How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling

JinHyeong Park; Kyeong-Hwa Lee

doi:10.29333/ejmste/92557

Full Text (PDF)

JinHyeong Park ¹, Kyeong-Hwa Lee ² ^*

More Detail

¹ Gongju National University of Education, Korea² Seoul National University, Korea^* Corresponding Author

Abstract

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.

Keywords

abduction
Euler
Napier
nature of modeling

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 14, Issue 9, September 2018, Article No: em1587

https://doi.org/10.29333/ejmste/92557

Publication date: 25 Jun 2018

Article Views: 2448

Article Downloads: 1102

Open Access References How to cite this article

References

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.
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/10.1007/978-1-4615-4813-3_2.
Burton, D. M. (2011). The history of mathematics. New York: McGraw-Hill.
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.
Fischbein, E. (1987). Intuition in science and mathematics: An educational approach, Dordecht: Reidel.
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/BF02655886.
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.
Lee, K.-H. (2009). The role of analogical reasoning in mathematical knowledge construction. Journal of Educational Research in Mathematics, 19(3), 355-369.
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/10.1007/0-387-24270-8_27.
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.
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:1013874514650.
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.
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.
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/eurasia.2016.1289a.
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/hrt012.
Peirce, C. S. (C.P.) (1931–1935, 1958) Collected Papers of Charles Sanders Peirce. Cambridge, MA: Harvard UP.
Peng, Y., & Reggia, J. A. (1990). Abductive inference models for diagnostic problem-solving. New York: Springer. https://doi.org/10.1007/978-1-4419-8682-5.
Prawat, R. S. (1999). Dewey, Peirce, and the learning paradox, American Educational Research Journal, 36(1), 47-76. https://doi.org/10.3102/00028312036001047.
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.
Sfard, A. (2008). Thinking as communicating, human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.

How to cite this article

APA

Park, J., & Lee, K.-H. (2018). How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1587. https://doi.org/10.29333/ejmste/92557

Vancouver

Park J, Lee KH. How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling. EURASIA J Math Sci Tech Ed. 2018;14(9):em1587. https://doi.org/10.29333/ejmste/92557

AMA

Park J, Lee KH. How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling. EURASIA J Math Sci Tech Ed. 2018;14(9), em1587. https://doi.org/10.29333/ejmste/92557

Chicago

Park, JinHyeong, and Kyeong-Hwa Lee. "How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 9 (2018): em1587. https://doi.org/10.29333/ejmste/92557

Harvard

Park, J., and Lee, K.-H. (2018). How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1587. https://doi.org/10.29333/ejmste/92557

MLA

Park, JinHyeong et al. "How Can Mathematical Modeling Facilitate Mathematical Inquiries? Focusing on the Abductive Nature of Modeling". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 9, 2018, em1587. https://doi.org/10.29333/ejmste/92557