Abstract
Across a wide spectrum of disciplines and forms of investigation, scientists invent and revise models. Although central to scientific practice, models cannot simply be imported into classrooms. Instead, pedagogy must be designed so that students can come to understand natural systems by inventing and revising models of these systems. Considering theories of analogical development, we suggest rooting first experiences of modeling in resemblance — physical microcosms — and in inscription — children’s drawings and related writings. From these starting points, we seek to stretch inscription into mathematization, so that children describe natural systems by recourse to mathematical systems and structures. Engagement in these practices has epistemic consequences, fundamentally altering how children view the natural world.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bazerman, C. (1988). Shaping written knowledge: The genre and activity of the experimental article in science. Madison: University of Wisconsin Press.
Chi, M. T. H. (2005). Commonsense conceptions of emergent processes: Why some misconceptions are robust. The Journal of the Learning Sciences, 14, 161–199.
Genter, D., & Toupin, C. (1986). Systematicity and surface similarity in the development of analogy. Cognitive Science, 10, 277–300.
Kline, M. (1980). Mathematics: The loss of certainty. Oxford: Oxford University Press.
Latour, B. (1993). We have never been modern. Cambridge, MA: Harvard University Press.
Latour, B. (1999). Pandora’s hope: Essays on the reality of science studies. London: Cambridge University Press.
Lehrer, R., & Pritchard, C. (2002). Symbolizing space into being. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolization, modelling and tool use in mathematics education. (pp. 59–86). Dordrecht, Netherlands: Kluwer Academic Press.
Lehrer, R., & Schauble, L. (2005). Developing modeling and argument in the elementary grades. In T. Romberg, & T. P. Carpenter (Eds.), Understanding mathematics and science matter, (pp. 29–53). Mahwah, NJ: Lawrence Erlbaum Associates.
Lehrer, R., & Schauble, L. (2006). Cultivating model-based reasoning in science education. In R. Keith Sawyer (Ed.), Cambridge Handbook of the Learning Sciences (pp. 371–387). Cambridge: Cambridge University Press.
Olson, D. R. (1994). The world on paper: The conceptual and cognitive implications of writing and reading. New York: Cambridge University Press.
Penner, D. E. (2000). Explaining systems: Investigating middle school students’ understanding of emergent phenomena. Journal of Research in Science Teaching, 37, 784–806.
Pickering, A. (1995). The mangle of practice: Time, agency, and science. Chicago: University of Chicago Press.
Resnick, M. (1994). Turtles, termites, and traffic jams: Explorations in massively parallel microworlds. Cambridge, MA: MIT Press.
Wilensky, U., & Stroup, W. (1999). Learning through participatory simulations: Network-based design for systems learning in classrooms. Computer Supported Collaborative Learning Conference, Stanford University, California.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Lehrer, R., Schauble, L. (2007). A Developmental Approach for Supporting the Epistemology of Modeling. 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_14
Download citation
DOI: https://doi.org/10.1007/978-0-387-29822-1_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29820-7
Online ISBN: 978-0-387-29822-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)