CAPABILITIES OF MODERN LARGE LANGUAGE MODELS IN MODERNIZING EDUCATIONAL AND METHODOLOGICAL COMPLEXES OF MATHEMATICAL DISCIPLINES
DOI:
https://doi.org/10.55287/22275398_2026_60_211-222Keywords:
large language models, artificial intelligence, educational and methodological complex, mathematical disciplines, Moodle, GIFT, assessment tools fund, practice-oriented learning, prompt engineeringAbstract
The article examines the capabilities of modern large language models (LLMs) in modernizing educational and methodological complexes (EMC) of mathematical disciplines in higher education. It is shown that generative neural networks can automate the most labor-intensive stages of updating methodological support: restructuring and updating existing materials, adapting them to students' fields of study, developing practice-oriented cases, creating interactive illustrative materials in HTML+JavaScript format, as well as automated generation of test items in GIFT format for the Moodle LMS and the formation of the assessment tools fund as a whole. A generalized algorithm for teacher-LLM interaction based on prompt engineering is proposed, and specific examples of generated artifacts are given. Scenarios for using the resulting developments in the real educational process — in lectures, practical classes, students' independent work, and knowledge assessment — are considered separately, and the advantages of this approach are substantiated: saving teachers' time, variability and personalization of assignments, and increased visibility and practice orientation of training. The limitations and risks of using LLMs are identified — hallucinations, errors in mathematical derivations, academic integrity issues — and the need for mandatory expert verification of all generated materials by the teacher is substantiated. It is concluded that the hybrid "teacher + AI" model is promising, in which the LLM serves as a tool for accelerating routine work, while pedagogical expertise remains the key condition for quality.
References
1. Karpenko, S. N., Kuzenkova, G. V., Shestakova, N. V., Borisov, N. A., & Kuznetsov, A. I. (2016). Sozdanie sistemy elektronnogo testirovaniya na baze SDO Moodle kak elementa fonda otsenochnykh sredstv [Developing an electronic testing system based on the Moodle learning management system as a component of an assessment toolkit]. Sovremennye informatsionnye tekhnologii i IT-obrazovanie, 12(3-2), 55–61. (In Russian).
2. Ochkov, V. F., Tikhonov, A. I., & Shatskikh, Yu. V. (2025). Novyy podkhod k prepodavaniyu matematiki v vuzakh [A new approach to teaching mathematics at universities]. Otkrytoe obrazovanie, (5), 55–64. DOI: 10.21686/1818-4243-2025-5-55-64. (In Russian).
3. Belova, D. V., Vetrenko, E. A., Ponomarev, A. V., Fedoseeva, O. V., & Shadrina, N. N. (2024). Ispolzovanie onlayn-resursov i sistem kompyuternoy matematiki dlya povysheniya kachestva obucheniya studentov, izuchayushchikh distsipliny «Lineynaya algebra» i «Matematicheskiy analiz» v vysshikh uchebnykh zavedeniyakh [Using online resources and computer algebra systems to improve the quality of university instruction in linear algebra and mathematical analysis]. Upravlenie obrazovaniem: Teoriya i praktika, 14(10-2), 151–160. DOI: 10.25726/a0088-6732-1782-b. (In Russian).
4. Derbush, M. V. (2025). Tekhnologiya podgotovki budushchikh uchiteley matematiki k ispolzovaniyu neyrosetey dlya razrabotki didakticheskikh materialov [A methodology for preparing prospective mathematics teachers to use neural networks in developing teaching materials]. Pedagogika. Voprosy teorii i praktiki, 10(8). DOI: 10.30853/ped20250146. (In Russian).
5. Kalinin, A. A., Koroleva, N. Yu., Ryzhova, N. I., & Fedorova, Yu. V. (2024). Iskusstvennyy intellekt v obrazovatelnom kontente: Aktualnyy trend i prakticheskie aspekty evolyutsii uchebnogo protsessa [Artificial intelligence in educational content: A current trend and practical aspects of the evolution of teaching and learning]. Nauka i shkola, (5), 98–113. DOI: 10.31862/1819-463X-2024-5-98-113. (In Russian).
6. Dubakov, A. V., & Petrova, V. E. (2026). Ispolzovanie iskusstvennogo intellekta v proektirovanii materialov dlya izuchayushchikh russkiy yazyk kak inostrannyy [Using artificial intelligence to design materials for learners of Russian as a foreign language]. Vestnik Shadrinskogo gosudarstvennogo pedagogicheskogo universiteta, (2(70)), 62–69. (In Russian).
7. Dontsov, M. A. (2025). Generativnyy iskusstvennyy intellekt v rabote prepodavatelya [Generative artificial intelligence in teaching practice]. Pedagogika. Zhurnal psikhologo-pedagogicheskikh issledovaniy. (In Russian).
8. Paskova, A. A. (2024). Vozmozhnosti integratsii tekhnologiy generativnogo iskusstvennogo intellekta v protsessy formiruyushchego otsenivaniya v vysshem obrazovanii [Opportunities for integrating generative artificial intelligence technologies into formative assessment in higher education]. Vestnik Maykopskogo gosudarstvennogo tekhnologicheskogo universiteta, 16(2), 98–109. DOI: 10.47370/2078-1024-2024-16-2-98-109. (In Russian).
