Skip to main content
SpringerLink
Log in

Mathematical Modelling: Some Issues and Reflections

  • Chapter
  • First Online:
Mathematikunterricht im Kontext von Realität, Kultur und Lehrerprofessionalität

Zusammenfassung

In this chapter we reflect on issues in the teaching and learning of mathematical modelling that connect selected interests and themes from our work with cognate issues and themes in the published work of Gabriele Kaiser. These engage respective topics of authenticity of the modelling enterprise, issues associated with modelling in educational contexts, implications concerning metacognition for both students and teachers, alternative conceptions of the purpose of modelling that are found in the field of educational practice, associated criticisms that are levelled at mathematical modelling in educational settings, and beliefs of teaching practitioners about the nature and value of mathematical modelling as a curriculum component. In reflecting across the domains encompassed by these topic areas, our purpose is to highlight factors that remain telling challenges to the continued development of our field, and emphasise issues that make this field a special one because of the rich outcomes that can be achieved.

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 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Australian Curriculum, Assessment & Reporting Authority (2010). Australian Curriculum. Mathematics. Available from http://www.australiancurriculum.edu.au/Mathematics/Aims

  • Blum, W., Galbraith, P. L., Henn, H.-W. & Niss, M (Eds.) (2007). Modelling and applications in mathematics education: New ICMI studies series No. 10. New York: Springer.

    Book  Google Scholar 

  • Blum, W. (2008). Opportunities and problems for “Quality Mathematics Teaching” - the SINUS and DISUM projects. Regular lecture ICME 10 [CD-ROM].

    Google Scholar 

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

    Article  Google Scholar 

  • Busse, A. & Kaiser, G. (2003). Context in applications and modelling – an empirical approach. In: Q.-X. Ye, W. Blum, K. Houston, & Q.-Y. Jiang (Eds.), Mathematical modelling in education and culture, Chichester: Horwood, 3-15.

    Google Scholar 

  • Galbraith, P. L. & Clatworthy, N. J. (1990). Beyond standard models: meeting the challenge of modelling. Educational Studies in Mathematics. 21(2), 137-163.

    Article  Google Scholar 

  • Galbraith, P. L. & Stillman, G (2001). Assumptions and Context: pursuing their role in modelling activity. In: J. Matos, S. Houston, W. Blum & S. Carreira (Eds.), Modelling and Mathematics Education, Chichester: Horwood, 317–327.

    Google Scholar 

  • Galbraith, P. L. & 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 

  • Geiger, V., Faragher, R. & Goos, M. (2010) CAS-enabled technologies as ‘agents provocateur, in teaching and learning mathematical modelling in secondary classrooms’, Mathematics Education Research Journal, 22(2), 48–68.

    Article  Google Scholar 

  • Goos, M. (2002). Understanding metacognitive failure. Journal of Mathematical Behavior, 21(3), 283–302.

    Article  Google Scholar 

  • Jablonka, E. & Gellert, U. (2007). Mathematisation – demathematisation. In: U. Gellert & E. Jablonka (Eds.), Mathematisation and demathematisation: social, philosophical and educational ramifications, Rotterdam: Sense Publishers, 1–18.

    Google Scholar 

  • Jablonka, E. & Gellert, U. (2011). Equity concerns about Mathematical Modelling. In: B. Atweh, M. Graven & W. Secada (Eds.), Mapping Equity and Quality in Mathematics Education, Part 2., New York: Springer, 223–236.

    Google Scholar 

  • Haines, C. (2006). Who is a good modeller and how do we know? In: A. Büchter, H. Humenberger, S. Hußmann & S. Prediger (Eds.), Realitätsnaher Mathematikunterricht vom Fach aus und für die Praxis. Festband für Hans-Wolfgang Henn, Hildesheim: Franzbecker, 59–68.

    Google Scholar 

  • Julie, C. (2007). Learners’ context preferences and mathematical literacy. In: C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics, Chichester, UK: Horwood, 195–202.

    Google Scholar 

  • Kaiser, G. (2005). Mathematical modelling in school – Examples and experiences. In: H.-W. Henn & G. Kaiser (Eds.), Mathematikunterricht im Spannungsfeld von Evolution und Evaluation. Festband für Werner Blum, Hildesheim: Franzbecker, 99–108.

    Google Scholar 

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

    Chapter  Google Scholar 

  • 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 

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

    Article  Google Scholar 

  • Kaiser, G. Schwarz, B. & Buchholtz, N. (2011). Authentic modelling problems in mathematics education In: G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling, New York: Springer, 591–601.

    Chapter  Google Scholar 

  • Maaß, K. (2007). Modelling in class: What do we want the students to learn? In: C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics, Chichester, UK: Horwood, 63–78.

    Google Scholar 

  • OECD (2001). Knowledge and skills for life: first results from PISA 2000. Paris. OECD.

    Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In: G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. New York: Springer.

    Google Scholar 

  • Stillman, G., Brown, J. & Galbraith, P. (2008). Research into the teaching and learning of applications and modelling in Australasia. In: H. Forgasz et al. (Eds.), Research in mathematics education in Australasia 2004-2007, Rotterdam, The Netherlands: Sense, 141–164.

    Google Scholar 

  • Stillman, G., Brown, J. & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at Year 9. In: R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modelling students’ mathematical competencies, New York: Springer, 385–398.

    Chapter  Google Scholar 

  • Stillman, G., Brown, J. & Galbraith, P. (2010). Editorial. Mathematics Education Research Journal, 22(2), 1–6.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Australian Catholic University (Ballarat), Ballarat, Australia

    Gloria Stillman

  2. University of Queensland, Queensland, Australia

    Peter Galbraith

Authors
  1. Gloria Stillman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Galbraith
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    Werner Blum

  2. FB 10 Mathematik und Naturwissenschaften, Universität Kassel, Heinrich-Plett-Str. 40, Kassel, 34132, Germany

    Rita Borromeo Ferri

  3. Institut für Mathematische Bildung, Pädagogische Hochschule Freiburg, Kunzenweg 21, Freiburg, 79117, Germany

    Katja Maaß

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Stillman, G., Galbraith, P. (2012). Mathematical Modelling: Some Issues and Reflections. In: Blum, W., Borromeo Ferri, R., Maaß, K. (eds) Mathematikunterricht im Kontext von Realität, Kultur und Lehrerprofessionalität. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-8348-2389-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation