Teaching Probability Theory and Mathematical Statistics with Practical Problems
DOI:
https://doi.org/10.47134/ppm.v2i4.1969Keywords:
Event, Event Probability, Classical, Statistical and Geometrical Definitions of Probability, Practical ProblemsAbstract
This article is devoted to the role, content, and opportunities for effective teaching of elements of Probability Theory and Mathematical Statistics in the mathematics curriculum of general secondary education. It reveals the necessity of explaining the fundamental concepts of school-level probability theory—such as event, event probability, and its definitions, as well as probability calculation—through practical problems, and provides relevant problem examples. In the international PISA assessment test, questions related to this subject are also included, and students from our country have shown low performance specifically in these types of questions. This indicates that a special approach is needed for teaching this subject. In other words, in teaching the subject, it is necessary to increase students' interest through practical problems, strengthen their knowledge, and ensure that the lesson process is conducted effectively. In conclusion, it can be stated that the use of real-life, interdisciplinary, and integrated problems by the teacher in the lesson process serves to increase the effectiveness of the lesson, engage more students in the learning process, and develop their logical, statistical, and probabilistic thinking
References
Abdushukurov, A. (2010). Probability Theory and Mathematical Statistics. Tashkent. (In Uzbek)
Alimov, Sh. A., Kholmukhmedov, O. R., & Mirzaakhmedov, M. A. (2019). Algebra: Textbook for Grade 9. Tashkent: O‘qituvchi Publishing. (In Uzbek)
Barakayev, M., Turgunova, K., et al. (2023). Methodology of teaching theory of probability and elements of mathematical statistics with the help of practical problems. Journal of Propulsion Technology, 44(6), 2712–2718. ISSN: 1001-4055.
Batanero, C., Godino, J. D., & Roa, R. (2014). Training teachers to teach probability. Journal of Statistics Education, March 2014. Retrieved from https://www.researchgate.net/publication/240359028
Friedman, H. (2017). Quantum walks: The first detected passage time problem. Physical Review E, 95(3), ISSN 2470-0045, https://doi.org/10.1103/PhysRevE.95.032141 DOI: https://doi.org/10.1103/PhysRevE.95.032141
Gorshenin, A.K. (2017). On some mathematical and programming methods for construction of structural models of information flows. Informatika I Ee Primeneniya, 11(1), 58-68, ISSN 1992-2264, https://doi.org/10.14357/19922264170105 DOI: https://doi.org/10.14357/19922264170105
Gorshenin, A.K. (2018). Software Tools for Statistical Analysis of Some Precipitation Characteristics. Pattern Recognition and Image Analysis, 28(4), 783-791, ISSN 1054-6618, https://doi.org/10.1134/S1054661818040119 DOI: https://doi.org/10.1134/S1054661818040119
Hetmanenko, L. (2024). The role of interactive learning in mathematics education: Fostering student engagement and interest. Multidisciplinary Science Journal, 6, 2024ss0733. https://doi.org/10.31893/multiscience.2024ss0733 DOI: https://doi.org/10.31893/multiscience.2024ss0733
Joshi, M.S. (2016). The efficient computation and the sensitivity analysis of finite-Time ruin probabilities and the estimation of risk-based regulatory capital. Astin Bulletin, 46(2), 431-467, ISSN 0515-0361, https://doi.org/10.1017/asb.2016.5 DOI: https://doi.org/10.1017/asb.2016.5
Liu, S. (2021). Statistics of catastrophic hazardous liquid pipeline accidents. Reliability Engineering and System Safety, 208, ISSN 0951-8320, https://doi.org/10.1016/j.ress.2020.107389 DOI: https://doi.org/10.1016/j.ress.2020.107389
Liu, S., Guo, R., et al. (2015). An effective teaching method of the course “Probability Theory and Mathematical Statistics” in higher education by formative evaluation. In Proceedings of the International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC 2015) (pp. 1088–1091). DOI: https://doi.org/10.2991/meic-15.2015.247
Mender, R. D. M. (n.d.). Mathematics teaching strategy in statistics and probability. International Journal of Research Publications, 310–321.
Ngan, S.C. (2025). A concrete extension principle for fuzzy set theory. Expert Systems with Applications, 280, ISSN 0957-4174, https://doi.org/10.1016/j.eswa.2025.127328 DOI: https://doi.org/10.1016/j.eswa.2025.127328
Peterson, T., & Thomas, M. (2021). Integrating technology in teaching probability: A modern approach. Mathematics Education Research Journal, 29(2), 89–110.
Ramirez, C.A. Mejia (2024). Comparison of some Logistic Regression Methodologies in Supervised Classification for Functional Data. 2024 IEEE International Autumn Meeting on Power Electronics and Computing Ropec 2024, https://doi.org/10.1109/ROPEC62734.2024.10877135 DOI: https://doi.org/10.1109/ROPEC62734.2024.10877135
Sallem, H. (2024). A model-based risk-minimizing proton treatment planning concept for brain injury prevention in low-grade glioma patients. Radiotherapy and Oncology, 201, ISSN 0167-8140, https://doi.org/10.1016/j.radonc.2024.110579 DOI: https://doi.org/10.1016/j.radonc.2024.110579
Song, Q. (2022). Research on quantum cognition in autonomous driving. Scientific Reports, 12(1), ISSN 2045-2322, https://doi.org/10.1038/s41598-021-04239-y DOI: https://doi.org/10.1038/s41598-021-04239-y
Suh, C. (2024). Probability for information technology. Probability for Information Technology, 1-353, https://doi.org/10.1007/978-981-97-4032-1 DOI: https://doi.org/10.1007/978-981-97-4032-1_1
Sukhov, V.D. (2024). Multilevel splitting for rare events estimation in permutation tests. Scientific and Technical Journal of Information Technologies Mechanics and Optics, 24(4), 654-660, ISSN 2226-1494, https://doi.org/10.17586/2226-1494-2024-24-4-654-660 DOI: https://doi.org/10.17586/2226-1494-2024-24-4-654-660
Volpi, E. (2019). Save hydrological observations! Return period estimation without data decimation. Journal of Hydrology, 571, 782-792, ISSN 0022-1694, https://doi.org/10.1016/j.jhydrol.2019.02.017 DOI: https://doi.org/10.1016/j.jhydrol.2019.02.017
Wang, F., & Xu, X. (n.d.). Discussion on the teaching method of probability theory and mathematical statistics. Unpublished manuscript.
Wang, Y. (2021). Online Partial Conditional Plan Synthesis for POMDPs with Safe-Reachability Objectives: Methods and Experiments. IEEE Transactions on Automation Science and Engineering, 18(3), 932-945, ISSN 1545-5955, https://doi.org/10.1109/TASE.2021.3057111 DOI: https://doi.org/10.1109/TASE.2021.3057111
Xiong, W. (2016). Research on the probability theory and mathematical statistics teaching. In Proceedings of the 6th International Conference on Electronic, Mechanical, Information and Management (EMIM 2016) (pp. 883–885). Atlantis Press. DOI: https://doi.org/10.2991/emim-16.2016.181
Yu, H. (2017). Learning a fuzzy decision tree from uncertain data. Proceedings of the 2017 12th International Conference on Intelligent Systems and Knowledge Engineering ISKE 2017, 2018, 1-7, https://doi.org/10.1109/ISKE.2017.8258728 DOI: https://doi.org/10.1109/ISKE.2017.8258728




