Methodological Approaches To Solving Complex Geometric Problems Of Pyramids
Keywords:
Pyramid, Geometric Figure, Triangle, Quadrilateral, Polygon, Tetrahedron, Distance
Abstract
This study addresses the complexities of solving geometric problems involving pyramids, focusing on methodological approaches to enhance understanding and application in educational settings. Despite extensive research in geometric problem-solving, a significant knowledge gap remains in effectively teaching complex pyramid problems. Utilizing a blend of empirical and theoretical methods, including pedagogical experience analysis, teacher consultations, and interdisciplinary synthesis, the study developed practical tasks and control measurements. Findings reveal that a systematic approach to teaching pyramid geometry significantly improves student comprehension and problem-solving skills. The results underscore the importance of integrating diverse methodological strategies in mathematics education, offering implications for curriculum development and instructional practices.
References
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2. Bozhina, G. N., & Maynagasheva, E. B. (2011). К вопросу о подготовке к ЕГЭ по математике. Методы решения геометрических задач. Математический вестник педвузов и университетов Волго-Вятского региона, (13), 293-303.
3. Skafa, E. I. (2022). Эвристические технологии обучения конструированию математических задач.
4. Pak, N. I., Barkhatova, D. A., & Hegai, L. B. (2022). Метод пирамиды в условиях цифровизации образования. Вестник Российского университета дружбы народов. Серия: Информатизация образования, 19(1), 7-19.
5. Pereguda, A. V. (2022). Подготовка к итоговой аттестации в процессе решения планиметрических задач. Современная наука: проблемы и перспективы, 100-105.
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7. Fedyakov, V. E. (2008). Использование свойств ортогональной проекции плоского многоугольника при решении некоторых стереометрических задач. Математический вестник педвузов и университетов Волго-Вятского региона, (10), 346-348.
8. Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 805-842). Charlotte, NC: Information Age Publishing.
9. Tall, D. (2013). How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics. Cambridge, UK: Cambridge University Press.
10. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 334-370). New York, NY: Macmillan.
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15. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
16. W. Zhang, A. Almgren, V. Beckner, J. Bell, and ..., “AMReX: a framework for block-structured adaptive mesh refinement,” The Journal of Open …, 2019, [Online]. Available: https://escholarship.org/content/qt00j3z3rd/qt00j3z3rd.pdf
17. S. Bak, H. D. Tran, K. Hobbs, and T. T. Johnson, “Improved geometric path enumeration for verifying relu neural networks,” … CAV 2020, Los Angeles, CA, USA …, 2020, doi: 10.1007/978-3-030-53288-8_4.
18. J. C. Pang, K. M. Aquino, M. Oldehinkel, P. A. Robinson, and ..., “Geometric constraints on human brain function,” Nature, 2023, [Online]. Available: https://www.nature.com/articles/s41586-023-06098-1
19. N. Lei et al., “A geometric understanding of deep learning,” Engineering, 2020, [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2095809919302279
20. R. P. Boas, Invitation to complex analysis. books.google.com, 2020. [Online]. Available: https://books.google.com/books?hl=en&lr=&id=m4bhDwAAQBAJ&oi=fnd&pg=PP1&dq=solving+complex+geometric&ots=6YJSqumZfX&sig=AtVREptFA4gvVpurhHDFjVftEyw
21. C. J. Permann, D. R. Gaston, D. Andrš, R. W. Carlsen, and ..., “MOOSE: Enabling massively parallel multiphysics simulation,” SoftwareX, 2020, [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2352711019302973
22. A. Ranjan, V. Jampani, L. Balles, K. Kim, and ..., “Competitive collaboration: Joint unsupervised learning of depth, camera motion, optical flow and motion segmentation,” Proceedings of the …, 2019, [Online]. Available:
http://openaccess.thecvf.com/content_CVPR_2019/html/Ranjan_Competitive_Collaboration_Joint_Unsupervised_Learning_of_Depth_Camera_Motion_Optical_CVPR_2019_paper.html
23. Z. Li, D. Z. Huang, B. Liu, and A. Anandkumar, “Fourier neural operator with learned deformations for pdes on general geometries,” Journal of Machine Learning …, 2023, [Online]. Available: https://www.jmlr.org/papers/v24/23-0064.html
24. M. Levi, The mathematical mechanic: using physical reasoning to solve problems. torrossa.com, 2023. [Online]. Available: https://www.torrossa.com/gs/resourceProxy?an=5563652&publisher=FZO137
25. D. Arndt, W. Bangerth, B. Blais, T. C. Clevenger, and ..., “The deal. II library, version 9.2,” Journal of Numerical …, 2020, doi: 10.1515/jnma-2020-0043.
26. Y. Chen, J. Arkin, C. Dawson, Y. Zhang, N. Roy, and ..., “Autotamp: Autoregressive task and motion planning with llms as translators and checkers,” arXiv preprint arXiv …, 2023, [Online]. Available: https://arxiv.org/abs/2306.06531
27. C. C. Nadell, B. Huang, J. M. Malof, and W. J. Padilla, “Deep learning for accelerated all-dielectric metasurface design,” Opt Express, 2019, [Online]. Available: https://opg.optica.org/abstract.cfm?uri=oe-27-20-27523
Published
2024-06-25
How to Cite
Kenjaevna, K. K. (2024). Methodological Approaches To Solving Complex Geometric Problems Of Pyramids. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(3), 163-168. Retrieved from https://cajmtcs.casjournal.org/index.php/CAJMTCS/article/view/643
Section
Articles
