STEM-integration of the Pythagorean Theorem and Its Generalizations through Programming in R and Python
DOI:
https://doi.org/10.63437/3083-6433-2025-2(35)-13Keywords:
STEM-education, Pythagorean theorem, innovative teaching methodsAbstract
The article examines the integration of the Pythagorean theorem and its generalizations into STEM-education through the use of modern programming technologies. Current trends in the implementation of innovative methods of teaching mathematics are analyzed, with particular attention paid to the application of gamification, information and communication technologies, and mobile applications.
A methodological framework is developed for designing a series of mini-projects that combine historical and mathematical context with programming tools in R and Python. The article presents a detailed analytical algorithm for creating a calendar of Pythagorean theorem days, based on calculating Pythagorean triples for calendar dates in the d.m.yy format, where d² + m² = y². The algorithm efficiently identifies valid dates without exhaustive search by computing the difference of squares. As a result, twelve Pythagorean dates were identified for the period from 2001 to 2026.
The proposed mini-projects include generating Pythagorean triples, simulating the Pythagorean fractal tree, analyzing the Spiral of Theodorus, modeling the harmony of spheres, creating interactive proof animations, and exploring generalizations of the theorem in higher dimensions. The study demonstrates the effectiveness of an interdisciplinary approach for fostering students’ critical thinking, digital literacy, and mathematical competencies within the framework of modern STEM-education.
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References
Використані літературні джерела
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8. Metikasari S., Mardiyana, Triyanto. Mathematics learning disabilities of the slow learner students on Pythagorean theorem. Journal of Physics: Conference Series. 2019. Vol. 1321. P. 022120. DOI: https://doi.org/10.1088/1742-6596/1321/2/022120.
9. Nugraha H. C., Rusmin P. H. Educational game design on Pythagorean theorem for game-based learning using 6i’s component. 2015 4th International Conference on Interactive Digital Media (ICIDM). Bandung. 2015. P. 1-5. DOI: https://doi.org/10.1109/IDM.2015.7516330.
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11. Wasserman N. H., Rossi D. Mathematics and science teachers’ use of and confidence in empirical reasoning: Implications for STEM teacher preparation. School Science and Mathematics. 2015. Vol. 115, No. 1. P. 22-34. DOI: https://doi.org/10.1111/ssm.12099.
12. Wijayanti P., Hidayanti A. N. Proving the Pythagorean theorem to junior high school students through the Asian method. Journal of Physics: Conference Series. 2019. Vol. 1417. P. 012060. DOI: https://doi.org/10.1088/1742-6596/1417/1/012060.
References
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2. Deshpande, D. S., Riccomini, P. J., Hughes, E. M., & Raulston, T. J. (2021). Problem solving with the Pythagorean theorem: A think aloud analysis of secondary students with learning disabilities. Learning Disabilities, 19(1), 23-47. Retrieved from: https://www.scopus.com/inward/record.uri?eid=s2.0-85123622269.
3. Escobar, S. V., Tulcanaza, V. A., Mediavilla, L. J., Reyes, F. G., Castro, O. L., & Benavides, X. R. (2020). Gamification as a didactic tool in the teaching of the Pythagorean theorem. Technology, Sustainability and Educational Innovation (TSIE), 189-200. DOI: https://doi.org/10.1007/978-3-030-37221-7_15.
4. Fachrudin, A. D., et al. (2019). Ancient China history-based task to support students’ geometrical reasoning and mathematical literacy in learning Pythagoras. Journal of Physics: Conference Series, 1417, 012042. DOI: https://doi.org/10.1088/1742-6596/1417/1/012042.
5. He, X., et al. (2021). The impact of STEM education on mathematical development in children aged 5–6 years. International Journal of Educational Research, 109, 101795. DOI: https://doi.org/10.1016/j.ijer.2021.101795.
6. Horvath, A., & Farkas, G. (2025). Challenges in STEM teaching at engineering education. Lecture Notes in Mechanical Engineering, 199-211. DOI: https://doi.org/10.1007/978-3-031-83583-4_14.
7. MD-Ali, R., & Mui Kim, K. (2018). GeoGebra in learning of mathematics towards supporting STEM education. The Journal of Social Sciences Research, SPI6, 776-782. DOI: https://doi.org/10.32861/jssr.spi6.776.782.
8. Metikasari, S., Mardiyana, & Triyanto. (2019). Mathematics learning disabilities of the slow learner students on Pythagorean theorem. Journal of Physics: Conference Series, 1321, 022120. DOI: https://doi.org/10.1088/1742-6596/1321/2/022120.
9. Nugraha, H. C., & Rusmin, P. H. (2015). Educational game design on Pythagorean theorem for game-based learning using 6i’s component. 2015 4th International Conference on Interactive Digital Media (ICIDM), Bandung, Indonesia, 1-5. DOI: 10.1109/IDM.2015.7516330.
10. Nurwita, F., Kusumah, Y. S., & Juandi, D. (2023). Developing learning media based on Android application for improving math problem-solving skill of junior high school students on Pythagorean theorem. AIP Conference Proceedings, 2734(1), Article 090059. DOI: https://doi.org/10.1063/5.0163595.
11. Wasserman, N. H., & Rossi, D. (2015). Mathematics and science teachers’ use of and confidence in empirical reasoning: Implications for STEM teacher preparation. School Science and Mathematics, 115(1), 22-34. DOI: https://doi.org/10.1111/ssm.12099.
12. Wijayanti, P., & Hidayanti, A. N. (2019). Proving the Pythagorean theorem to junior high school students through the Asian method. Journal of Physics: Conference Series, 1417, 012060. DOI: https://doi.org/10.1088/1742-6596/1417/1/012060.
