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Analysis of student's understanding of the concept of derivative with a discrete approach | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 18، دوره 16، شماره 2، اردیبهشت 2025، صفحه 219-234 اصل مقاله (942.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.32273.4791 | ||
| نویسندگان | ||
| Amin Badiyepeima Jahromi1؛ Amirali Tabatabai* 1؛ Majid Haghverdi2 | ||
| 1Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran | ||
| تاریخ دریافت: 16 شهریور 1402، تاریخ پذیرش: 10 آذر 1402 | ||
| چکیده | ||
| This paper studies the engineering students' understanding of derivatives with a discrete approach using sequences introduced by Weigand (2014). This approach proposes a step-by-step method of difference sequence for functions defined on Z and Q. This concept was taught as part of a mathematics course in an engineering college at an Iranian university. HomeWorks with questions based on derivatives with a discrete approach were constructed and performed for the participants. Their written answers, which were used to explore the students' mental structures of these mentioned concepts, were analyzed using APOS (Action-Process-Object-Schema) theory. We performed interviews so that the students could explain their written answers. The results show that students tend to adopt an algorithmic approach when solving derivative problems and students' understanding of the meaning of derivative with a discrete approach was mainly procedural. Also according to the observed mental structures, a suggested genetic decomposition for the derivative with a discrete approach is presented. | ||
| کلیدواژهها | ||
| Derivative؛ Difference sequences؛ APOS theory؛ Genetic decomposition | ||
| مراجع | ||
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[1] A. Ariza, S. Llinares, and J. Valls, Students’ understanding of the function-derivative relationship when learning economic concepts, Math. Educ. Res. J. 27 (2015), no. 4, 615–635. [2] I. Arnon, J. Cottrill, E. Dubinsky, A. Okta，c, S.R. Fuentes, M. Trigueros, and K. Weller, APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, New York, Heidelberg, Dordrecht, London, Springer, 2014. [3] M. Asiala, A. Brown, D.J. DeVries, E. Dubinsky, D. Mathews, and K. Thomas, A framework for research and development in undergraduate mathematics education, Res. Colleg. Math. Educ. 6 (1996), no. 2, 1–32. [4] M. Asiala, J. Cottrill, E. Dubinsky, and K.E. Schwingendorf, The development of students’ graphical understanding of the derivative, J. Math. Behav. 16 (1997), no. 4, 399–430. [5] M. Berger, Making mathematical meaning: from preconcepts to pseudoconcepts to concepts, Pythagoras 63 (2006), 14–21. [6] V. Borji and R. Mart´ınez-Planell, What does ‘y is defined as an implicit function of x’ mean?: An application of APOS-ACE, J. Math. Behav. 56 (2019), 100739. [7] D. Breidenbach, E. Dubinsky, J. Hawks, and D. Nichols, Development of the process conception of function, Educ. Stud. Math. 23 (1999), 247–285. [8] I. Cetin, Students’ understanding of loops and nested loops in computer programming: An APOS theory perspective, Canad. J. Sci. Math. Technol. Educ. 15 (2015), 155–170. [9] I. Cetin, Students’ understanding of limit concept: An APOS perspective, Doctoral Thesis, Middle East Technical University, Turkey, 2009. [10] J.M. Clark, F. Cordero, J. Cottrill, B. Czarnocha, D.J. DeVries, D. St. John, T. Tolias, and D. Vidakovic, Constructing a schema: The case of the chain rule, J. Math. Behav. 16 (1999), no. 4, 345–364. [11] E. Dubinsky and M. McDonald, APOS: A constructivist theory of learning in undergraduate mathematics education research, New ICMI Stud. Ser. 7 (2001), 275–282. [12] A. Dominguez, P. Barniol, and G. Zavala, Test of understanding graphs in calculus: Test of students’ interpretation of calculus graphs, EURASIA J. Math. Sci. Technol. Educ. 13 (2017), no. 10, 6507-6531. [13] T. Eisenherg, On the development of a sense for functions, The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America, Washington, 1999, pp. 153-174. [14] J. Garcıa -Garcıa and C. Dolores-Flores, Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions, Math. Educ. Res. J. 33 (2019), no. 1, 1–22. [15] V. Giraldo, L. M. Carvalho and D. Tall, Descriptions and definitions in the teaching of elementary calculus, Int. Group Psycho. Math. Educ. 2 (2003), 445–452. [16] R. Martınez-Planell, M. Trigueros, and D. McGee, Student understanding of directional derivatives of functions of two variables, Proc. 37th Ann. Meet. North Amer. Chapter Int. Group Psycho. Math. Educ., East Lansing, MI: Michigan State University, 2015. [17] A. Orton, Student’s understanding of differentiation, Educ. Stud. Math. 14 (1983), 235–250. [18] D. Tall, Students’ difficulties in calculus, plenary address, Proc. ICME 7 (1993), 13–28. [19] M. Thomas and S. Stewart, Eigenvalues and eigenvectors: Embodied, symbolic and formal thinking, Math. Educ. Res. J. 23 (2011), no. 3, 275–296. [20] T. Uygur and A. Ozdas, Misconceptions and difficulties with the chain rule, The Mathematics Education into the 21st Century Project, University of Technology, Malaysia, 2015, pp. 209-213. [21] H.D. Weigand, A discrete approach to the concept of derivative, ZDM Math. Educ. 46 (2014), 603–619. [22] K. Weller, I. Arnon, and E. Dubinsky, Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion, Canad. J. Sci., Math. Technol. Educ. 9 (2009), 5–28. [23] K. Weller, I. Arnon, and E. Dubinsky, Preservice teachers’ understandings of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief, Canad. J. Sci., Math. Technol. Educ. 11 (2011), 129–159. [24] M. Zandieh, A theoretical framework for analyzing student understanding of the concept of derivative, CBMS Issues Math. Educ. 8 (2000), 103–127. | ||
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