Skip to main content
SpringerLink
Log in
Book cover

Teaching Mathematical Modelling: Connecting to Research and Practice pp 57–66Cite as

Should Interpretation Systems Be Considered to Be Models if They Only Function Implicitly?

  • Chapter
  • First Online:

Abstract

The term “mathematical model” or just “model” is interpreted differently by different people in current international discussions about mathematical modelling. For many, the term “model” is restricted to interpretation systems which are explicit objects of thought. In this paper we ask the question, if interpretation systems should be considered to be models if they only function implicitly. Furthermore we describe characteristics of what we mean by “implicit models” – as well as possible transitions from implicit to explicit models, and what these transitions look like from a cognitive-psychological perspective.

Though unconsciousness is, strictly speaking, a business of professional psychologist, it is so closely connected with my main subject that I cannot help dealing scantily with it. (Hadamard 1945, p. 21)

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

References

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

    Chapter  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 

  • Hadamard, J. (1945). The psychology of invention in the mathematical field. Toronto: Princeton University Press.

    Google Scholar 

  • Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classrooms – Problems and opportunities. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Applications and modelling in mathematics education (pp. 99–108). New York: Springer.

    Chapter  Google Scholar 

  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310.

    Article  Google Scholar 

  • Kintsch, W., & Greeno, J. (1985). Understanding word arithmetic problems. Psychological Review, 92(1), 109–129.

    Article  Google Scholar 

  • Lesh, R., & Caylor, E. (2007). Introduction to the special issue: Modeling as application versus modeling as a way to create mathematics. International Journal of Computers for Mathematical Learning, 12(3), 173–194.

    Article  Google Scholar 

  • Lesh, R., & Doerr, H. (2003). Beyond constructivism: Models & modeling perspectives on mathematics teaching, learning, and problems solving. Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2 & 3), 157–190.

    Google Scholar 

  • Lesh, R., & Yoon, C. (2004). Evolving communities of mind – In which development involves several interacting & simultaneously developing strands. Mathematical Thinking and Learning, 6(2), 205–226.

    Article  Google Scholar 

  • Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), The second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte: Information Age Publishing.

    Google Scholar 

  • Maaß, K. (2004). Mathematisches modellieren im Unterricht. Ergebnisse einer empirischen Studie. Hildesheim: Franzbecker.

    Google Scholar 

  • Nesher, P. (1982). Levels of description in the analysis of addition and subtraction. In T. P. Carpenter, J. M. Moser, & T. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 25–38). Hillsdale: Erlbaum.

    Google Scholar 

  • Opt’ Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students‘ mathematical-related beliefs: A quest for conceptual clarity and comprehensive categorization. In G. Leder, E. Pekhonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 13–37). Dordrecht: Kluwer.

    Google Scholar 

  • Pekhonen, E., & Törner, G. (1996). Mathematical beliefs and different aspects of their meaning. Zentralblatt für Didaktik der Mathematik, 28(4), 101–108.

    Google Scholar 

  • Schoenfeld, A. H. (1992). 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 

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

    Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Kassel, Kassel, Germany

    Rita Borromeo Ferri

  2. Counseling and Educational Psychology, Indiana University, Bloomington, IN, USA

    Richard Lesh

Authors
  1. Rita Borromeo Ferri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard Lesh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rita Borromeo Ferri .

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

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ferri, R.B., Lesh, R. (2013). Should Interpretation Systems Be Considered to Be Models if They Only Function Implicitly?. 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_4

Download citation

Publish with us

Policies and ethics

Search

Navigation