Description in course of mathematical methods for physics and possible development of course program
Abstract
The essence of mathematics is a thought process in constructing, applying abstract ideas, and their logical interrelationships. This process is essential in solving quantitative and qualitative physics problems, where abstract ideas are required to represent physical phenomena. This study aims to give detail description of the process of mathematical methods for physics lectures. Improvement in pre-service physics teachers' critical thinking is designed to strengthen their critical thinking and problem-solving skills. The methodology of research is qualitative descriptive. The research subjects were 97 pre-service physics teachers who had followed the mathematical methods for physics courses and teaching lecturers. Data collection consisted of questionnaires, and interviews. Observations are needed for describing the implementation of mathematical methods for physics courses, document analysis, and data collection, including lesson plan and assessment. The results showed that mathematical methods for physics courses need improvement in the learning process. It is concluded that lecture activities integrating computers into physics and mathematics are necessary to be implemented. It is expected that the program will improve students' ability in problem-solving, critical thinking skills, communication, digital era literacy, creative and innovative creations, and group work. Specifically, implementation of the program in the ordinary differential equations course can provide learning experiences to students regarding the process of reasoning in physics using mathematical principles.
References
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Kjeldsen, T. H., & Lützen, J. (2015). Interactions between mathematics and physics: The history of the concept of function—teaching with and about nature of mathematics. Science & Education, 24(5–6), 543–559. https://doi.org/10.1007/s11191-015-9746-x
Klein, P., Dengel, A., & Kuhn, J. (2018). Students’ visual attention while solving multiple representation problems in upper-division physics. In O. Z.-T. Et (Ed.), Positive Learning in the Age of Information (pp. 67–87). Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-19567-0_6
Klein, P., Viiri, J., & Kuhn, J. (2019). Visual cues improve students’ understanding of divergence and curl: Evidence from eye movements during reading and problem solving. Physical Review Physics Education Research, 15(1), 010126. https://doi.org/10.1103/PhysRevPhysEducRes.15.010126
Kneubil, F. B., & Robilotta, M. R. (2015). Physics teaching: Mathematics as an epistemological tool. Science & Education, 24(5–6), 645–660. https://doi.org/10.1007/s11191-014-9727-5
Li, J., & Singh, C. (2018). Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law. European Journal of Physics, 39(1), 015702. https://doi.org/10.1088/1361-6404/aa8d55
López-Gay, R., MartÃnez Sáez, J., & MartÃnez Torregrosa, J. (2015). Obstacles to mathematization in physics: The case of the differential. Science & Education, 24(5–6), 591–613. https://doi.org/10.1007/s11191-015-9757-7
Marton, F., & Pong, W. Y. (2005). On the unit of description in phenomenography. Higher Education Research & Development, 24(4), 335–348. https://doi.org/10.1080/07294360500284706
MeÅ¡ić, V., Neumann, K., Aviani, I., Hasović, E., Boone, W. J., Erceg, N., Grubelnik, V., SuÅ¡ac, A., GlamoÄić, D. S., Karuza, M., Vidak, A., AlihodŽić, A., & Repnik, R. (2019). Measuring students’ conceptual understanding of wave optics: A Rasch modeling approach. Physical Review Physics Education Research, 15(1), 1–20. https://doi.org/10.1103/PhysRevPhysEducRes.15.010115
Mota, A. R., Didiş Körhasan, N., Miller, K., & Mazur, E. (2019). Homework as a metacognitive tool in an undergraduate physics course. Physical Review Physics Education Research, 15(1), 010136. https://doi.org/10.1103/PhysRevPhysEducRes.15.010136
Nielsen, S. S., & Nielsen, J. A. (2019). A competence-oriented approach to models and modelling in lower secondary science education: Practices and rationales among danish teachers. Research in Science Education. https://doi.org/10.1007/s11165-019-09900-1
Odden, T. O. B., Lockwood, E., & Caballero, M. D. (2019). Physics computational literacy: An exploratory case study using computational essays. Physical Review Physics Education Research, 15(2), 020152. https://doi.org/10.1103/PhysRevPhysEducRes.15.020152
Pospiech, G., Eylon, B., Bagno, E., & Lehavi, Y. (2015). The role of mathematics for physics teaching and understanding. Conference: Mathematics in Physics Education, 3(May-June). https://doi.org/10.1393/ncc/i2015-15110-6
