Proportion: Learning Proportional Reasoning Together

  • Jochen Rick
  • Alexander Bejan
  • Christina Roche
  • Armin Weinberger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7563)


Proportional reasoning is a broadly applicable skill that is fundamental to mathematical understanding. While the cognitive development of proportional reasoning is well understood, traditional learning methods are often ineffective. They provide neither real-time feedback nor sophisticated tools to scaffold learning. Learners often cannot connect embodied notions (this glass is half full) to their symbolic representations (\(\frac{1}{2}\)). In this paper, we introduce Proportion—a tablet applications for two co-located learners to work together to solve a series of increasingly difficult ratio / proportion problems. We motivate the work in previous research on proportional reasoning, detail the design and outline the questions this design-based research aims to address.


Conceptual Change Word Problem Symbolic Representation Mathematical Understanding Proportional Reasoning 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lamon, S.J.: Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education 24(1), 41–61 (1993)CrossRefGoogle Scholar
  2. 2.
    Noelting, G.: The development of proportional reasoning and the ratio concept: Part I — differentiation of stages. Educational Studies in Mathematics 11, 217–253 (1980)CrossRefGoogle Scholar
  3. 3.
    Tourniaire, F., Pulos, S.: Proportional reasoning: A review of the literature. Educational Studies in Mathematics 16, 181–204 (1985)CrossRefGoogle Scholar
  4. 4.
    Abrahamson, D., Trimic, D.: Toward an embodied-interaction design framework for mathematical concepts. In: Proceedings of IDC 2011, pp. 1–10. ACM Press, New York (2011)Google Scholar
  5. 5.
    Vosniadou, S., Ioannides, C., Dimitrakopoulou, A., Papademetriou, E.: Designing learning environments to promote conceptual change in science. Learning and Instruction 11(4&5), 381–419 (2001)CrossRefGoogle Scholar
  6. 6.
    Leong, Z.A., Horn, M.S.: Representing equality: A tangible balance beam for early algebra education. In: Proceedings of IDC 2011, pp. 173–176. ACM Press, New York (2011)Google Scholar
  7. 7.
    Roschelle, J.: Learning by collaborating: Convergent conceptual change. The Journal of the Learning Sciences 2(3), 235–276 (1992)CrossRefGoogle Scholar
  8. 8.
    Rick, J., Marshall, P., Yuill, N.: Beyond one-size-fits-all: How interactive tabletops support collaborative learning. In: Proceedings of IDC 2011, pp. 109–117. ACM Press, New York (2011)Google Scholar
  9. 9.
    Chi, M.T.H., Leeuw, N., Chiu, M.H., Lavancher, C.: Eliciting self-explanations improves understanding. Cognitive Science 18(3), 439–477 (1994)Google Scholar
  10. 10.
    Lambiotte, J.G., Dansereau, D.F., Angela, M., O’Donnell, M.D.Y., Skaggs, L.P., Hall, R.H.: Effects of cooperative script manipulations on initial learning and transfer. Cognition and Instruction 5(2), 103–121 (1988)CrossRefGoogle Scholar
  11. 11.
    Rick, J., Harris, A., Marshall, P., Fleck, R., Yuill, N., Rogers, Y.: Children designing together on a multi-touch tabletop: An analysis of spatial orientation and user interactions. In: Proceedings of IDC 2009, pp. 106–114. ACM Press, New York (2009)CrossRefGoogle Scholar
  12. 12.
    Pontual Falcão, T., Price, S.: What have you done! The role of ’interference’ in tangible environments for supporting collaborative learning. In: Proceedings of CSCL 2009, ISLS, pp. 325–334 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jochen Rick
    • 1
  • Alexander Bejan
    • 1
  • Christina Roche
    • 1
  • Armin Weinberger
    • 1
  1. 1.Department of Educational TechnologySaarland UniversityGermany

Personalised recommendations