Skip to main content
SpringerLink
Log in

A global survey of international perspectives on modelling in mathematics education

  • Analyses
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In this article we survey the current debate on modelling and, describe different perspectives on this debate. We relate these perspectives with earlier perspectives and show similarities and differences between these different approaches.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barbosa, J.C.. (2006). Mathematical Modelling in classroom: a critical and discursive perspective.Zentralblatt für Didaktik der Mathematik, 38(3), 293–301.

    Article  Google Scholar 

  • Blomhoj, M. (2004). Mathematical Modelling— A Theory for Practice. In B. Clarke et al. (Eds.),International Perspectives on Learning and Teaching Mathematics (pp. 145–159). Göteborg: National Center for Mathematics Education.

    Google Scholar 

  • Blomhøj, M. & Hoff Kjeldsen, T. (2006). Teaching mathematical modelling through project work—Experiences from an in-service course for upper secondary teachers.Zentralblatt für Didaktik der mathematik, 38 (2), 163–177.

    Article  Google Scholar 

  • Blum, W. (1996). Anwendungsbezüge im Mathematikunterricht—Trends und Perspektiven. In G. Kadunz, H. Kautschitsch, G. Ossimitz & E. Schneider (Ed.),Trends und Perspektiven (pp. 15–38). Wien: Hölder-Pichler-Tempsky.

    Google Scholar 

  • Blum, W. et al. (2002). ICMI Study 14: Applications and Modelling in Mathematics Education—discussion Document.Journal für Mathematik-Didaktik 23(3/4), 262–280.

    Google Scholar 

  • Blum, W. & Niss, M. (1991). Applied Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects.Educational Studies in Mathematics, 22, 37–68.

    Article  Google Scholar 

  • Blum, W. & Leiß, D. (2005). “Filling Up”—the Problem of Independence-preserving Teacher Interventions in Lessons with Demanding Modelling Tasks. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Burghes, D.N., & Huntley, I. (1982). Teaching mathematical modelling—reflections and advice.International Journal of Mathematical Education in Science and Technology 13, 6, 735–754.

    Article  Google Scholar 

  • Borromeo Ferri, R., (2006). Theoretical and empirical differentiations of phases in the modelling process.Zentralblatt für Didaktik der Mathematik, 38 (2), 86–95.

    Article  Google Scholar 

  • Burkhardt, H., (2006). Modelling in mathematics classrooms: relfections on past developments and the future.Zentralblatt für Didaktik der Mathematik, 38 (2), 178–195.

    Article  Google Scholar 

  • D'Ambrosio, U. (1999) Literacy, Matheracy and technocracy: a trivium for today.Mathematical thinking and learning, 1 (2), 131–153.

    Article  Google Scholar 

  • De Lange, J., (1987).Mathematics—insight and meaning. Utrecht: Rijksuniversiteit Utrecht.

    Google Scholar 

  • Doerr, H.M. (2006). Teachers' ways of listening and responding to students' emerging mathematical models.Zentralblatt für Didaktik der Mathematik, 38(3), 255–268.

    Article  Google Scholar 

  • Dorier, J.-L. (2005). An introduction to mathematical modelling—an experiment with students in economics. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Freudenthal, H. (1973).Mathematics as an Educational Task. Dordrecht: Reidel.

    Google Scholar 

  • Freudenthal, H. (1981). Mathematik, die uns angeht.Mathematiklehrer, 2, 3–5.

    Google Scholar 

  • Galbraith, P. & Stillman, G. (2006). A framework for identifying student blockages during transitions in the Modelling, process.Zentralblatt für Didaktik der Mathematik, 38, (2), 143–162.

    Article  Google Scholar 

  • Garcia Garcia, J. & Ruiz Higueras, L. (2005). Mathematical Praxeologies of Increasing Complexity: Variation systems modelling in Secondary Education. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • García, F.J., Gascón, J., Ruiz Higueras, L. & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics.Zentralblatt für Didaktik der Mathematik, 38(3), 226–246.

    Article  Google Scholar 

  • Gellert, U., Jablonka, E. & Keitel, C. (2001). Mathematical Literacy and Common Sense in Mathematics Education. In: B. Atweh, H. Forgasz & B. Nebres (Eds.),Sociocultural Research on Mathematics Education (pp. 57–76), Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Haines, C.P. & Crouch, R. (2005). Getting to grips with real world contexts: Developing research in mathematical modelling. (To appear in)Proceedings of the 4th European Congress of, Mathematics Education, in St. Feliu de guixols, Spain, Feb 16–22, 2005.

  • Henning, H. & Keune, M. (2005). Levels of Modelling Competence. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Iversen, S.M. & Larson, C.J. (2006). Simple thinking using complex math vs. complex thinking using simple math.Zentralblatt für Didaktik der Mathematik, 38(3), 281–292.

