, Volume 40, Issue 2, pp 225–234 | Cite as

Building a local conceptual framework for epistemic actions in a modelling environment with experiments

  • Stefan HalverscheidEmail author
Original article


A local conceptual framework for the construction of mathematical knowledge in learning environments with experiments is developed. For this purpose, the mathematical modelling framework and the epistemic action model for abstraction in context are used simultaneously. In a case study, experiments of pre-service teachers with the motion of a ball on a circular billiard table are analysed within the local conceptual framework. The role of the experiments for epistemic actions of mathematical abstractions is described. In the case study, two different types of students’ approaches to the role of experiments can be distinguished.


Mathematics Education Action Model Modelling Situation Dynamic Geometry Software Epistemic Action 
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. Artigue, M. (1990). Obstacles as objects of comparative studies in mathematics and in physics. Zentralblatt für Didaktik der Mathematik (ZDM), 22(6), 200–204.Google Scholar
  2. Blum, W. (1996). Anwendungsbezüge im Mathematikunterricht—Trends und Perspektiven. In G. Kadunz, H. Kautschitsch, G. Ossimitz & E. Schneider (Eds.), Trends und Perspektiven. Schriftenreihe Didaktik der Mathematik, Vol. 23 (pp. 15–38). Wien: Hölder-Pichler-Tempsky.Google Scholar
  3. Blum, W. et al. (2003). ICME study 14 Applications and modelling in mathematics education—discussion document. Educational studies in mathematics, 51, 149–171. CrossRefGoogle Scholar
  4. Blum, W., Galbraith, P., Henn, H.-W., & Niss, M. (Eds.) (2006). Applications and Modelling in Mathematics Education. New York: Springer.Google Scholar
  5. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—state, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37–68.CrossRefGoogle Scholar
  6. Borromeo-Ferri, R. (2006). Individual modelling routes of pupils—analysis of modelling problems in mathematics lessons from a cognitive perspective. In C. Haines, et al. (Eds.), ICTMA-12: model transitions in the real world. Chichester: Horwood.Google Scholar
  7. De Lange, J. (1989). Trends and barriers to applications and modelling in mathematics curricula. In W. Blum, M. Niss, & I. Huntley (Eds.), Modelling, applications and applied problem solving. (pp. 196–204). Chichester: Ellis Horwoord.Google Scholar
  8. Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2001). Abstraction in context: the case of peer interaction. Cognitive Science Quarterly, 1(3), 307–368.Google Scholar
  9. Dreyfus, T., & Kidron, I. (2006) Interacting parallel constructions: a solitary learner and the bifurcation diagram. Recherches en Didactique des Mathématiques. 26(3), 295–336.Google Scholar
  10. Eisenhart, M. A. (1991). Conceptual frameworks for research circa 1991: Ideas from a cultural anthropologist; implications for mathematics education researchers. Proceedings of the 13th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 202–219). Blacksburg, VA.Google Scholar
  11. Hersh, R. (1991). Mathematics has a front and a back. Synthese, 88, Vol. 2. Google Scholar
  12. Kaiser, G. (2006). Modelling and modelling competencies in school. In C. P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (pp. 110–119). Chichester: Horwood Publishing.Google Scholar
  13. Kaiser, G., & Mass, K. (2006). Modelling in lower secondary mathematics classrooms: problems, opportunities. In W. Blum, P. Galbraith, H.-W. Henn, M. Niss (Eds.), Applications and modelling in mathematics education. The 14th ICMI Study (pp. 99–108). New York: Springer.Google Scholar
  14. Kleiner, I. (1991). Rigor and proof in mathematics: a historical perspective. Mathematics Magazine, 64, 291–314.CrossRefGoogle Scholar
  15. Maaß, K. (2004). Mathematisches Modellieren im Unterricht. Hildesheim: Franzbecker.Google Scholar
  16. Maaß, K. (2006). What are modelling competences? Zentralblatt für Didaktik der Mathematik (ZDM), 38(2), 113–142.CrossRefGoogle Scholar
  17. Mitchelmore, M., & White, P. (2004). Abstraction in mathematics and mathematics learning. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 329–336). Bergen, Norway: Program Committee.Google Scholar
  18. Pollak, H. O. (1969). How can we teach applications of mathematics? Educational studies in mathematics, 2, 393–404.CrossRefGoogle Scholar
  19. Pontecorvo, C., & Girardet, H. (1993). Arguing and reasoning in understanding historical topics. Cognition and Instruction, 11, 365–395.CrossRefGoogle Scholar
  20. Steiner, H. G. (1990). Needed cooperation between science education and mathematics education. Zentralblatt für Didaktik der Mathematik, 22(6), 194–197.Google Scholar
  21. Tabach, M., Hershkowitz, R., & Schwarz, B. (2006). Constructing and consolidating of algebraic knowledge within dyadic processes: a case study. Educational studies in mathematics, 63, 235–258.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2008

Authors and Affiliations

  1. 1.Universität BremenBremenGermany

Personalised recommendations