Abstract
Abstract Through the use of three mathematical examples, our study explores the origins of students abilities to model (a) the process in which students acquire the ability to both model and learn transferable modeling abilities across modeling activities, and (b) the way in which the modeling cycle should be characterized. We conclude by suggesting that philosophical issues are present in understanding how the modeling ability emerges in students who have never modelled. This is linked to efforts to find activities and methods that will enable better modeling capabilities to be learned.
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References
Blomhøj, M., and Jensen, T. H. (2003). Developing mathematical modeling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139.
Blomhøj, M., and Jensen, T. H. (2007). What’s all the fuss about competencies? In Blum, W., Galbraith, P., Henn, H.-W., and Niss, M. (Eds.), Modeling and Applications in Mathematics Education – The 14th ICMI Study (pp. 45–56). New York: Springer Science + Business Media. Blum, W., and Niss, M. (1991). Applied mathematical problem solving, modeling, and links to other subjects - State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68. Goldin, G., and McClintock, C. E. (Eds.) (1984). Task Variables in Mathematical Problem Solving. Hillsdale, NJ: Erlbaum.
Gravemeijer, K. (2007). Emergent modeling as a precursor to mathematical modeling. In W. Blum, P. Galbraith, H.-W. Henn, and M. Niss (Eds.), Modeling and Applications in Mathematics
Education – The 14th ICMI Study (pp. 137–144). New York: Springer Science + Business Media.
Kaiser, G., and Maass, K. (2007). Modeling inlower secondary mathematics classroom - Problems and opportunities. In W. Blum, P. Galbraith, H.-W. Henn, and M. Niss (Eds.), Modeling and Applications in Mathematics Education – The 14th ICMI Study (pp. 99–108). New York: Springer Science + Business Media.
Lesh, R., and Doerr, H. (Eds.) (2003). Beyond Constructivism: Models and Modeling Perspectives on Mathematical Problem Solving, Learning and Teaching. Mahwah, NJ: Erlbaum.
Lesh, R., and Zawojewski, J. (2007). Problem solving and modeling. In F.K. Lester, Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 763–804). Charlotte, NC: Information Age Publishing.
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis, and S. Papastavridis (Eds.), 3rd Mediterranean Conference on Mathematical Education (pp. 115–124). Athens, Greece: Hellenic Mathematical Society and Cyprus Mathematical Society.
Ottesen, J. (2001). Do not ask what mathematics can do for modeling. Ask what modeling can do for mathematics! In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 335–346). Dordrecht: Kluwer Academic Publishers.
Rodriguez Gallegos, R. (2007). Les equations differentielles comme outil de modelisation mathematique en Classe de Physique et de Mathematiques au lycee: une etude de manuels et de Processus de modelisation d’eleves en Terminale S. Doctoral Dissertation. Grenoble: Universite Joseph Fourier, I.
Schoenfeld, A. (1985). Mathematical Problem Solving. New York: Academic Press.
Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In G. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 334–370). New York: Macmillan Publishing Company.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
Vollrath, H.-J. (1993). Paradoxien des Verstehens von Mathmatik. Journal für MathematikDidaktik, 14(1), 35–58.
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Niss, M. (2013). Modeling a Crucial Aspect of Students’ Mathematical Modeling. In: Lesh, R., Galbraith, P., Haines, C., Hurford, A. (eds) Modeling Students' Mathematical Modeling Competencies. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6271-8_4
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