Abstract
Mathematics has been described as the science of patterns. Natural science can be characterized as the investigation of patterns in nature. Central to both domains is the notion of model as a unit of coherently structured knowledge. Modeling Theory is concerned with models as basic structures in cognition as well as scientific knowledge. It maintains a sharp distinction between mental models that people think with and conceptual models that are publicly shared. This supports a view that cognition in science, math, and everyday life is basically about making and using mental models. We review and extend elements of Modeling Theory as a foundation for R&D in math and science education.
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References
Arnold, V. I. (1997). On Teaching Mathematics. The long text of his hard-hitting address and traces of its aftershocks are easily found by googling his name.
Cassam, Q. (2007). The Possibility of Knowledge. Oxford: Oxford University Press.
Cassirer, E. (1953). The Philosophy of Symbolic Forms. New Haven: Yale University Press, Four volumes.
Evans, V., and Green, M. (2006). Cognitive Linguistics, an Introduction. London: Lawrence Erlbaum.
Goldman, S., Graesser, A., and van den Broek, P. (2001) Narrative Comprehension, Causality and Coherence. London: Lawrence Erlbaum.
Hadamard, J. (1945). An Essay on the Psychology of Invention in the Mathematical Field. New York: Dover.
Hertz, H. (1956). The Principles of Mechanics. English translation, New York: Dover.
Hestenes, D. (1992). Modeling games in the Newtonian world, American Journal of Physics, 60, 732–748.
Hestenes, D. (1999). New Foundations for Classical Mechanics (Dordrecht/Boston: Reidel, 1986), (2nd ed.). Dordrecht/Boston: Kluwer.
Hestenes, D. (2003). Oersted Medal Lecture 2002: Reforming the mathematical language of physics. American Journal of Physics, 71,104–121. Available at the Geometric Calculus website: <http://modelingnts.la.asu.edu>
Hestenes, D. (2007). Notes for a modeling theory of science. Cognition and physics education. In A.L. Ellermeijer (Ed.), Modelling in Physics and Physics Education. Available at the Modeling Instruction website: http://modeling.asu.edu.
Kline, M. (1980). Mathematics, the Loss of Certainty. New York: Oxford University Press.
Lakoff, G., and Johnson, M. (1999). Philosophy in the Flesh. Basic Books: New York.
MacLane, S. (1986). Mathematics, Form and Function. Springer-Verlag: New York.
Romer, R. (1993). Reading equations and confronting the phenomena; the delights and dilemmas of physics teaching. American Journal of Physics, 61, 128–124.
Schwartz, D. L., and Moore, J. L. (1998). The role of mathematics in explaining the material world: Mental models for proportional reasoning. Cognitive Science, 22, 471–516.
Shapiro, S. (1997). Philosophy of Mathematics, Structure and Ontology. New York: Oxford University Press.
Sherin, B. (2001). How students understand physics equations. Cognitive Science, 19, 479–541.
Sherin, B. (2006). Common sense clarified: Intuitive knowledge and its role in physics expertise. Journal of Research in Science Teaching, 43, 535–555.
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Hestenes, D. (2013). Modeling Theory for Math and Science Education. 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_3
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DOI: https://doi.org/10.1007/978-94-007-6271-8_3
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