Authors and Affiliations

  1. Graduate School of Education, Naruto University of Education, Naruto, Japan

    Akihiko Saeki

  2. Faculty of Education, Saitama University, Saitama, Japan

    Akio Matsuzaki

Authors
  1. Akihiko Saeki
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  2. Akio Matsuzaki
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Corresponding author

Correspondence to Akihiko Saeki .

Editor information

Editors and Affiliations

  1. Education VIC | Faculty of Education, Australian Catholic University, Ballarat, Victoria, Australia

    Gloria Ann Stillman

  2. Faculty of Education, University of Hamburg, Hamburg, Germany

    Gabriele Kaiser

  3. Department of Mathematics, University of Kassel, Kassel, Germany

    Werner Blum

  4. Education VIC | Faculty of Education, Australian Catholic University, Melbourne, Victoria, Australia

    Jill P. Brown

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Saeki, A., Matsuzaki, A. (2013). Dual Modelling Cycle Framework for Responding to the Diversities of Modellers. 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_7

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