The review of concept image and concept definition: A hermeneutic phenomenological study on the derivative concepts
DOI:
https://doi.org/10.33830/ijdmde.v1i1.7610Keywords:
Concept image, Concept definition, Derivative concept, Phenomenological hermeneuticAbstract
Calculus classes often focus on studying derivatives, a fundamental topic in mathematics. Upon finishing their studies, potential mathematics teachers will educate students about advanced concepts such as derivatives in the classroom. Therefore, comprehending derivative concepts is essential for teaching children effectively. This study aims to determine how potential mathematics teachers view themselves concerning derivative concepts based on their concept image and concept definition. The study utilized a hermeneutic phenomenological approach together with qualitative approaches in its research strategy. The research data was obtained through interviews and clinical tests from six participants from one of the universities in Kuningan Regency, Indonesia. The research findings indicate that participants' concept image of derivative concepts is limited to symbolic representations. Most participants did not view derivative concepts as providing a deeper understanding but rather as a technique to solve procedural problems. The results indicate that utilizing a range of representations in the learning process can improve the development of a more thorough conceptual understanding, leading to better comprehension of derivative concepts.
References
Arnal-Palacián, M., & Claros-Mellado, J. (2022). Specialized content knowledge of pre-service teachers on the infinite limit of a sequence. In Mathematics Teaching Research Journal (Vol. 169, Issue 1).
Asiala, M., Cottrill, J., Dubinsky, E., & Schwingendorf, K. E. (1997). The development of students’ graphical understanding of the derivative. The Journal of Mathematical Behavior, 16(4), 399–431. https://doi.org/10.1016/S0732-3123(97)90015-8
Aspinwall, L., Shaw, K. L., & Presmeg, N. C. (1996). Uncontrollable mental imagery: graphical connections between a function and its derivative. Educational Studies in Mathematics, 33(3), 301–317. https://doi.org/10.1023/A:1002976729261
Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema. Journal for Research in Mathematics Education, 31(5), 557–578. https://doi.org/10.2307/749887
Bezuidenhout, J. (1998). First‐year university students’ understanding of the rate of change. International Journal of Mathematical Education in Science and Technology, 29(3), 389–399. https://doi.org/10.1080/0020739980290309
Borji, V., Alamolhodaei, H., & Radmehr, F. (2018). Application of the APOS-ACE theory to improve students’ graphical understanding of derivatives. EURASIA Journal of Mathematics, Science and Technology Education, 14(7). https://doi.org/10.29333/ejmste/91451
Bressoud, D. (2015). Insights from the MAA National study of college calculus. The Mathematics Teacher, 109(3), 179–185. https://doi.org/10.5951/mathteacher.109.3.0178
Creswell, J. W. (2015). Revisiting Mixed Methods and Advancing Scientific Practices (S. N. Hesse-Biber & R. B. Johnson, Eds.). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199933624.013.39
Desfitri, R. (2016). In-Service teachers’ understanding of the concept of limits and derivatives and the way they deliver the concepts to their high school students. Journal of Physics: Conference Series, 693, 012016. https://doi.org/10.1088/1742-6596/693/1/012016
Destiniar, D., Rohana, R., & Ardiansyah, H. (2021). Pengembangan media pembelajaran berbasis aplikasi android pada materi turunan fungsi aljabar. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1797. https://doi.org/10.24127/ajpm.v10i3.4050
Dubinsky, E., Schoenfeld, A., Kaput, J., Kessel, C., Darken, B., Wynegar, R., Kuhn, S., Ganter, S. L., Jiroutek, M. R., Schwingendorf, K. E., Mccabe, G. P., Kuhn, J., Mcdonald, M. A., Mathews, D. M., Strobel, K. H., & Zandieh, M. J. (n.d.). The Need for Evaluation in the Calculus
Reform Movement: A Comparison of Two Calculus Teaching Methods 42 A Longitudinal Study of the C 4 L Calculus Reform Program: Comparisons of C 4 L and Traditional Students 63 A Theoretical Framework for Analyzing Student Understanding of the Concept of Derivative 103.