    Article  Google Scholar 

  • Kaiser-Messmer, G. (1986).Anwendungen im Mathematikunterricht. Vol. 1 Theoretische Konzeptionen. Bad Salzdetfurth: Franzbecker.

    Google Scholar 

  • Kaiser, G. (1995). Realitätsbezüge im Mathematikunterricht—Ein Überblick über die aktuelle, und historische Diskussion. In G. Graumann et al. (Eds.),Materialien für einen realitätsbezogenen Mathematikunterricht (pp. 66–84): Bad Salzdetfurth: Franzbecker.

    Google Scholar 

  • Kaiser, G. (2005). Introduction to the Working Group “Applications and modelling” (G14) (To appear in)Proceedings of the 4th European Congress of Mathematics Education in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university.Zentralblatt für Didaktik der Mathematik, 38(2), 196–208.

    Article  Google Scholar 

  • Lesh, R. & Doerr, H. (Eds.) (2003). Beyond Constructivism:A models and modeling perspective on mathematics problem solving, learning, and teaching. Mahwah: Lawrence Erlbaum Associates, Mahwah.

    Google Scholar 

  • Lesh, R. & Sriraman, B. (2005a). John Dewey Revisited—Pragmatism and the models-modeling perspective on mathematical learning. In A. Beckmann et al. (Eds.),Proceedings of the 1st International Symposium on Mathematics and its Connections to the Arts and Sciences (pp. 32–51). May 18–21, 2005, Pedagogical University of Schwaebisch Gmuend. Hildesheim: Franzbecker.

  • Lesh, R. & Sriraman, B. (2005b) Mathematics 0 education as a design science.Zentralblatt für Didaktik der Mathematik 37(6), 490–505.

    Article  Google Scholar 

  • Lester, F.K. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education.Zentralblatt für Didaktik der Mathematik, 37(6), 457–467.

    Article  Google Scholar 

  • Lingefjärd, T. (2005). Applied or pure MATHEMATICS. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Lingefjärd, T. (2006). Faces of mathematical modelling.Zentralblatt für Didaktik der Mathematik, 38 (2), 96–112.

    Article  Google Scholar 

  • Maaß, K. (2004).Mathematisches Modellieren im Unterricht. Hildescheim Franzbecker.

    Google Scholar 

  • Maaß, K. (2006). What are modelling competencies?Zentralblatt für Didaktik der Mathematik, 38 (2), 113–142.

    Article  Google Scholar 

  • Michelsen, C. (2006). Functions: a modelling tool in mathematics and science.Zentralblatt für Didaktik der Mathematik, 38(3), 269–280.

    Article  Google Scholar 

  • Niss, M., (2001). University mathematics based on problem-oriented student projects: 25 years of experiences with the Roskilde model. In D. Holton, (ed.):The teaching and learning of mathematics at university level: an ICMI study, (pp. 405–422). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Pierce, P. & Stacey, K. (2006). Enhancing the image of mathematics by association with simple, pleasures from real world contexts.Zentralblatt für Didaktik der Mathematik, 38(3), 214–225.

    Article  Google Scholar 

  • Pollak, H. (1969). How can we teach applications of mathematics?Educational Studies in Mathematics, 2, 393–404.

    Article  Google Scholar 

  • Revuz, A. (1971). The position of geometry in mathematical education.Educational Studies in Mathematics, 4, 48–52.

    Article  Google Scholar 

  • Skemp, R. (1987). The psychology of learning mathematics. Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Sriraman, B. (2005). Conceptualizing the notion of model-eliciting. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

  • Sriraman, B. & Lesh, R. (2006). Modeling conceptions revisited.Zentralblatt für Didaktik der Mathematik 38(3), 247–254.

    Article  Google Scholar 

  • Steiner, H.-G. (1968). Examples of exercises in mathematization on the secondary school level.Educational Studies in Mathematics, 1, 181–201.

    Article  Google Scholar 

  • Treffers, A. (1987).Three dimensions: a model of goal and theory descriptions in mathematics instruction—the Wiskobas Project Dordrecht: Kluwer.

    Google Scholar 

  • Vos, P. (2005). Assessment of mathematics in a laboratory-like environment: the importance of replications. (To appear in)Proceedings of the 4th European Congress of Mathematics Education, in St. Feliu de Guixols, Spain, Feb 16–22, 2005.

Download references

Author information

Authors and Affiliations

  1. University of Hamburg Faculty of Education, Von-Melle-Park 8, 20146, Hamburg, Germany

    Gabriele Kaiser (Chief Editor)

  2. The Montana Mathematics Enthusiast Dept. of Mathematics, The University of Montana, 59812, Missoula, MT, USA

    Bharath Sriraman (Editor)

Authors
  1. Gabriele Kaiser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bharath Sriraman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kaiser, G., Sriraman, B. A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik 38, 302–310 (2006). https://doi.org/10.1007/BF02652813

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02652813

ZDM-Classification

Search

Navigation