Misconceptions of Derivative and Integral in Solving Kinematic Problems: A Phenomenological Exploration of the Experiences of Student-Teachers in Physics Education

Raei, Fatemeh; Karami-Gharehgeshlagi, Fahimeh

doi:10.48310/esip.2026.21611.1026

Misconceptions of Derivative and Integral in Solving Kinematic Problems: A Phenomenological Exploration of the Experiences of Student-Teachers in Physics Education

Document Type : Original Paper

Authors

¹ Department of Mathematics Education, Farhangian University, Tehran, Iran

² Department of Physics Education, Farhangian University, Tehran, Iran

10.48310/esip.2026.21611.1026

Abstract

Undoubtedly, conceptual mastery of derivatives and integrals as the language for describing changes in nature is the cornerstone of a deep understanding of physics and its effective teaching. This qualitative study aimed to explore the conceptual understanding, attitudes, and common misconceptions of student-teachers in Physics Education regarding the fundamental concepts of derivatives and integrals and their physical applications. Data were collected through an open-ended questionnaire containing ten key questions about initial perceptions, understanding of kinematic relationships, and teaching strategies from 15 physics education student-teachers during the 2024-2025 academic year and were analyzed qualitatively. Findings revealed that although most participants were proficient in the formal relationship between derivatives and integrals in the domain of kinematics (position, velocity, acceleration), their understanding of the "reason why" behind these relationships (such as the physical reason why the integral of acceleration equals velocity) was often superficial. A key misconception was the reduction of the integral concept to "finding the antiderivative," neglecting its physical interpretation as "summing infinitely small quantities." Additionally, unsuccessful initial educational experiences and purely formula-based teaching were identified as the main factors causing fear and ambiguity. Consequently, it seems essential to strengthen the conceptual foundation of these tools through an intuitive approach, based on modeling physical phenomena and using graphical representations, to prepare future teachers.

Keywords

Main Subjects

Teacher Education

References

[1] Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.

[2] Bressoud, D. M. (2014). The legacy of the calculus. The American Mathematical Monthly, 121(5), 383-406. https://doi.org/10.4169/amer.math.monthly.121.05.383

[3] Sherin, B. L. (2001). How students understand physics equations. Cognition and Instruction, 19(4), 479-541. https://doi.org/10.1207/S1532690XCI1904_3

[4] Amaliah, Nur Utami; Sutopo, Sutopo; Latifah, Eny; and Zulnaidi, Hutkemri (2024) "Identify Resources Activated by Students when Solving Straight Motion Kinematics Problems with Different Representation," Jurnal Pendidikan Sains: Vol. 12: No. 2, Article 5. https://citeus.um.ac.id/jps/vol12/iss2/5

[5] Trowbridge, D. E., & McDermott, L. C. (1981). Investigation of student understanding of the concept of acceleration in one dimension. American Journal of Physics, 49(3), 242-253. https://doi.org/10.1119/1.12505

[6] Orton, A. (1983). Students' understanding of integration. Educational Studies in Mathematics, 14(1), 1-18. https://doi.org/10.1007/BF00704699

[7] Ferrini-Mundy, J., & Gaudard, M. (1992). Secondary school calculus: Preparation or pitfall in the study of college calculus. Journal for Research in Mathematics Education, 23(1), 56-71. https://doi.org/10.2307/749163

[8] Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema. Journal for Research in Mathematics Education, 31(5), 557-578. https://doi.org/10.2307/749888

[9] Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics Education, 8, 103-127.

[10] Jones, S. R. (2015). The prevalence of area-based reasoning in students' understanding of definite integrals. The Journal of Mathematical Behavior, 38, 12-24. https://doi.org/10.1016/j.jmathb.2015.01.004

[11] Sealey, V. (2006). Definite integrals, Riemann sums, and area under a curve: What is necessary and what is sufficient. Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 46-53.

[12] Walsh, L. N., Howard, R. G., & Bowe, B. (2007). Phenomenographic study of students’ problem solving approaches in physics. *Physical Review Special Topics - Physics Education Research, 3*(2), 020108. https://doi.org/10.1103/PhysRevSTPER.3.020108

[13] Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62(8), 750-762. https://doi.org/10.1119/1.17449

[14] Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Erlbaum.

[15] Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167-194). Erlbaum.

[16] McDermott, L. C., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55(6), 503-513. https://doi.org/10.1119/1.15104

[17] Haidemen, H. (2021). Student Understanding of Kinematics: A Phenomenographic Study. [Unpublished doctoral dissertation]. State University.

