Skip to main content
SpringerLink
Log in

Re-conceptualizing Mathematics Education as a Design Science

  • Chapter
  • First Online:
Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

In this chapter we propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of science and mathematics and ongoing findings of M&M research are drawn to illustrate our notion of mathematics education research as a design science. Our ideas are intended as a framework and do not constitute a “grand” theory. That is, we provide a framework (a system of thinking together with accompanying concepts, language, methodologies, tools, and so on) that provides structure to help mathematics education researchers develop both models and theories, which encourage diversity and emphasize Darwinian processes such as: (a) selection (rigorous testing), (b) communication (so that productive ways of thinking spread throughout relevant communities), and (c) accumulation (so that productive ways of thinking are not lost and get integrated into future developments).

Erich Ch. Wittmann has authored several papers with the same title and has been instrumental in proposing the design science approach to mathematics education.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Begle, E. G. (1979). Critical Variables in Mathematics Education. Washington D.C.: The Mathematics Association of America and the National Council of Teachers of Mathematics.

    Google Scholar 

  • Biehler, R., Scholz, R. W., Strässer, R., & Winkelmann, B. (Eds.) (1994). Didactics of Mathematics as a Scientific Discipline. Norwell, MA: Kluwer.

    Google Scholar 

  • Bishop, A. J. et al. (2003). Second International Handbook on Mathematics Education. Dordrecht: Kluwer.

    Google Scholar 

  • Coray, D., Furinghetti, F., Gispert, H., Hodgson, B., & Schubring, G. (Eds.) (2003). One Hundred Years of l’Enseignement Mathématique, Monograph no. 39. Geneva.

    Google Scholar 

  • Cramer, F. (1993). Chaos and Order. New York: VCH Publishers.

    Google Scholar 

  • Dietrich, O. (2004). Cognitive evolution. In F. M. Wuketits & C. Antweiler (Eds.), Handbook of Evolution (pp. 25–77). Wiley-VCH Verlag GmbH & Co: Weinheim.

    Google Scholar 

  • English, L. D. (Ed.) (2002). Handbook of International Research in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2 & 3), 225–248.

    Article  Google Scholar 

  • Holton, G. (1973). Thematic Origins of Scientific Thought. Cambridge, Massachusetts: Harvard University Press.

    Google Scholar 

  • Kelly, A. E., & Lesh, R. (2000). Handbook of Research Design in Mathematics and Science Education. New Jersey: Lawrence Erlbaum & Associates.

    Google Scholar 

  • Kelly, A. E., Lesh, R. A., & Baek, J. Y. (Eds.) (2008). Handbook of Design Research Methods in Education: Innovations in Science, Technology, Engineering, and Mathematics Learning and Teaching. New York: Routledge.

    Google Scholar 

  • Kilpatrick, J. (1969a). Problem solving in mathematics. Review of Educational Research, 39(4), 523–533.

    Google Scholar 

  • Kilpatrick, J. (1969b). Problem solving and creative behavior in mathematics. In J. W. Wilson & L. R. Carry (Eds.), Studies in Mathematics : Vol. 19. Reviews of Recent Research in Mathematics Education (pp. 153–187). Standford, CA: School Mathematics Study Group.

    Google Scholar 

  • Kirschbaum, D. Introduction to complex systems. Retrieved from http://www.calresco.org.

  • Lesh, R., & English, L. (2005). Trends in the evolution of the models-modelling perspective on mathematical learning and problem solving. International Reviews on Mathematical Education, 37(6), 487–489.

    Google Scholar 

  • Lesh, R., & Sriraman, B. (2005). John Dewey revisited—pragmatism and the models-modeling perspective on mathematical learning. In A. Beckmann, C. Michelsen, & B. Sriraman (Eds.), Proceedings of the 1st International Symposium on Mathematics and its Connections to the Arts and Sciences (pp. 32–51). May 18–21, 2005, University of Schwaebisch Gmuend. Germany: Franzbecker Verlag.

    Google Scholar 

  • Lesh, R., Hamilton, E., & Kaput, J. (Eds.) (2005). Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lester, F. K. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. International Reviews on Mathematical Education, 37(6), 457–467.

    Google Scholar 

  • Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning and Teaching (pp. 501–518). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Lester, F. (1994). Musings about mathematical problem-solving research: 1970–1994. Journal for Research in Mathematics Education, 25(6), 660–675.

    Article  Google Scholar 

  • Moreno, & Sriraman (2005). The articulation of symbol and mediation in mathematics education. International Reviews on Mathematical Education, 37(6), 476–486.

    Google Scholar 

  • Pôlya, G. (1945). How to Solve it. Princeton, NJ: Princeton University Press. 2nd edition, 1957.

    Google Scholar 

  • Schoenfeld, A. H. (1993). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 334–370). New York: Macmillan.

    Google Scholar 

  • Silver, E. A. (Ed.) (1985). Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Steen, L. (1999). Review of Mathematics Education as research domain. Journal for Research in Mathematics Education, 30(2), 235–241.

    Article  Google Scholar 

  • Steen, L. A. (2001). Revolution by stealth. In D. A. Holton (Ed.), The Teaching and Learning of Mathematics at University Level (pp. 303–312). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Wiliam, D. (2003). The impact of educational research on mathematics education. In A. J. Bishop et al. (Eds.), Second International Handbook on Mathematics Education (pp. 471–490). Dordrecht: Kluwer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Education, Indiana University, Bloomington, USA

    Richard Lesh

  2. Department of Mathematical Sciences, The University of Montana, Missoula, USA

    Bharath Sriraman

Authors
  1. Richard Lesh
    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

Corresponding author

Correspondence to Bharath Sriraman .

Editor information

Editors and Affiliations

  1. Dept. Mathematical Sciences, University of Montana-Missoula, Missoula, 59812-0864, U.S.A.

    Bharath Sriraman

  2. Centre for Learning Innovation, Queensland University of Technology, Victoria Park Road, Kelvin Grove, 4059, Australia

    Lyn English

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lesh, R., Sriraman, B. (2010). Re-conceptualizing Mathematics Education as a Design Science. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00742-2_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00741-5

  • Online ISBN: 978-3-642-00742-2

  • eBook Packages: Humanities, Social Sciences and LawEducation (R0)

Publish with us

Policies and ethics

Search

Navigation