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Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

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Abstract

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.

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REFERENCES

  • Alpers, B. (2002). CAS as environments for implementing mathematical microworlds. International Journal of Computer Algebra in Mathematics Education, 9, 177–204.

    Google Scholar 

  • Challis, N. (2002). Expressive and explicit CAS-is it enough? International Journal of Computer Algebra in Mathematics Education, 9, 155–166.

    Google Scholar 

  • Cuoco, A. (1994). Multiple representations for functions. In J.J. Kaput and E. Dubinsky (Eds.), Research Issues in Undergraduate Mathematics Learning, MAA Notes 33 (pp. 121–140).

  • DeMarois, P. & Tall, D. (1996). Facets and layers of the function concept. Proceedings of PME 20 (Valencia), Vol. 2 (pp. 297–304).

    Google Scholar 

  • DeMarois, P. & Tall, D. (1999). Function:Organizing principle or cognitive root? Proceedings of PME 23 (Haifa), Vol. 2 (pp. 257–264).

    Google Scholar 

  • Dubinsky, E. & Harel, G. (1992). In G. Harel & E. Dubinsky (Eds.), The Nature of the Process Conception of Function (pp. 85–106).

  • Edwards, L. (1998). Embodying mathematics and science: Microworlds as representations. Journal of Mathematical Behavior, 17, 53–78.

    Google Scholar 

  • Goldenberg, P., Lewis, P. & O'Keefe, J. (1992). In G. Harel & E. Dubinsky (Eds.), Dynamic Representation and the Development of a Process Understanding of Function (pp. 235–260).

  • Harel, G. & Dubinsky, E. (Eds.) (1992). The Concept of Function. Aspects of Epistemology and Pedagogy. MAA Notes 25.

  • Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of function. Journal of Mathematical Behavior, 17, 123–134.

    Google Scholar 

  • Janvier, C. (1981). Use of situations in mathematical education. Educational Studies in Mathematics, 12, 113–122.

    Google Scholar 

  • Kent, P. (2000). Expressiveness and abstraction with computer algebra software. Journeéd′étude: Environnement informatiques de calcul symbolique et apprentissage des mathématique, Rennes, France.

  • Leinhardt, G., Zaslavsky, O. & Stein, M.K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60, 1–64.

    Google Scholar 

  • Monk, S. (1992). In G. Harel & E. Dubinsky (Eds.), Students' Understanding of a Function Given by a Physical Model (pp. 175–194).

  • Müller-Philipp, S. (1994). Der Funktionsbegriff im Mathematikunterricht-Eine Analyse für die Sekundarstufe I unter Berücksichtigung lernpsychologischer Erkenntnisse und der Einbeziehung des Computers als Lernhilfe. Münster, New York: Waxmann.

    Google Scholar 

  • Nemirovsky, R., Kaput, J. & Roschelle, J. (1998). Enlarging mathematical activity from modeling phenomena to generating phenomena. In A. Oliver & K. Newstead (Eds.), Proceedings of PME 22 (Stellenbosch), Vol. 3 (pp. 287–294).

  • O'Callaghan, B. (1998). Computer-intensive algebra and students' conceptual knowledge of functions. Journal for Research in Mathematics Education, 29, 21–40.

    Google Scholar 

  • Roschelle, J., Kaput, J. & Stroup, W. (2000). SimCalc: Accelerating students' engagement with the mathematics of change, In M. Jacobson & R.B. Kozma (Eds.), Innovations in Science and Mathematics Education (pp. 47–76). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Schwingendorf, K., Hawks, J. & Beineke, J. (1992). In G. Harel & E. Dubinsky (Eds.), Horizontal and Vertical Growth of the Student's Conception of Function (pp. 133–149).

  • Sierpinska, A. (1992). In G. Harel & E. Dubinsky (Eds.), On Understanding the Notion of Function. (pp. 25–58).

  • Tall, D. & Bakar, M. (1992). Students' mental prototypes for functions and graphs. International Journal of Mathematics Education in Science and Technology, 23, 39–50.

    Google Scholar 

  • Thompson, P. (1994). Students, functions, and the undergraduate curriculum, In E. Dubinsky, A.H. Schoenfeld & J.J. Kaput (Eds.), Research in Collegiate Mathematics Education (pp. 21–44). Providence, RI: AMS.

    Google Scholar 

  • Vinner, S. & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356–366.

    Google Scholar 

  • Weigand, H.-G. (1988). DEZur Bedeutung von Zeitfunktionen für den Mathematikunterricht. Journal für Mathematikdidaktik, 9, 55–86.

    Google Scholar 

  • Weigand, H.-G. & Weller, H. (2001). Changes of working styles in a computer algebra environment-the case of functions. International Journal of Computers for Mathematical Learning, 6, 87–111.

    Google Scholar 

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Gerny, M., Alpers, B. Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students. International Journal of Computers for Mathematical Learning 9, 25–57 (2004). https://doi.org/10.1023/B:IJCO.0000038245.60482.24

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  • DOI: https://doi.org/10.1023/B:IJCO.0000038245.60482.24

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