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Drivers for Mathematical Modelling: Pragmatism in Practice

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Trends in Teaching and Learning of Mathematical Modelling

Abstract

In mathematical modelling, the way that certain topics are introduced depends upon many complex interacting factors, but for the teacher, learner or researcher being in touch with the real world is a key factor. Behaviours of students when faced with real-world problems are commonly represented in terms of activity within a modelling cycle but not all behaviours fit such a model; students exhibit non-linear behaviours and even within such cycles they can, and do, follow individual modelling routes. In this context, with competing and varied drivers for mathematical modelling and recognising issues of assessment, this chapter addresses the following questions: How well do students link mathematical knowledge to the task? How far away is the real world? Is mathematical modelling itself a driver for mathematical modelling?

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References

  • Anderson, J., Austin, K., Barnard, A., & Jagger, J. (1998). Do third-year mathematics undergraduates know what they are supposed to know? International Journal of Mathematics Education in Science and Technology, 29(3), 401–420.

    Article  Google Scholar 

  • András, S., & Szilágyi, J. (2010). Modelling drug administration regimes for asthma: A Romanian experience. Teaching Mathematics and Its Applications, 29(1), 1–13.

    Article  Google Scholar 

  • Barker, K. (2007). Economic modelling: Theory, reality, uncertainty and decision-making. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling ICTMA12: Education, engineering and economics (pp. 25–42). Chichester: Horwood.

    Google Scholar 

  • BBC News (2000). Kidney dialysis patients. http://news.bbc.co.uk/1/hi/health/991860.stm. Accessed 7 Oct 2009.

  • Blum, W., & Leiβ, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling ICTMA12: Education, engineering and economics (pp. 222–231). Chichester: Horwood.

    Chapter  Google Scholar 

  • Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling ICTMA12: Education, engineering and economics (pp. 260–270). Chichester: Horwood.

    Google Scholar 

  • Burley, D. M., & Trowbridge, E. A. (1984). Experiences of mathematical modelling at Sheffield University. In J. S. Berry, D. N. Burghes, D. J. G. Jones, & A. O. Moscardini (Eds.), Teaching and applying mathematical modelling (pp. 131–142). Chichester: Ellis Horwood Ltd.

    Google Scholar 

  • Crouch, R. M., & Haines, C. R. (2004). Mathematical modelling: Transitions between the real world and the mathematical model. International Journal of Mathematics Education in Science and Technology, 35(2), 197–206.

    Article  Google Scholar 

  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 69–78). New York: Springer.

    Chapter  Google Scholar 

  • GAISMA (2009). Sunrise, sunset, sun path information for locations worldwide. http://www.gaisma.com. Accessed 16 June 2009.

  • Galbraith, P. L., & Stillman, G. (2001). Assumptions and context: Pursuing their role in modelling activity. In J. F. Matos, W. Blum, K. Houston, & S. P. Carreira (Eds.), Modelling and mathematics education: ICTMA9 applications in science and technology (pp. 300–310). Chichester: Horwood.

    Google Scholar 

  • Galbraith, P., Haines, C., & Izard, J. (1998). How do students’ attitudes to mathematics influence the modelling activity? In P. Galbraith, W. Blum, G. Booker, & I. D. Huntley (Eds.), Mathematical modelling: Teaching and assessment in a technology-rich world (pp. 265–278). Chichester: Horwood.

    Google Scholar 

  • Haines, C. R. (2009). Sunshine in DQME?Paper prepared for the Comenius project: Developing quality in mathematics education II. University of Dortmund, Dortmund, Germany.

    Google Scholar 

  • Haines, C. R., & Crouch, R. M. (2001). Recognising constructs within mathematical modelling. Teaching Mathematics and Its Applications, 20(3), 129–138.

    Article  Google Scholar 

  • Haines, C., & Crouch, R. (2005). Applying mathematics: Making multiple-choice questions work. Teaching mathematics and Its Applications, 24, 107–113.

    Article  Google Scholar 

  • Haines, C. R., & Crouch, R. M. (2007). Mathematical modelling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 417–424). New York: Springer.

