How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling
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Gongju National University of Education, Korea
Seoul National University, Korea
Publish date: 2018-06-25
EURASIA J. Math., Sci Tech. Ed 2018;14(9):em1587
The purpose of this study is to investigate the nature of mathematical modeling and identify characteristics of mathematical inquiries triggered by mathematical modeling. We investigated three cases of mathematical inquiries facilitated by mathematical modeling. As a result of this study, we revealed the abductive nature of mathematical modeling. We also determined that mathematical inquiries triggered by mathematical modeling have abductive, recursive, analogical, and context-dependent aspects.
Kyeong-Hwa Lee   
Seoul National University, Korea
1. Ärlebäck, J. B., & Doerr, H. M. (2015). At the core of modelling: Connecting, coordinating and integrating models. In K. Krainer & N. Vondrová (Eds.), Proceedings of the 9th Congress of European Research in Mathematics Education. Prague: Charles University.
2. Bailer-Jones, D. M. (1999), Tracing the Development of Models in the Philosophy of Science. In L. Magnani, N. J. Nersessian, & P. Thagard (Eds), Model-based reasoning in scientific discovery (pp. 23–40). New York: Springer. https://doi.org/10.1007/978-1-....
3. Burton, D. M. (2011). The history of mathematics. New York: McGraw-Hill.
4. Eco, U. (1983). Horns, hooves, insteps: Some hypotheses on three types of abduction. In U. Eco & T. Sebeok (Eds.), The sign of three: Dupin, Holmes, Peirce (pp. 198–220). Bloomington, IN: Indiana University Press.
5. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach, Dordecht: Reidel.
6. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process, ZDM, 38(2), 143-162. https://doi.org/10.1007/BF0265....
7. Kehle, P. E., & Lester, F. K. (2003). A semiotic look at modeling behavior. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: a models and modelling perspective (pp. 97–122). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
8. Lee, K.-H. (2009). The role of analogical reasoning in mathematical knowledge construction. Journal of Educational Research in Mathematics, 19(3), 355-369.
9. Lenhard, J. (2005). Deduction, perception and modeling: The two Peirces on the essence of mathematics, In M. H. G. Hoffinann, J. Lenhard & F. Seeger (Eds.) Activity and Sign - Grounding Mathematics Education (pp. 313-324). New York: Springer. https://doi.org/10.1007/0-387-....
10. Lesh, R., & Doerr, H. (2003). In what ways does a models and modeling perspective move beyond constructivism? In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 519-556). Mahwah, NJ: Lawrence Erlbaum Associates.
11. McClain, K., & Cobb, P. (2001). Supporting students’ ability to reason about data, Educational studies in mathematics, 45, 103-129. https://doi.org/10.1023/A:1013....
12. Ottesen, J. T. (2001) Do not ask mathematics can do for modelling. In D. Holton (Ed) The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 335–346.). London: Kluwer Academic Publishers.
13. Park, J., & Lee, K.-H. (2013). A semiotic analysis on mathematization in mathematical modeling process. Journal of Educational Research in Mathematics, 23(2). 95-116.
14. Park, J., & Lee, K.-H. (2016). How can students generalize the chain rule? The roles of abduction in mathematical modeling. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2257-2278. https://doi.org/10.12973/euras....
15. Park, J., Park, M., Park, M.-S., Cho, J., & Lee, K.-H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment, Teaching Mathematics and Its Applications, 32, 123-139. https://doi.org/10.1093/teamat....
16. Peirce, C. S. (C.P.) (1931–1935, 1958) Collected Papers of Charles Sanders Peirce. Cambridge, MA: Harvard UP.
17. Peng, Y., & Reggia, J. A. (1990). Abductive inference models for diagnostic problem-solving. New York: Springer. https://doi.org/10.1007/978-1-....
18. Prawat, R. S. (1999). Dewey, Peirce, and the learning paradox, American Educational Research Journal, 36(1), 47-76. https://doi.org/10.3102/000283....
19. Rothenberg, J. (1989). The Nature of Modeling. In L.E. William, K.A. Loparo, N.R. Nelson (Eds.). Artificial Intelligence, Simulation, and Modeling (pp. 75-92). New York: John Wiley and Sons, Inc.
20. Sfard, A. (2008). Thinking as communicating, human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.