Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Vahid Borji; Hassan Alamolhodaei; Farzad Radmehr

doi:10.29333/ejmste/91451

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Vahid Borji ¹, Hassan Alamolhodaei ¹ ^* , Farzad Radmehr ¹

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¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, IRAN
^* Corresponding Author

Abstract

APOS-ACE (Action, Process, Object, and Schema-Activities, Classroom discussion, and Exercises) is applied in this article to explore the teaching and learning of derivative by giving emphasis on its graphical understanding. For this purpose, a Genetic Decomposition is developed based on the outcomes of previous studies and on our personal teaching experiences. An ACE cycle is designed with the help of the Maple software and implemented on a group of freshmen Iranian students (experimental group). The outcomes of this implementation are evaluated by comparing the performance of the experimental group to the performance of another equivalent student group (control group), to which the same subject was taught in the traditional, lecture-based way. Our findings demonstrated students’ who were in the experimental group shown a better understanding of the derivate compared to the control group. Therefore, such ACE cycle with Maple could be used more frequently for teaching calculus, especially derivative.

Keywords

teaching and learning
derivative
graphs of functions
tangent at a point of a graph
APOS theory
genetic decomposition
ACE cycle
Maple software

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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

https://doi.org/10.29333/ejmste/91451

EURASIA J Math Sci Tech Ed, 2018 - Volume 14 Issue 7, pp. 2947-2967

Publication date: 11 May 2018

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Vancouver

Borji V, Alamolhodaei H, Radmehr F. Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative. EURASIA J Math Sci Tech Ed. 2018;14(7):2947-67. https://doi.org/10.29333/ejmste/91451

APA

Borji, V., Alamolhodaei, H., & Radmehr, F. (2018). Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), 2947-2967. https://doi.org/10.29333/ejmste/91451

AMA

Borji V, Alamolhodaei H, Radmehr F. Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative. EURASIA J Math Sci Tech Ed. 2018;14(7), 2947-2967. https://doi.org/10.29333/ejmste/91451

Chicago

Borji, Vahid, Hassan Alamolhodaei, and Farzad Radmehr. "Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 7 (2018): 2947-2967. https://doi.org/10.29333/ejmste/91451

Harvard

Borji, V., Alamolhodaei, H., and Radmehr, F. (2018). Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), pp. 2947-2967. https://doi.org/10.29333/ejmste/91451

MLA

Borji, Vahid et al. "Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 7, 2018, pp. 2947-2967. https://doi.org/10.29333/ejmste/91451