Pratiwi, H. Y., Hudha, M. N., Asri, M., & Ahmad, N. J. (2019). The impact of guided inquiry model integrated with peer instruction towards science process skill and physics learning achievement. Momentum: Physics Education Journal, 3(2), 78–85. https://doi.org/10.21067/mpej.v3i2.2768
Redfors, A., Hansson, L., Hansson, Ö., & Juter, K. (2014). The role of mathematics in the teaching and learning of physics. Ebook Proceedings of the ESERA 2013 Conference, 2, 376–383. https://www.diva-portal.org/smash/get/diva2:710055/FULLTEXT01.pdf
Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5–6), 561–590. https://doi.org/10.1007/s11191-015-9749-7
Ryan, Q. X., Frodermann, E., Heller, K., Hsu, L., & Mason, A. (2016). Computer problem-solving coaches for introductory physics: Design and usability studies. Physical Review Physics Education Research, 12(1), 010105. https://doi.org/10.1103/PhysRevPhysEducRes.12.010105
Saprudin, S., Liliasari, L., Setiawan, A., & Prihatmanto, A. S. (2020). Optical Gamification (OG); Serial versus random model to improve pre-service physics teachers’ concept mastery. International Journal of Emerging Technologies in Learning (IJET), 15(09), 39. https://doi.org/10.3991/ijet.v15i09.11779
Schermerhorn, B. P., & Thompson, J. R. (2019). Physics students’ construction of differential length vectors in an unconventional spherical coordinate system. Physical Review Physics Education Research, 15(1), 010111. https://doi.org/10.1103/PhysRevPhysEducRes.15.010111
Sutopo, S., & Waldrip, B. (2014). Impact of a representational approach on students’ reasoning and conceptual understanding in learning mechanics. International Journal of Science and Mathematics Education, 12(4), 741–765. https://doi.org/10.1007/s10763-013-9431-y
Taleyarkhan, M., Dasgupta, C., Garcia, J. M., & Magana, A. J. (2018). Investigating the impact of using a CAD simulation tool on students’ learning of design thinking. Journal of Science Education and Technology, 27(4), 334–347. https://doi.org/10.1007/s10956-018-9727-3
Treagust, D. F., Duit, R., & Fischer, H. E. (2017). Multiple representations in physics education (D. F. Treagust, R. Duit, & H. E. Fischer (eds.); Vol. 10). Springer International Publishing. https://doi.org/10.1007/978-3-319-58914-5
Walsh, C., Quinn, K. N., Wieman, C., & Holmes, N. G. (2019). Quantifying critical thinking: Development and validation of the physics lab inventory of critical thinking. Physical Review Physics Education Research, 15(1), 010135. https://doi.org/10.1103/PhysRevPhysEducRes.15.010135
Williams, M. (2018). The missing curriculum in physics problem-solving education. Science & Education, 27(3–4), 299–319. https://doi.org/10.1007/s11191-018-9970-2
Young, N. T., Allen, G., Aiken, J. M., Henderson, R., & Caballero, M. D. (2019). Identifying features predictive of faculty integrating computation into physics courses. Physical Review Physics Education Research, 15(1), 010114. https://doi.org/10.1103/PhysRevPhysEducRes.15.010114
Bajracharya, R. R., Emigh, P. J., & Manogue, C. A. (2019). Students’ strategies for solving a multirepresentational partial derivative problem in thermodynamics. Physical Review Physics Education Research, 15(2), 020124. https://doi.org/10.1103/PhysRevPhysEducRes.15.020124
Bajracharya, R. R., & Thompson, J. R. (2016). Analytical derivation: An epistemic game for solving mathematically based physics problems. Physical Review Physics Education Research, 12(1), 010124. https://doi.org/10.1103/PhysRevPhysEducRes.12.010124
Barzilai, S., & Eilam, B. (2018). Learners’ epistemic criteria and strategies for evaluating scientific visual representations. Learning and Instruction, 58(March 2017), 137–147. https://doi.org/10.1016/j.learninstruc.2018.06.002
Bollen, L., van Kampen, P., & De Cock, M. (2015). Students’ difficulties with vector calculus in electrodynamics. Physical Review Special Topics - Physics Education Research, 11(2), 020129. https://doi.org/10.1103/PhysRevSTPER.11.020129
Branchetti, L., Cattabriga, A., & Levrini, O. (2019). Interplay between mathematics and physics to catch the nature of a scientific breakthrough: The case of the blackbody. Physical Review Physics Education Research, 15(2), 020130. https://doi.org/10.1103/PhysRevPhysEducRes.15.020130
Ceuppens, S., Deprez, J., Dehaene, W., & De Cock, M. (2018). Design and validation of a test for representational fluency of 9th grade students in physics and mathematics: The case of linear functions. Physical Review Physics Education Research, 14(2), 020105. https://doi.org/10.1103/PhysRevPhysEducRes.14.020105
Chassy, P., & Jones, J. (2019). The role of mathematics in the learning of physics. Journal of Mathematical and Theoritical Physics, 2(1), 8–10. https://medcraveonline.com/OAJMTP/OAJMTP-02-00045.pdf
Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches (5th Ed.). SAGE Publications, Inc.
