Skip to main content
SpringerLink
Log in

Authentic Mathematical Modelling Experiences of Upper Secondary School: A Case Study

  • Chapter
  • First Online:
Mathematical Modelling and Applications

Abstract

The purpose of the research project presented in this chapter was to see if it was possible for authentic mathematical modelling, based on the characteristics and behaviours of a real-world modelling team, to be carried out at secondary school level. From the author’s previous opportunity to work as a member of a professional modelling team, an authentic mathematical modelling experience for secondary school students was developed and researched. Classroom activities were created and trialled with a group of 16- and 17-year-old New Zealand students. Data were collected from the learning activities. The results demonstrated that an authentic experience of the process of mathematical modelling is possible at secondary school.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Alsina, C. (2007). Teaching applications and modelling at tertiary level. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 469–474). New York: Springer.

    Chapter  Google Scholar 

  • Ang, K. C. (2013). Real-life within a traditional curriculum: Lessons from a Singapore experience. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 131–140). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Armstrong, P. K., & Bajpai, A. C. (1988). Modelling in GCSE mathematics. Teaching Mathematics and its Applications, 7(3), 121–131.

    Google Scholar 

  • Biembengut, M., & Hein, N. (2010). Mathematical modelling: Implications for teaching. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 481–490). New York: Springer.

    Chapter  Google Scholar 

  • Blomhøj, M. (2009). Different perspectives in research on the teaching and learning of mathematical modelling – Categorising the TSG21 papers. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics. Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematical Education in Monterrey, Mexico, July 6–13, 2008 (pp. 1–17). Roskilde: Roskilde University.

    Google Scholar 

  • Blum, W., Galbraith, P., & Niss, M. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3–32). New York: Springer.

    Chapter  Google Scholar 

  • Boaler, J. (2001). Mathematical modelling and new theories of learning. Teaching Mathematics and its Applications, 20(3), 121–126.

    Article  Google Scholar 

  • Borba, M. (2011). Can modelling be taught and learnt? – a commentary. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 31–36). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Cobb, P., Zhao, Q., & Visnovska, J. (2008). Learning from and adapting the theory of realistic mathematics education. Education et didactique, 2(1), 105–124.

    Article  Google Scholar 

  • De Lange, J. (1996). Using and applying mathematics in education. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Larbode (Eds.), International handbook of mathematics education (pp. 49–98). London: Kluwer Academic.

    Google Scholar 

  • Dindyal, J., & Kaur, B. (2010). Mathematical applications and modelling: Concluding comments. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling yearbook 2010 (pp. 325–335). Singapore: World Scientific.

    Google Scholar 

  • Dym, C. (2004). Principles of mathematical modeling. Amsterdam: Elsevier Academic.

    Google Scholar 

  • Frejd, P. (2013). Modes of modelling assessment – A literature review. Educational Studies in Mathematics, 84(3), 413–438.

    Article  Google Scholar 

  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM Mathematics Education, 38(2), 143–162.

    Article  Google Scholar 

  • Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Culemborg: Technipress.

    Google Scholar 

  • Ikeda, T. (2007). Possibilities for, and obstacles to teaching applications and modelling in the lower secondary school. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 457–462). New York: Springer.

    Chapter  Google Scholar 

  • Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. ZDM Mathematics Education, 38(2), 82–85.

    Google Scholar 

  • Kaiser, G., Lederich, C., & Rau, V. (2010). Theoretical approaches and examples for modelling in mathematics education. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling yearbook 2010 (pp. 219–246). Singapore: World Scientific.

    Google Scholar 

  • Lege, J. (2007). “To model, or to let them model?” that is the question! In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 425–432). New York: Springer.

    Chapter  Google Scholar 

  • Lesh, R., & Doerr, H. M. (2003). Foundations of models and modeling perspective on mathematics teaching and learning. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving (pp. 3–34). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Maaß, K. (2005). Barriers and opportunities for the integration of modelling in mathematics classes: Results of an empirical study. Teaching Mathematics and Its Applications, 24(2–3), 61–74.

    Article  Google Scholar 

  • Maaß, K. (2006). What are modelling competencies? ZDM Mathematics Education, 38(2), 113–142.

    Article  Google Scholar 

  • New Zealand Qualifications Authority. (2013). Standards and assessments. http://www.nzqa.govt.nz/ncea/assessment/search.do?query=Algebra&view=all&level=02. Last accessed 9 Feb 2013.

  • Palm, T. (2007). Features and impact of authenticity of applied mathematical school tasks. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 201–208). New York: Springer.

    Chapter  Google Scholar 

  • Schmidt, B. (2011). Modelling in the classroom: Obstacles from the teacher’s perspective. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 641–651). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Skolverket. (2012). The subject syllabus for mathematics. http://www.skolvert.se/polopoly_fs/1.17554!/Menu/article/attachment/Mathematics.pdf. Last accessed 13 May 2013.

  • Stillman, G., Brown, J., & Galbraith, P. (2008). Research into teaching and learning of applications and modelling in Australasia. In H. Forgasz, A. Barkatsas, A. J. Bishop, B. Clarke, S. Keast, W. T. Seah, & P. Sullivan (Eds.), Research in mathematics education in Australasia: 2004–2007 (pp. 141–164). Rotterdam: Sense.

    Google Scholar 

  • Stillman, G., Brown, J., Galbraith, P., & Ng, K. (2016). Research into mathematical applications and modelling. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2105 (pp. 281–304). Singapore: Springer.

    Google Scholar 

  • Tam, K. C. (2011). Modelling in the common core standards. Journal of Mathematics Education at Teachers College, 2(1), 28–33.

    Google Scholar 

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

    Google Scholar 

  • Wake, G. (1997). Hi-tech angles: Mathematics at work. New Zealand Science Review, 54(1–2), 5–9.

    Google Scholar 

  • Yanagimoto, A., & Yoshimura, N. (2013). Mathematical modelling of a real-world problem: The decreasing number of bluefin tuna. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 229–239). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Yoon, C., Dreyfus, T., & Thomas, M. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(1), 141–157.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Level 1 2-14 Wakefield St, Auckland, New Zealand

    Kerri Spooner

Authors
  1. Kerri Spooner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kerri Spooner .

Editor information

Editors and Affiliations

  1. Australian Catholic University, Ballarat, Victoria, Australia

    Gloria Ann Stillman

  2. University of Kassel, Kassel, Germany

    Werner Blum

  3. University of Hamburg, Hamburg, Germany

    Gabriele Kaiser

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Spooner, K. (2017). Authentic Mathematical Modelling Experiences of Upper Secondary School: A Case Study. In: Stillman, G., Blum, W., Kaiser, G. (eds) Mathematical Modelling and Applications. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-62968-1_52

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62968-1_52

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62967-4

  • Online ISBN: 978-3-319-62968-1

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation