Identifying Challenges within Transition Phases of Mathematical Modeling Activities at Year 9

  • Gloria Stillman
  • Jill Brown
  • Peter Galbraith
Part of the International Perspectives on the Teaching and Learning of Mathematical Modelling book series (IPTL)


The Galbraith, Stillman, Brown, and Edwards Framework (2007) for identifying blockages hindering progress in transitions in the modeling process is applied to a modeling task undertaken by 21 Year 9 students. The Framework identified where challenges occurred; but, because some blockages proved to be more robust than others, another construct “level of intensity” was added. The blockages described here occurred during the formulation phase of the modeling cycle. We infer that blockages induced by lack of reflection, or by incorrect or incomplete knowledge, are different in nature and cognitive demand from those involving the revision of mental schemas (i.e., cognitive dissonance). The nature and intensity of the blockage have consequences for teacher intervention and task implementation.


Cognitive Dissonance Goal Post Dynamic Geometry Goal Line Dynamic Geometry Software 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Atherton, J. S. (2003). Learning and Teaching Cognitive Dissonance [on-line]. Available: Retrieved April 30, 2007.
  2. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86–95.CrossRefGoogle Scholar
  3. Crouch, R., and Haines, C. (2004). Mathematical modelling: Transitions between the real world and the mathematical model. International Journal of Mathematics Education Science and Technology, 35, 197–206.CrossRefGoogle Scholar
  4. Festinger, L. (1957). A Theory of Cognitive Dissonance. Evanston, IL: Row Peterson.Google Scholar
  5. Galbraith, P., and Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38 (2), 143–162.CrossRefGoogle Scholar
  6. Galbraith, P., Stillman, G., Brown, J., and Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, and S. Khan, (Eds.), Mathematical Modelling: Education, Engineering and Economics (pp. 130–140). Chichester, UK: Horwood.Google Scholar
  7. Leiß, D. (2005). Teacher intervention versus self-regulated learning? Teaching Mathematics and Its Applications, 24(2–3), 75–89.CrossRefGoogle Scholar
  8. Piaget, J. (1950). The Psychology of Intelligence. London: Routledge & Kegan Paul.Google Scholar
  9. Potari, D. (1993). Mathematisation in a real-life investigation. In J. de Lange, C. Keitel, I. Huntley, and M. Niss (Eds.), Innovations in Maths Education by Modelling and Applications (pp. 235–243). Chichester, UK: Ellis Horwood.Google Scholar
  10. Stillman, G. (1998). The Emperor’s New Clothes? Teaching and assessment of mathematical applications at the senior secondary level. In P. Galbraith, W. Blum, G. Booker, & I.D. Huntley (Eds.), Mathematical Modelling: Teaching and Assessment in a Technology-rich World (pp. 243–254). Chichester, UK: Horwood.Google Scholar
  11. Stillman, G., Galbraith, P., Brown, J., and Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom in mathematics. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice. (Proceedings of the 30th annual conference of the Mathematics Research Group of Australasia, Hobart, pp. 688–707). Adelaide: MERGA.Google Scholar
  12. Warick, J. (2007). Some reflections on the teaching of mathematical modelling. The Mathematics Teacher, 17(1), 32–41.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.The University of MelbourneMelbourneAustralia
  2. 2.Australian Catholic UniversityMelbourneAustralia
  3. 3.University of QueenslandBrisbaneAustralia

Personalised recommendations