[18] Lindell, R. S. (1999). The effect of learning cycle laboratories on the understanding of kinematics graphs. [Unpublished master's thesis]. University of Nebraska.

[19] Trowbridge, D. E., & McDermott, L. C. (1980). Investigation of student understanding of the concept of velocity in one dimension. American Journal of Physics, 48(12), 1020-1028. https://doi.org/10.1119/1.12298

[20] Thornton, R. K., & Sokoloff, D. R. (1998). Assessing student learning of Newton's laws: The Force and Motion Conceptual Evaluation and the Evaluation of Active Learning Laboratory and Lecture Curricula. American Journal of Physics, 66(4), 338-352. https://doi.org/10.1119/1.18863

[21] Burgoon, J. N., Heddle, M. L., & Duran, E. (2011). Re-Examining the Similarities Between Teacher and Student Conceptions About Physical Science. Journal of Science Teacher Education, 22(2), 101-114. https://doi.org/10.1007/s10972-010-9196-x

[22] Moodley, K., & Gaigher, E. (2019). Teaching Electric Circuits: Teachers' Perceptions and Learners' Misconceptions. Research in Science Education, 49(1), 73-89. https://doi.org/10.1007/s11165-017-9615-5

[23] Lortie, D. C. (1975). Schoolteacher: A Sociological Study. University of Chicago Press.

[24] Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004

[25] Van Manen, M. (2016). Researching lived experience: Human science for an action sensitive pedagogy (2nd ed.). Routledge.

[26] Moustakas, C. (1994). Phenomenological research methods. Sage.

[27] Colaizzi, P. F. (1978). Psychological research as the phenomenologist views it. In R. S. Valle & M. King (Eds.), Existential-phenomenological alternatives for psychology (pp. 48–71). Oxford University Press.

[28] Craik, F. I. M., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. Journal of Verbal Learning and Verbal Behavior, 11(6), 671–684. https://doi.org/10.1016/S0022-5371(72)80001-X

[29] Allen, M. (2014). Misconceptions in Primary Science. McGraw-Hill Education (UK).

[30] Hammer, D. (1996). Misconceptions or P-Prims: How May Alternative Perspectives of Cognitive Structure Influence Instructional Perceptions and Intentions. Journal of the Learning Sciences, 5(2), 97-127. https://doi.org/10.1207/s15327809jls0502_1

[31] Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition. The Journal of the Learning Sciences, 3(2), 115-163. https://doi.org/10.1207/s15327809jls0302_1

[32] Harasim, L. (2017). Learning theory and online technologies. Routledge.

[33] Kamalianfar, A., Jaberi, M. A., & Mirab, M. R. (2021). Investigating of new physics student-teacher misconception. Journal of Education in Basic Sciences, 7(24), 84-94. https://doi.org/10.22034/JEBS.2021.248263

[34] Kaltakci Gurel, D., Eryilmaz, A., & McDermott, L. C. (2015). A Review and Comparison of Diagnostic Instruments to Identify Students' Misconceptions in Science. EURASIA Journal of Mathematics, Science and Technology Education, 11(5). https://doi.org/10.12973/eurasia.2015.1369a

[35] Resbiantoro, G., & Setiani, R. (2022). A review of misconception in physics: the diagnosis, causes, and remediation. Journal of Turkish Science Education, 19(2). https://doi.org/10.36681/tused.2022.56

[36] Deci, E. L., & Ryan, R. M. (2000). The "what" and "why" of goal pursuits: Human needs and the self-determination of behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01

[37] Gomez-Zwiep, S. (2008). Elementary Teachers' Understanding of Students' Science Misconceptions: Implications for Practice and Teacher Education. Journal of Science Teacher Education, 19(5), 437-454. https://doi.org/10.1007/s10972-008-9102-y

[38] Korganci, N., Miron, C., Dafinei, A., & Antohe, S. (2015). The Importance of Inquiry-Based Learning on Electric Circuit Models for Conceptual Understanding. *Procedia - Social and Behavioral Sciences, 191*, 2463-2468. https://doi.org/10.1016/j.sbspro.2015.04.530

[39] Suprapto, N. (2020). Do we experience misconceptions?: An ontological review of misconceptions in science. Studies in Philosophy of Science and Education, 1(2), 50-55. https://doi.org/10.46627/sipose.v1i2.31

[40] Negahban, M., Emamjomeh, M. R., Ahmadi Kalateh Ahmad, F., Asareh, A., & Kabiri, M. (2025). Common misconceptions in general physics concepts: A case study of student-teachers in elementary education. Iranian Journal of Curriculum Studies, 20(76), 207–234. https://doi.org/10.22034/jcs.2025.490154.2369