Abstract
We show how the nucleus of an idea can be developed into modeling problems for secondary school using principles for problem design enunciated in Galbraith (2007). Once the germ has been developed for a task, the idea can be extended as necessary into related problems closer to the personal experience of the adolescents in secondary school. The issues and contexts secondary students choose to investigate, and the questions that they pose when given free reign or minimal constraints, are illustrated from an Australian modeling challenge. Finally, using these contexts as starting points, it is suggested such situations can be developed to engage students in important teaching issues involving necessary constituents of the modeling process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burkhardt, H. (2007). Functional mathematics and teaching modeling. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 177–186). Chichester, UK: Horwood.
Caron, F., and Bélair, J. (2007). Exploring university students’ competencies in modelling. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 120–129). Chichester, UK: Horwood.
Galbraith, P. (2007). Dreaming a ‘possible dream’: More windmills to conquer. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 44–62). Chichester, UK: Horwood.
Galbraith, P., and Stillman, G. (2001). Assumptions and context: Pursuing their role in modelling activity. In J. F. Matos, S. K. Houston, W. Blum, and S. P. Carreira (Eds.), Mathematical Modelling and Mathematics Education: Applications in Science and Technology (pp. 317–327). Chichester, UK: Horwood Publishing.
Galbraith, P., and Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143–162.
Gravmeijer, K. (2007). Emergent modelling as aprecursor to mathematical modelling. In W. Blum, P. Galbraith, M. Niss, and H.-W. Henn (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (New ICMI Studies Series) (Vol. 10, pp. 137–144). New York: Springer.
Hickman, F. R. (1986). Mathematical modelling in physics. Physics Education, 21, 173–180.
Invasive Animals Competitive Research Centre. (2006). Science of Cane Toad Invasion and Control. Proceedings of the Invasive Animals CRC/CSIRO/Qld NRM & W Cane Toad Workshop, June 2006, Brisbane. Canberra: Author.
Julie, C. (2002). Making relevance relevant in mathematics teacher education. Proceedings of the 2nd International Conference on the Teaching of Mathematics (at the undergraduate level). Hoboken, NJ: Wiley CD.
Julie, C. (2007). Learners’ context preferences and mathematical literacy. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 194–202). Chichester, UK: Horwood.
Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 110–119). Chichester, UK: Horwood.
Penrose, O. (1978). How can we teach mathematical modelling? Journal of Mathematical Modelling for Teachers, 1, 31.
Spurlock, M. (Director). (2004). Supersize Me. [Film] New York: Kathbur Pictures.
Wikipedia: http://en.wikipedia.org/wiki/Main_Page
Zbiek, R., and Connor, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89 – 112.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Galbraith, P.L., Stillman, G., Brown, J. (2010). Turning Ideas into Modeling Problems. In: Lesh, R., Galbraith, P., Haines, C., Hurford, A. (eds) Modeling Students' Mathematical Modeling Competencies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0561-1_11
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0561-1_11
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0560-4
Online ISBN: 978-1-4419-0561-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)