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
Edwards, B. S., & Ward, M. B. (2004). Surprises from Mathematics Education Research: Student (Mis)use of Mathematical Definitions. The American Mathematical Monthly, 111(5), 411–424. https://doi.org/10.1080/00029890.2004.11920092
Ferrini-Mundy, J. (n.d.). Principles and Standards for School Mathematics: A Guide for Mathematicians. In NOTICES OF THE AMS (Vol. 47, Issue 8). http://www.nctm.org/
Fuentealba, C., Badillo, E., Sánchez-Matamoros, G., & Cárcamo, A. (2018). The Understanding of the Derivative Concept in Higher Education. EURASIA Journal of Mathematics, Science and Technology Education, 15(2). https://doi.org/10.29333/ejmste/100640
Giraldo, V., Mariano Carvalho, L., & Tall, D. (n.d.). Descriptions and definitions in the teachingof elementary calculus.
Heng, M. A., & Sudarshan, A. (2013). “Bigger number means you plus!”—Teachers learning to use clinical interviews to understand students’ mathematical thinking. Educational Studies in Mathematics, 83(3), 471–485. https://doi.org/10.1007/s10649-013-9469-3
Hunting, R. P. (1997). Clinical interview methods in mathematics education research and practice. The Journal of Mathematical Behavior, 16(2), 145–165. https://doi.org/10.1016/S0732-3123(97)90023-7
Moru, E. K. (2020). An APOS Analysis of University Students’ Understanding of Derivatives: A Lesotho Case Study. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 279–292. https://doi.org/10.1080/18117295.2020.1821500
Mufidah, A. D., Suryadi, D., & Rosjanuardi, R. (2019). Teacher images on the derivatives concept. Journal of Physics: Conference Series, 1157, 042119. https://doi.org/10.1088/1742-6596/1157/4/042119
Nurwahyu, B., Maria, G., & Mustangin, M. (2020). Students’ Concept Image and Its Impact on Reasoning towards the Concept of the Derivative. European Journal of Educational Research, 9(4), 1723–1734. https://doi.org/10.12973/eu-jer.9.4.1723
Orton, A. (1983). Students’ understanding of differentiation. Educational Studies in Mathematics, 14(3), 235–250. https://doi.org/10.1007/BF00410540
Park, J. (2015). Is the derivative a function? If so, how do we teach it? Educational Studies in Mathematics, 89(2), 233–250. https://doi.org/10.1007/s10649-015-9601-7
Prihandhika, A., Fatimah, S., & Dasari, D. (2018). The Improvement of Mathematical Connection Ability and Habits of Studentsr Mind with Missouri Mathematics Project and Discovery Learning. Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018). https://doi.org/10.2991/miseic-18.2018.61
Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020). Epistemological Obstacles: An Overview of Thinking Process on Derivative Concepts by APOS Theory and Clinical Interview. Journal of Physics: Conference Series, 1521(3), 032028. https://doi.org/10.1088/1742-6596/1521/3/032028
Rivera-Figueroa, A., & Ponce-Campuzano, J. C. (2013). Derivative, maxima and minima in a graphical context. International Journal of Mathematical Education in Science and Technology, 44(2), 284–299. https://doi.org/10.1080/0020739X.2012.690896
Sbaragli, S., Arrigo, G., Amore, B., Pinilla, F., Frapolli, M. I., Frigerio, A., & Villa, D. (2011). Epistemological and Didactic Obstacles: the influence of teachers" beliefs on the conceptual education of students. In Mediterranean Journal for Research in Mathematics Education (Vol. 10).
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
Thompson, P., & Silverman, J. (2008). The Concept of Accumulation in Calculus. In Making the Connection (pp. 43–52). The Mathematical Association of America. https://doi.org/10.5948/UPO9780883859759.005
Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2–3), 229–274. https://doi.org/10.1007/BF01273664
Tokgöz, E. (2012). Numerical method/analysis of students’ conceptual derivative knowledge. In International Journal on New Trends in Education and Their Implications October. www.ijonte.org
Vinner, S. (1983). Concept definition, concept image, and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293–305. https://doi.org/10.1080/0020739830140305
Vinner, S., & Dreyfus, T. (1989). Images and Definitions for the Concept of Function. Journal for Research in Mathematics Education, 20(4), 356–366. https://doi.org/10.5951/jresematheduc.20.4.0356
Vrancken, S., & Engler, A. (2014). Una introducción a la derivada desde la variación y el cambio: resultados de una investigación con estudiantes de primer año de la universidad. Bolema: Boletim de Educação Matemática, 28(48), 449–468. https://doi.org/10.1590/1980-4415v28n48a22
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