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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
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.
Croft, W., and Cruse, D. A. (2004). Cognitive Linguistics. Cambridge: Cambridge University Press.
diSessa, A. (1993). Toward an epistemology of physics. Cognition & Instruction, 10, 105–225.
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.
Hammer, D., and Elby, A. (2003). Tapping epistemological resources for learning physics. Journal of the Learning Sciences, 12, 53–90.
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.
Kant, I. (1781, 1787). Critique of Pure Reason (Palgrave Macmillan, 2003). German editions translated by Norman Kemp Smith (1929).
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.
Lakoff, G., and Núñez, R. (2000). Where Mathematics Comes from. New York: Basic Books.
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., Martin, T., and Pfaffman, J. (2005). How mathematics propels the development of physical knowledge. Journal of Cognition and Development, 6, 65–88.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Hestenes, D. (2010). Modeling Theory for Math and Science Education. In: Lesh, R., Galbraith, P., Haines, C., Hurford, A. (eds) Modeling Students' Mathematical Modeling Competencies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0561-1_3
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0561-1_3
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0560-4
Online ISBN: 978-1-4419-0561-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)