Deprez, T., Gijsen, S. E., Deprez, J., & De Cock, M. (2019). Investigating student understanding of cross products in a mathematical and two electromagnetism contexts. Physical Review Physics Education Research, 15(2), 020132. https://doi.org/10.1103/PhysRevPhysEducRes.15.020132
Docktor, J. L., & Mestre, J. P. (2014). Synthesis of discipline-based education research in physics. Physical Review Special Topics - Physics Education Research, 10(2), 020119. https://doi.org/10.1103/PhysRevSTPER.10.020119
Doran, Y. J. (2017). The role of mathematics in physics: Building knowledge and describing the empirical world. Onomazein, 35, 209–226. http://onomazein.letras.uc.cl/Articulos/N-SFL/SFL08-Doran.pdf
Erol, M., & Çolak, İ. Ö. (2020). Mathematical modelling of electrical potential difference in a non-uniform electric field. Momentum: Physics Education Journal, 4(2), 64–72. https://doi.org/10.21067/mpej.v4i2.4440
Gifford, J. D., & Finkelstein, N. D. (2020). Categorical framework for mathematical sense making in physics. Physical Review Physics Education Research, 16(2), 020121. https://doi.org/10.1103/PhysRevPhysEducRes.16.020121
Gosper, M., & Ifenthaler, D. (2014). Curriculum models for the 21st century (M. Gosper & D. Ifenthaler (eds.)). Springer New York. https://doi.org/10.1007/978-1-4614-7366-4
Hasim, N. A. B., Karim, M. M. B. A., & Rahman, N. B. A. (2020). Aids in physics: Design and development. Momentum: Physics Education Journal, 4(2), 57–63. https://doi.org/10.21067/mpej.v4i2.4432
Hill, M., & Sharma, M. D. (2015). Students’ representational fluency at university: A cross-sectional measure of how multiple representations are used by physics students using the representational fluency survey. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1633–1655. https://doi.org/10.12973/eurasia.2015.1427a
Hu, D., Chen, K., Leak, A. E., Young, N. T., Santangelo, B., Zwickl, B. M., & Martin, K. N. (2019). Characterizing mathematical problem solving in physics-related workplaces using epistemic games. Physical Review Physics Education Research, 15(2), 020131. https://doi.org/10.1103/PhysRevPhysEducRes.15.020131
Husnaini, S. J., & Chen, S. (2019). Effects of guided inquiry virtual and physical laboratories on conceptual understanding, inquiry performance, scientific inquiry self-efficacy, and enjoyment. Physical Review Physics Education Research, 15(1), 010119. https://doi.org/10.1103/PhysRevPhysEducRes.15.010119
Jensen, J. H., Niss, M., & Jankvist, U. T. (2017). Problem solving in the borderland between mathematics and physics. International Journal of Mathematical Education in Science and Technology, 48(1), 1–15. https://doi.org/10.1080/0020739X.2016.1206979
Kjeldsen, T. H., & Lützen, J. (2015). Interactions between mathematics and physics: The history of the concept of function—teaching with and about nature of mathematics. Science & Education, 24(5–6), 543–559. https://doi.org/10.1007/s11191-015-9746-x
Klein, P., Dengel, A., & Kuhn, J. (2018). Students’ visual attention while solving multiple representation problems in upper-division physics. In O. Z.-T. Et (Ed.), Positive Learning in the Age of Information (pp. 67–87). Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-19567-0_6
Klein, P., Viiri, J., & Kuhn, J. (2019). Visual cues improve students’ understanding of divergence and curl: Evidence from eye movements during reading and problem solving. Physical Review Physics Education Research, 15(1), 010126. https://doi.org/10.1103/PhysRevPhysEducRes.15.010126
Kneubil, F. B., & Robilotta, M. R. (2015). Physics teaching: Mathematics as an epistemological tool. Science & Education, 24(5–6), 645–660. https://doi.org/10.1007/s11191-014-9727-5
Li, J., & Singh, C. (2018). Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law. European Journal of Physics, 39(1), 015702. https://doi.org/10.1088/1361-6404/aa8d55
López-Gay, R., MartÃnez Sáez, J., & MartÃnez Torregrosa, J. (2015). Obstacles to mathematization in physics: The case of the differential. Science & Education, 24(5–6), 591–613. https://doi.org/10.1007/s11191-015-9757-7
Marton, F., & Pong, W. Y. (2005). On the unit of description in phenomenography. Higher Education Research & Development, 24(4), 335–348. https://doi.org/10.1080/07294360500284706
MeÅ¡ić, V., Neumann, K., Aviani, I., Hasović, E., Boone, W. J., Erceg, N., Grubelnik, V., SuÅ¡ac, A., GlamoÄić, D. S., Karuza, M., Vidak, A., AlihodŽić, A., & Repnik, R. (2019). Measuring students’ conceptual understanding of wave optics: A Rasch modeling approach. Physical Review Physics Education Research, 15(1), 1–20. https://doi.org/10.1103/PhysRevPhysEducRes.15.010115
