Skip to main content
Log in

Modelling in Mathematics Classrooms: reflections on past developments and the future

  • Analyses
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

This paper describes the development of mathematical modelling as an element in school mathematics curricula and assessments. After an account of what has been achieved over the last forty years, illustrated by the experiences of two mathematician-modellers who were involved, I discuss the implications for the future—for what remains to be done to enable modelling to make its essential contribution to the «functional mathematics», the mathematical literacy, of future citizens and professionals. What changes in curriculum are likely to be needed? What do we know about achieving these changes, and what more do we need to know? What resources will be needed? How far have they already been developed? How can mathematics teachers be enabled to handle this challenge which, scandalously, is new to most of them? These are the overall questions addressed.

The lessons from past experience on the challenges of large-scale of implementation of profound changes, such as teaching modelling in school mathematics, are discussed. Though there are major obstacles still to overcome, the situation is encouraging.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Andrews, J. G., & McLone, R. L. (1976).Mathematical Modelling. London: Butterworth

    Google Scholar 

  • Blum, W., Galbraith, P., Henn, H-W., & Niss, M. (Eds.), (2006).Applications and Modelling in Mathematics Education. New ICMI Studies Series no. 10, New York: Springer. To appear.

    Google Scholar 

  • Brousseau, G. (1997).Theory of didactical situations in mathematics: didactique des mathematiques, 1970~1990. Dordrecht: Kluwer.

    Google Scholar 

  • Burkhardt, H. (1964).Modelling with Mathematics. unpublished lecture notes, University of Birmingham, Department of Mathematical Physics

  • Burkhardt, H., & Wishart, D. M. G. (1967).Broad Spectrum Appleid Mathematics. unpublished lecture notes. University of Birmingham School of Mathematical Sciences

  • Burkhardt, H. (1981).The Real World and Mathematics. Blackie-Birkhauser; reprinted 2000, Shell Centre Publications, Nottingham, U.K., URL: http://www.mathshell.com/scp/index.htm

  • Burkhardt, H., Fraser, R., Coupland, J., Phillips, R., Pimm, D., & Ridgway, J. (1988). Learning activities & classroom roles with and without the microcomputer.Journal of Mathematical Behavior, 6, 305–338.

    Google Scholar 

  • Burkhardt, H., & Schoenfeld, A. H. (2003). Improving Educational Research: towards a more useful, more influential and better funded enterprise.Educational Researcher 32, 3–14.

    Article  Google Scholar 

  • Burkhardt, H. (2004).Assessing mathematical Proficiency: What is important? In A. H. Schoenfeld (Ed.), (forthcoming)Assessing Students' Mathematics Learning: Issues, Costs and Benefits Volume XXX. Mathematical Sciences Research Institute Publications. Cambridge: Cambridge University Press.

    Google Scholar 

  • Burkhardt, H. (2005).From design research to large-scale impact: Engineering research in education. In J. Van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), (forthcoming).Educational design research. London: Routledge.

    Google Scholar 

  • Burkhardt, H., Muller, E. R. et al. (2006).Applications and Modelling for Mathematics. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.),Modelling and Applications in Mathematics Education. New ICMI Studies Series no. 10, New York: Springer. To appear.

    Google Scholar 

  • COMAP (1988).For All Practical Purposes. Solomon Garfunkel (Project Director) et al. 6th Edition, New York: W. H. Freeman

    Google Scholar 

  • COMAP (1997-1998).Mathematics: Modeling Our World. Cincinnati: South-Western Ed. Publ.

    Google Scholar 

  • Crowther Report 15~18 (1959).A Report of the Central Advisory Council for Education, HMSO, London.

    Google Scholar 

  • ICTMA (1982-). Complete listing of ICTMA Conference Proceedings http://www.infj.ulst.ac.uk/ictma/books.html

  • MARS (1995-98).Balanced Assessment for the Mathematics Curriculum. Parsippany, NJ: Pearson Learning/Dale Seymour Publications.

    Google Scholar 

  • Newell, A., and Simon, H. A. (1972).Human Problem Solving. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • PISA (1999).Measuring Student Knowledge and Skills—A New Framework for Assessment, OECD, ed. Paris: OECD.

    Google Scholar 

  • PISA (2003).The PISA 2003 Assessment Framework: Mathematics, Reading, Science and problem Solving Knowledge and Skills, OECD, ed. Paris, URL https://www.pisa.oecd.org/dataoecd/38/51/3370 7192.pdf

  • OLPC (2005).One Laptop per Child, MIT Media Lab., http://laptop.media.mit.edu/

  • Pollak, H. O. (2003). A History of the Teaching of Modelling, in Stanic, G. M. A. and Kilpatrick, J. (Eds.),A History of School Mathematics. (pp 647–672), National Council of Teachers of Mathematics, Reston, VA.

    Google Scholar 

  • Polya, G. (1945).How to solve it. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Schoenfeld, A. H. (1985).Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  • Schoenfeld, A. H. (2002). Research methods in (mathematics) education. In L. English (Ed.),Handbook of international research in mathematics education (pp. 435–488). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.),Handbook for Research on Mathematics Teaching and Learning, (pp. 334–370), New York: MacMillan.

    Google Scholar 

  • Shell Centre (1984), Swan, M., Pitt, J., Fraser, R. E., & Burkhardt, H.,Problems with Patterns and Numbers. Joint Matriculation Board, Manchester, U.K.: reprinted 2000, Shell Centre Publications, Nottingham, U.K., URL: http://www.mathshell.com/scp/index.htm

    Google Scholar 

  • Shell Centre (1987~89). Swan, M., Binns, B., Gillespie, J., & Burkhardt, H.,Numeracy through Problem Solving, five modules for curriculum and assessment in mathematical literacy, Harlow: Longman, revised 2000, Nottingham, U.K.: Shell Centre Publications,

    Google Scholar 

  • SMSG (1958~72). Chronology at http://jwilson.coe.uga.edu/SMSG/SMSG.html; SMSG (1962).Mathematics for the Elementary School, School Mathematics Study Group

  • Swan, M. with the Shell Centre team: (1986).The Language of Functions and Graphs, Manchester, U.K.: Joint Matriculation Board, reprinted 2000, Nottingham, U.K.: Shell Centre Publications,

    Google Scholar 

  • Steen, L. A. v: (2002).Mathematics and Democracy: the case for quantitative literacy, National Council on Education and the Disciplines (NCED), USA. URL http://www.maa.org/ql/mathanddemocracy.html

  • Treilibs, V., Burkhardt, H., & Low, B. (1980).Formulation processes in mathematical modelling, Nottingham: Shell Centre Publications.

    Google Scholar 

  • UMTC (1976-).Proceedings of the Undergraduate Mathematics Teaching Conferences, Nottingham: Shell Centre Publications

    Google Scholar 

  • USMES (1969).Unified Sciences and Mathematics for Elementary Schools:http://books.nap.edu/ openbook/0309052939/html/129.html

Download references

Author information

Authors and Affiliations

Authors

Additional information

with contributions byHenry Pollak

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burkhardt, H. Modelling in Mathematics Classrooms: reflections on past developments and the future . Zentralblatt für Didaktik der Mathematik 38, 178–195 (2006). https://doi.org/10.1007/BF02655888

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02655888

ZDM-Classification

Navigation