Applying Hamilton’s vector formula in mathematics education: enhancing student mathematical skills through innovative teaching methods

Liudmyla Hetmanenko

doi:10.51798/sijis.v5i3.784

Authors

Liudmyla Hetmanenko Borys Grinchenko Kyiv Metropolitan University https://orcid.org/0009-0006-9601-3288

DOI:

https://doi.org/10.51798/sijis.v5i3.784

Keywords:

Hamilton’s formula, Euler formula, orthocenter, homothety, mathematics teaching

Abstract

The relevance of this discussion is driven by the need to improve mathematics teaching methods to enhance students’ mathematical competencies, particularly critical thinking and problem-solving skills. With its broad didactic potential, Hamilton’s vector formula becomes an essential tool in the educational process. The study aims to examine the impact of integrating Hamilton’s vector formula on the development of students’ mathematical competencies. The research methodology includes a literature review, expert evaluations, a pedagogical experiment with control and experimental groups, testing, and student surveys. The study results showed that using Hamilton’s vector formula promotes the development of students’ critical and analytical thinking, increases their confidence in solving complex problems, and improves overall mathematical competencies. The experimental group demonstrated higher test scores and practical task performance than the control group. Students noted that working with Hamilton’s vector formula helped them better understand geometric concepts and see the practical application of theoretical knowledge. The survey showed a positive perception of the new methodology, although some initial difficulties were noted. The practical significance of the results lies in developing recommendations for the effective use of Hamilton’s vector formula in the educational process, which can significantly improve the quality of students’ mathematical training and contribute to their successful learning process in the future.

Author Biography

Liudmyla Hetmanenko, Borys Grinchenko Kyiv Metropolitan University

Senior Lecturer of the Department of Natural Sciences and Mathematics Education and Technologies, Institute of In-Service Teachers’ Training, Borys Grinchenko Kyiv Metropolitan University

References

Adharini, D., & Herman, T. (2021). Didactical design of vectors in mathematics to develop creative thinking ability and self-confidence of Year 10 students. Journal of Physics: Conference Series, 1882(1), 012089. https://doi.org/10.1088/1742-6596/1882/1/012089

Albert, M. J., Blázquez-Merino, M., López-Rey, Á., & Castro, M. (2021). Influence of technological resources on the development of mathematical competence in high school. IT Professional, 23(2), 19-25. https://doi.org/10.1109/MITP.2021.3062685

Batsurovska, I., Dotsenko, N., Gorbenko, O., & Kim, N. (2021). The technology of competencies acquisition by bachelors in higher education institutions in the conditions of the digital media communication environment. Presented at the ICNTLLSC 2021 International Conference on New Trends in Languages, Literature and Social Communications (ICNTLLSC 2021).

Bauyrzhan, M., & Pakhymbek, D. (2020). The importance of didactic games in forming the interest of students in mathematics. Оңтүстік Қазақстан Мемлекеттік Педагогикалық Институтының Хабаршысы, 26(4), 64-74. https://doi.org/10.47751/skspu-1937-0018

Brovka, N., Klimovich, M., & Rusakov, A. (2023). The analysis of the mathematical training content using cluster analysis: Didactic and technological aspects. 3rd International Conference on Technology Enhanced Learning in Higher Education (TELE), 225-229. https://doi.org/10.1109/TELE58910.2023.10184345

Conde Silva, M., Villalba Suárez, M. K., & Gallardo Pérez, H. J. (2019). Pedagogical guidelines for the development of competences that strengthen the teaching practices of the mathematics area. Journal of Physics: Conference Series, 1329(1), 012017. https://doi.org/10.1088/1742-6596/1329/1/012017

Díaz Quezada, V. (2020). Difficulties and performance in mathematics competences: Solving problems with derivatives. International Journal of Engineering Pedagogy (Ijep), 10(4), 35-35. https://doi.org/10.3991/ijep.v10i4.12473

Gocheva-Ilieva, S. G., Kulina, H. N., Voynikova, D. S., Ivanov, A. V., Iliev, A. I., & Atanasova, P. K. (2018). Acquiring mathematical competences towards modelling: Example using cluster analysis. IEEE Global Engineering Education Conference (EDUCON), 1469-1474. https://doi.org/10.1109/EDUCON.2018.8363406

González Hernández, F., Prada, R., & Gamboa, A. (2019). Conceptions and pedagogical practices on the mathematical processes of teachers. Journal of Physics: Conference Series, 1408(1), 012009. https://doi.org/10.1088/1742-6596/1408/1/012009