Mota, A. R., Didiş Körhasan, N., Miller, K., & Mazur, E. (2019). Homework as a metacognitive tool in an undergraduate physics course. Physical Review Physics Education Research, 15(1), 010136. https://doi.org/10.1103/PhysRevPhysEducRes.15.010136
Nielsen, S. S., & Nielsen, J. A. (2019). A competence-oriented approach to models and modelling in lower secondary science education: Practices and rationales among danish teachers. Research in Science Education. https://doi.org/10.1007/s11165-019-09900-1
Odden, T. O. B., Lockwood, E., & Caballero, M. D. (2019). Physics computational literacy: An exploratory case study using computational essays. Physical Review Physics Education Research, 15(2), 020152. https://doi.org/10.1103/PhysRevPhysEducRes.15.020152
Pospiech, G., Eylon, B., Bagno, E., & Lehavi, Y. (2015). The role of mathematics for physics teaching and understanding. Conference: Mathematics in Physics Education, 3(May-June). https://doi.org/10.1393/ncc/i2015-15110-6
Pratiwi, H. Y., Hudha, M. N., Asri, M., & Ahmad, N. J. (2019). The impact of guided inquiry model integrated with peer instruction towards science process skill and physics learning achievement. Momentum: Physics Education Journal, 3(2), 78–85. https://doi.org/10.21067/mpej.v3i2.2768
Redfors, A., Hansson, L., Hansson, Ö., & Juter, K. (2014). The role of mathematics in the teaching and learning of physics. Ebook Proceedings of the ESERA 2013 Conference, 2, 376–383. https://www.diva-portal.org/smash/get/diva2:710055/FULLTEXT01.pdf
Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5–6), 561–590. https://doi.org/10.1007/s11191-015-9749-7
Ryan, Q. X., Frodermann, E., Heller, K., Hsu, L., & Mason, A. (2016). Computer problem-solving coaches for introductory physics: Design and usability studies. Physical Review Physics Education Research, 12(1), 010105. https://doi.org/10.1103/PhysRevPhysEducRes.12.010105
Saprudin, S., Liliasari, L., Setiawan, A., & Prihatmanto, A. S. (2020). Optical Gamification (OG); Serial versus random model to improve pre-service physics teachers’ concept mastery. International Journal of Emerging Technologies in Learning (IJET), 15(09), 39. https://doi.org/10.3991/ijet.v15i09.11779
Schermerhorn, B. P., & Thompson, J. R. (2019). Physics students’ construction of differential length vectors in an unconventional spherical coordinate system. Physical Review Physics Education Research, 15(1), 010111. https://doi.org/10.1103/PhysRevPhysEducRes.15.010111
Sutopo, S., & Waldrip, B. (2014). Impact of a representational approach on students’ reasoning and conceptual understanding in learning mechanics. International Journal of Science and Mathematics Education, 12(4), 741–765. https://doi.org/10.1007/s10763-013-9431-y
Taleyarkhan, M., Dasgupta, C., Garcia, J. M., & Magana, A. J. (2018). Investigating the impact of using a CAD simulation tool on students’ learning of design thinking. Journal of Science Education and Technology, 27(4), 334–347. https://doi.org/10.1007/s10956-018-9727-3
Treagust, D. F., Duit, R., & Fischer, H. E. (2017). Multiple representations in physics education (D. F. Treagust, R. Duit, & H. E. Fischer (eds.); Vol. 10). Springer International Publishing. https://doi.org/10.1007/978-3-319-58914-5
Walsh, C., Quinn, K. N., Wieman, C., & Holmes, N. G. (2019). Quantifying critical thinking: Development and validation of the physics lab inventory of critical thinking. Physical Review Physics Education Research, 15(1), 010135. https://doi.org/10.1103/PhysRevPhysEducRes.15.010135
Williams, M. (2018). The missing curriculum in physics problem-solving education. Science & Education, 27(3–4), 299–319. https://doi.org/10.1007/s11191-018-9970-2
Young, N. T., Allen, G., Aiken, J. M., Henderson, R., & Caballero, M. D. (2019). Identifying features predictive of faculty integrating computation into physics courses. Physical Review Physics Education Research, 15(1), 010114. https://doi.org/10.1103/PhysRevPhysEducRes.15.010114
Authors
Sujito, S., Liliasari, L., Suhandi, A., & Soewono, E. (2021). Description in course of mathematical methods for physics and possible development of course program. Momentum: Physics Education Journal, 5(1), 73–84. https://doi.org/10.21067/mpej.v5i1.5184
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