    Chapter  Google Scholar 

  • Haines, C. R., & Crouch, R. M. (2009). Remarks on a modelling cycle and interpreting behaviours. In R. A. Lesh, P. L. Galbraith, & C. R. Haines (Eds.), Modelling students’ mathematical modelling competencies. New York: Springer.

    Google Scholar 

  • Haines, C. R., & Dunthorne, S. (Eds.). (1996). Mathematics learning and assessment: Sharing innovative practices. London: Arnold.

    Google Scholar 

  • Hamburg Tunnel Marathon (2009). Diagrams and details of the marathon can be found at http://www.100marathon-club.de.

  • Houston, K., & Neill, N. (2003). Investigating students’ modelling skills. In Q.-X. Ye, W. Blum, K. Houston, & Q.-Y. Jiang (Eds.), Mathematical modelling in education and culture: ICTMA 10 (pp. 54–66). Chichester: Horwood.

    Google Scholar 

  • Hunt, J. (2007). Communicating big themes in applied mathematics. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling ICTMA12: Education, engineering and economics (pp. 2–24). Chichester: Horwood.

    Google Scholar 

  • Ivy Rose Holistic (2009). Kidney dialysis diagram. http://www.ivy-rose.co.uk.

  • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling ICTMA12: Education, engineering and economics (pp. 110–119). Chichester: Horwood.

    Google Scholar 

  • Lamon, S. J., Parker, W. A., & Houston, S. K. (2003). Preface. In S. J. Lamon, W. A. Parker, & S. K. Houston (Eds.), Mathematical modelling: A way of life (pp. ix–x). Chichester: Horwood.

    Google Scholar 

  • National Science Foundation (2003). NSF PR 03-106-September 24 2003. Photo of aggregation by Kevin Foster (Strassmann/Queller), Rice University, USA, Illustration of life cycle by Mary Wu and Rich Kessin, Columbia University, USA. http://www.nsf.gov/od/lpa/news/03/pr03106_images.htm. Accessed 7 Oct 2009.

  • Niss, M., & Jensen, T. H. (Eds.). (2006). Competencies and mathematical learning – Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Under preparation for publication in the series Tekster fra IMFUFA, Roskilde University, Denmark. To be obtained from imfufa@ruc.dk.

    Google Scholar 

  • Pollak, H. O. (1983). Applications and teaching of mathematics. In J. S. Berry, D. N. Burghes, D. J. G. Jones, & A. O. Moscardini (Eds.), Teaching and applying mathematical modelling (pp. xv–xvi). Chichester: Ellis Horwood Ltd.

    Google Scholar 

  • Thames Water (2009). London Ring Main Map. http://www.thameswater.co.uk/cps/rde/xbcr/corp/ringmain-high-extensions-map.jpg. Accessed 30 Sept 2009.

  • The Times (2009a). Orbiting Carbon Observatory mission. The Times 25 Feb 2009.

    Google Scholar 

  • The Times (2009b). Accident in space. The Times 13 Feb 2009.

    Google Scholar 

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Acknowledgements

I thank Professor Gabriele Kaiser for her support in inviting me to give this plenary lecture at ICTMA 14; it is an honour that is much appreciated; Dr A.M. Fairhurst of IvyRose Ltd for providing Fig. 35.3 and Rosalind Crouch (formerly University of Hertfordshire, Hatfield, UK) with whom many ideas in this chapter have been discussed.

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Authors and Affiliations

  1. School of Engineering and Mathematical Sciences, City University, Northampton Square, London, EC1V 0HB, UK

    Christopher Haines

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  1. Christopher Haines
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Correspondence to Christopher Haines .

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Editors and Affiliations

  1. FB Erziehungswissenschaft, Inst. Didaktik der Mathematik, Universität Hamburg, Von Melle Park 8, Hamburg, 20146, Germany

    Gabriele Kaiser

  2. Abt. Mathematik/Informatik, Universität Kassel, Kassel, 34109, Germany

    Werner Blum

  3. University of Hamburg, Germany, Doscherstrasse 1, Hamburg, 22083, Germany

    Rita Borromeo Ferri

  4. University of Melbourne, Australia, 23 Grampian Street, Victoria, 3072, Australia

    Gloria Stillman

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Haines, C. (2011). Drivers for Mathematical Modelling: Pragmatism in Practice. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_35

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