Greefrath, G., Siller, H.-S., Vorhölter, K., & Kaiser, G. (2022). Mathematical modelling and discrete mathematics: Opportunities for modern mathematics teaching. ZDM – Mathematics Education, 54(4), 865-879. https://doi.org/10.1007/s11858-022-01339-5

Guo, Y., & Zhang, L. (2013). Analysis of strategies and methods for higher mathematics teaching. ICETIS 2013. https://doi.org/10.2991/icetis-13.2013.187

Khudoynazarov, E., & Yarmetov, J. (2021). Application of problem-based teaching methods in the development of mathematical thinking skills of students. Psychology, 58(1), 4537-4541. https://doi.org/10.17762/pae.v58i1.1559

Lu, W., & Xiawu, C. (2020). Talking about the current situation and countermeasures of mathematics information teaching in middle schools in Gannan Tibetan area. 2020 International Conference on Information Science and Education (ICISE-IE), 294-297. https://doi.org/10.1109/ICISE51755.2020.00071

Muin, & Fatma, M. (2021). Hypothetical learning trajectory design in development of mathematics learning didactic design in madrasah. Journal of Physics: Conference Series, 1836(1), 012070. https://doi.org/10.1088/1742-6596/1836/1/012070

Nagayev, V., Danchenko, I., Mitiashkina, T., & Kyrepin, V. (2022). Administrative fundamentals of ecological competence forming in agricultural engineering students under conditions of their professional training. In V. Tonkonogyi, V. Ivanov, J. Trojanowska, G. Oborskyi, & I. Pavlenko (Eds.), Advanced Manufacturing Processes III. Lecture Notes in Mechanical Engineering (pp. 1-4). Springer, Cham. https://doi.org/10.1007/978-3-030-91327-4_67

Nagayev, V., Gerliand, T., Kyrepin, V., Nagayeva, G., Sosnytska, N., & Yablunovska, K. (2021). Pedagogical technology of management of students’ educational and creative activities in the process of professional training of engineers. 2021 IEEE International Conference on Modern Electrical and Energy Systems (MEES), 1-4. https://doi.org/10.1109/MEES52427.2021.9598806

Ning, Y. (2021). Systematic analysis of big data mining technology in higher mathematics teaching. 2021 2nd International Conference on Information Science and Education (ICISE-IE), 990-993. https://doi.org/10.1109/ICISE-IE53922.2021.00226

Prabowo, A. S., Suryadi, D., & Dasari, D. (2021). Analysis of mathematical didactic situation constructed by prospective teachers based on learning trajectory. Journal of Physics: Conference Series, 1918(4), 042051. https://doi.org/10.1088/1742-6596/1918/4/042051

Rashidkizi Nokhatbayeva, K. (2020). The effects of heuristic teaching methods in mathematics. International Young Scholars Workshop, 9. https://doi.org/10.47344/iysw.v9i0.158

Rendl, M., & Štěch, S. (2018). Should learning (mathematics) at school aim at knowledge or at competences? Orbis Scholae, 6(2), 23-39. https://doi.org/10.14712/23363177.2015.38

Sagita Setiyani, L., & Sumiarsih. (2021). Designing teaching materials based on process skills approach to mathematical representation ability in polyhedron. Journal of Physics, 1957(1), 012015. https://doi.org/10.1088/1742-6596/1957/1/012015

Scherbina, I., Kagadiy, T., Sushko, L., & Babets, D. (2022). Development of methods of teaching mathematics in the formation of professional competences of economists. Agrosvit, 19, 40-47. https://doi.org/10.32702/2306-6792.2022.19.40

Tyata, R. B., Dahal, N., Pant, B. P., & Luitel, B. C. (2021). Exploring project-based teaching for engaging students’ mathematical learning. Mathematics Education Forum Chitwan, 6(6), 30-49. https://doi.org/10.3126/mefc.v6i6.42398

Vold, T. G. (2017). CEM using Hamilton’s principle with variation of the space-time vector potential. 2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimisation for RF, Microwave, and Terahertz Applications (NEMO), 206-208. https://doi.org/10.1109/NEMO.2017.7964235

Widya Kusumaningsih, Supandi, S., & Ariyanto, L. (2020). Ethnomathematics for congruence concept: A didactical design in a mathematics classroom. Journal of Physics: Conference Series, 1663(1), 012036. https://doi.org/10.1088/1742-6596/1663/1/012036