Abstract
This paper begins by describing teachers’ knowledge as the creation and development of increasingly sophisticated models or ways of interpreting the tasks of teaching. One study illuminates several ways that pre-service teachers perceive the processes of modelling and the limits of their experiences with stochastic models. Results from a second study indicate that teachers need to have a broad and deep understanding of the diversity of approaches that students might take with modeling tasks. The second study also suggests a reversal in the usual roles of teachers and students by engaging students as evaluators of models.
This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 9722235. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF.
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References
Bassanezi, R. (1994). Modelling as a teaching-learning strategy. For the Learning of Mathematics, 14(2), 31–35.
Doerr, H. M. (2000). How can I find a pattern in this random data? The convergence of multiplicative and probabilistic reasoning. Journal of Mathematical Behavior, 18(4), 431–454.
Doerr, H. M., & Lesh, R. A. (2003). A modeling perspective on teacher development. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 125–139). Mahwah, NJ: Lawrence Erlbaum Associates.
Dugdale, S. (1994). K-12 teachers’ use of a spreadsheet for mathematical modeling and problem solving. Journal of Computers in Mathematics and Science Teaching, 13(1), 43–68.
Kaput, J., & Roschelle, J, (1997). Deepening the impact of technology beyond assistance with traditional formalism in order to democratize access to ideas underlying calculus. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (pp. 105–112). Lahti, Finland: University of Helsinki.
Lingefjard, T. (2002). Mathematical modeling for preservice teachers: A problem from anesthesiology. International Journal of Computers for Mathematical Learning, 7, 117–143.
Weigand, H. & Weller, H. (1998). Modelling real-life problems involving periodic processes with computer algebra. The International Journal of Computer Algebra in Mathematics Education, 5(4), 251–267.
Zbiek, R. M. (1998). Prospective teachers’ use of computing tools to develop and validate functions as mathematical models. Journal for Research in Mathematics Education, 29(2), 184–201.
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Doerr, H.M. (2007). What Knowledge Do Teachers Need for Teaching Mathematics Through Applications and Modelling?. In: Blum, W., Galbraith, P.L., Henn, HW., Niss, M. (eds) Modelling and Applications in Mathematics Education. New ICMI Study Series, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-29822-1_5
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DOI: https://doi.org/10.1007/978-0-387-29822-1_5
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