How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling

JinHyeong Park; Kyeong-Hwa Lee

doi:10.12973/eurasia.2016.1289a

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JinHyeong Park ¹, Kyeong-Hwa Lee ²

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¹ Myongji University² Seoul National University

Abstract

The purpose of this study is to design a modeling task to facilitate students’ inquiries into the chain rule in calculus and to analyze the results after implementation of the task. Researchers have pointed out that students may encounter difficulties in understanding the chain rule due to the formal approaches used to teach and learn this concept. In this study, we take a modeling approach to the teaching and learning of the chain rule by facilitating the generalization of students’ models and modeling activities. We assumed abductive reasoning to be one of the key factors which can support the generalization of students’ models and modeling activities. We believe that analogical reasoning and diagrammatic reasoning are key factors in fostering students’ use of abduction. As a result, we determined that the students’ models and modeling activities were generalized to the chain rule by their use of abductive reasoning, and the students found the chain rule to be a generalized rule for describing changes of various quantities.

Keywords

mathematical modeling
analogy
abduction
diagrammatic reasoning
chain rule

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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 12, Issue 9, September 2016, 2331-2352

https://doi.org/10.12973/eurasia.2016.1289a

Publication date: 29 Jun 2016

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Article Downloads: 1978

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How to cite this article

APA

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 and Technology Education, 12(9), 2331-2352. https://doi.org/10.12973/eurasia.2016.1289a

Vancouver

Park J, Lee KH. How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling. EURASIA J Math Sci Tech Ed. 2016;12(9):2331-52. https://doi.org/10.12973/eurasia.2016.1289a

AMA

Park J, Lee KH. How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling. EURASIA J Math Sci Tech Ed. 2016;12(9), 2331-2352. https://doi.org/10.12973/eurasia.2016.1289a

Chicago

Park, JinHyeong, and Kyeong-Hwa Lee. "How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 9 (2016): 2331-2352. https://doi.org/10.12973/eurasia.2016.1289a

Harvard

Park, J., and Lee, K.-H. (2016). How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), pp. 2331-2352. https://doi.org/10.12973/eurasia.2016.1289a

MLA

Park, JinHyeong et al. "How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 9, 2016, pp. 2331-2352. https://doi.org/10.12973/eurasia.2016.1289a