Urus-Martan, Grozny, Russian Federation
This article considers the actual problem of development of the geometrical component of students' mathematical abilities, which is relevant not only for one national system of education, but as international monitoring studies (TIMSS, PISA, etc.) show in general and globally. The aim of the study is to identify personal characteristics (“geometric vision”, the ability of spatial representations, the role of students' intrinsic motivation, etc.) for use in the process of solving geometric problems. The technology was developed for use in the process of solving predominantly geometric problems, manifested in a personalized approach, prioritizing identified personal characteristics. As an example, a mathematical description of a stereometric problem is offered and its solution is analyzed in a psychological and pedagogical context, in the context of the development of the geometric component of students' mathematical abilities. The results of the analysis of theoretical and practical interpretation of the content, in the context of the problem under consideration, can serve as a basis for designing a modern model of teaching the younger generation: for building a model of development of the geometric component of their mathematical abilities and the technology of solving geometric problems (mainly stereometric), taking into account the priority tasks of secondary general education and federal working programmes of teaching the course ‘Geometry’.
TIMSS and PISA, development, perception, mathematical abilities of students, content, geometric problems, technology, characteristics of “geometric vision”, spatial representation abilities and the role of intrinsic motivation of students, a prototype of a stereometric problem from profile mathematics.
1. Visitaeva M. B. Olimpiada po matematike v Chechenskoy Respublike // Matematika v shkole. 2006. № 6. S. 52-57.
2. Visitaeva M. B. Lingvisticheskoe matematicheskoe modelirovanie uchebnoy rechi shkol'nikov // V sb.: Lingvisticheskoe modelirovanie v teorii kommunikacii. Materialy Vserossiyskoy nauchnoy onlayn-konferencii s mezhdunarodnym uchastiem, 15-16 yanvarya 2021 g. Chechenskiy gosudarstvennyy pedagogicheskiy universitet // Groznyy. Izd-vo, FGBOU VO ChGPU, 2021. S. 189-199. EDN: https://elibrary.ru/BCVYZC
3. Visitaeva M. B. Razvitie «geometricheskogo zreniya» obuchayuschihsya pri reshenii zadach na primenenie razvertok mnogogrannikov // Matematika v shkole. 2012. № 4. S. 7-16.
4. Gusev V. A. Psihologo-pedagogicheskie osnovy obucheniya matematike. M.: Izdat. centr «Akademiya», 2003. 432 s. EDN: https://elibrary.ru/QTKORN
5. Gleyzer G. D. Razvitie prostranstvennyh predstavleniy shkol'nikov pri obuchenii geometrii. M.: Pedagogika, 1978. 104 s.
6. Dalinger V. A. Kognitivno-vizual'naya deyatel'nost' pri reshenii matematicheskih zadach kak sredstvo realizacii vnutripredmetnyh svyazey : uchebnoe posobie. Moskva : Rusayns, 2022. 215 s.
7. Koval' E. G. Sredovye faktory formirovaniya kriticheskogo myshleniya u uchaschihsya osnovnoy shkoly / Koval' E. G. i V. A. Yasvin. // Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya: Filosofiya. Psihologiya. Pedagogika. 2025. T. 25, vyp. 1. S. 67-73. DOI: https://doi.org/10.18500/1819-7671-2025-25-1-67-73; EDN: https://elibrary.ru/UCJSET
8. Lomov B. F. O formirovanii graficheskih znaniy, umeniy i navykov u shkol'nikov. M., 1959. 270 c.
9. Postnov A. A. Formirovanie i razvitie prostranstvennyh predstavleniy u obuchayuschihsya vos'miletney shkoly s primeneniem sredstv naglyadnosti: na stereometricheskom materiale: 13.00.00 / Postnov Afrikan Aleksandrovich: dis. kand. ped. nauk. M. : Nauchno-issledovatel'skiy institut obschego i politehnicheskogo obrazovaniya, 1964. 307 s.
10. Rodionov M.A. Vozmozhnosti realizacii processual'noy obratnoy svyazi v processe obucheniya matematike // Rodionov M. A., Dedovec Zh. i Chernyshov V. P. // Sovremennye naukoemkie tehnologii. 2024. № 10. S. 212-216. DOI: https://doi.org/10.17513/snt.40197; EDN: https://elibrary.ru/BZGJIX
11. Rubinshteyn S. L. Osnovy obschey psihologii. SPb.: Piter, 2008. 715 s.
12. Sergeev E. A. Formirovanie motivacii dostizheniya uspeha studentov kak osnova gotovnosti k buduschey professional'noy deyatel'nosti // Vestnik Shadrinskogo gosudarstvennogo Pedagogicheskogo universiteta. 2025. № 1(65). S. 168-174. DOI: https://doi.org/10.52772/25420291_2025_1_168; EDN: https://elibrary.ru/ILRVHL
13. Tolkovyy slovar' russkogo yazyka : 100000 slov, terminov i vyrazheniy : [novoe izdanie] / Sergey Ivanovich Ozhegov ; pod obsch. red. L. I. Skvorcova. 28-e izd., pererab. Moskva : Mir i obrazovanie, 2015. 1375 s.
14. Chelnokova T. A. Metod sinektiki v obuchenii sovremennyh shkol'nikov // Vestnik Shadrinskogo gosudarstvennogo pedagogicheskogo universiteta. 2025. № 1(65). S. 118-123. DOI: https://doi.org/10.52772/25420291_2025_1_118; EDN: https://elibrary.ru/YCVNMM
15. Shmigirilova I. B. Razvitie analitiko-sinteticheskoy deyatel'nosti studentov v processe obucheniya matematicheskomu analizu / Shmigirilova I. B., Chugunova A. A. i Pustovalova N. I. // Science for Education Today. 2019. Tom 9, № 3. S. 121-134. DOI: https://doi.org/10.15293/2658-6762.1903.07; EDN: https://elibrary.ru/LTUWYI
16. Yakimanskaya I. S. Psihologicheskie osnovy matematicheskogo obrazovaniya. M.: Izdat. Centr, Akademiya, 2004. 320 s. EDN: https://elibrary.ru/QTWZLV
17. Mihajlović A., Egerić M. and Dejić M. Mathematical abilities: identification and development [online] file:///C:/Users/HP/Downloads/doc.pdf (data obrascheniya 4.01. 2025).
18. Nugraheni N and Sukestiyarno YL. Mathematical Ability Profiles in Solving Numeracy Problems // International Journal of Education and Research. 2023. Vol. 11 no. 11. [online] file:///C:/Users/HP/Downloads/01.pdf (data obrascheniya 3.07. 2024).