9. Piskun, A. A., Nevzorov, M. N., & Shurukhina, T. N. (2025). Pedagogicheskiy resurs iskusstvennogo intellekta v professionalno-orientirovannom obuchenii inostrannomu yazyku [The pedagogical potential of artificial intelligence in professionally oriented foreign language teaching]. Vestnik Leningradskogo gosudarstvennogo universiteta im. A. S. Pushkina, (4), 148–166. DOI: 10.35231/18186653_2025_4_148. (In Russian).
10. Molchanova, O. P., Burak, I. D., & Shchelokova, S. V. (2025). Iskusstvennyy intellekt v prepodavanii upravlencheskikh distsiplin: Vozmozhnosti i riski [Artificial intelligence in teaching management disciplines: Opportunities and risks]. Vestnik Moskovskogo universiteta. Seriya 6. Ekonomika, 60(3), 348–365. DOI: 10.55959/MSU0130-0105-6-60-3-15. (In Russian).
11. Ponedelkov, A. V., Averin, A. N., & Komarov, D. S. (2025). Predlozheniya Prezidenta Rossiyskoy Federatsii ob izmenenii podkhodov v podgotovke kadrov [Proposals by the President of the Russian Federation to change approaches to workforce training]. Politicheskie nauki, (2). DOI: 10.24412/3034-3364-2025-2-9. (In Russian).
12. Stefanovskaya, N. A., Medvedev, N. V., & Shults, O. E. (2026). Ispolzovanie bolshikh yazykovykh modeley v formirovanii professionalnoy kompetentnosti studentov-yuristov [The application of large language models in developing professional competence of law students]. Pedagogika. Voprosy teorii i praktiki, 11(3). DOI: 10.30853/ped20260061. Available at: https://cyberleninka.ru/article/n/ispolzovanie-bolshih-yazykovyh-modeley-v-formirovanii-professionalnoy-kompetentnosti-studentov-yuristov (accessed September 1, 2026). (In Russian).
13. Karpasyuk, I. V. (2021). Primenenie kompyuternykh sredstv vizualizatsii, multimediynykh i interaktivnykh tekhnologiy pri distantsionnom obuchenii matematicheskim distsiplinam [Using computer visualization tools, multimedia, and interactive technologies in distance teaching of mathematical disciplines]. Mir nauki. Pedagogika i psikhologiya, 9(2). Available at: https://cyberleninka.ru/article/n/primenenie-kompyuternyh-sredstv-vizualizatsii-multimediynyh-i-interaktivnyh-tehnologiy-pri-distantsionnom-obuchenii-matematicheskim (accessed September 1, 2026). (In Russian).
14. Butko, E. Yu., & Khudzhin, A. Yu. (2019). Elektronnoe obuchenie kak sredstvo povysheniya kachestva matematicheskoy podgotovki obuchayushchikhsya vuza (na primere primeneniya komponentov platformy Moodle) [E-learning as a means of improving the quality of university students’ mathematical training: A case study of Moodle platform components]. Nauka i shkola, (4), 126–134. (In Russian).
15. Plokhotnyuk, O. S. (2023). Osobennosti razrabotki variativnykh testovykh zadaniy s ispolzovaniem chat-bota s iskusstvennym intellektom ChatGPT v obuchenii budushchikh pedagogov inostrannomu yazyku [Features of developing varied test items using the AI chatbot ChatGPT in foreign language instruction for prospective teachers]. DOI: 10.25688/2072-9014.2023.65.3.10. (In Russian).
16. Kustovskaya, V. A., & Tekhneryadnova, A. M. (2026). Integratsiya neyrosetevykh instrumentov v SMART-postanovku obrazovatelnykh tseley: Vozmozhnosti, ogranicheniya i riski [Integrating neural network tools into SMART educational goal setting: Opportunities, limitations, and risks]. DOI: 10.62969/pedwiki-2026-2. Available at: https://cyberleninka.ru/article/n/integratsiya-neyrosetevyh-instrumentov-v-smart-postanovku-obrazovatelnyh-tseley-vozmozhnosti-ogranicheniya-i-riski (accessed August 26, 2026). (In Russian).
17. Dobrovolskaya, N. Yu. (2025). Primenenie generativnykh neyronnykh setey dlya personalizatsii obucheniya programmirovaniyu v vysshey shkole [Using generative neural networks to personalize programming instruction in higher education]. Vestnik Surgutskogo gosudarstvennogo pedagogicheskogo universiteta, (4(97)). DOI: 10.69571/SSPU.2025.97.4.015. (In Russian).
18. Kuzmenko, M. V. (2025). Iskusstvennyy intellekt v issledovatelskoy deyatelnosti i akademicheskom pisme: Analiticheskiy obzor napravleniy i ogranicheniy primeneniya [Artificial intelligence in research and academic writing: An analytical review of applications and limitations]. Nepreryvnoe obrazovanie: XXI vek, 13(3). DOI: 10.15393/j5.art.2025.10846. (In Russian).
19. Ivakhnenko, E. N., & Nikolsky, V. S. (2023). ChatGPT v vysshem obrazovanii i nauke: Ugroza ili tsennyy resurs? [ChatGPT in higher education and science: A threat or a valuable resource?]. Vysshee obrazovanie v Rossii, 32(4), 9–22. DOI: 10.31992/0869-3617-2023-32-4-9-22. (In Russian).
20. Andreeva, O. S., Novikova, Z. N., & Surkhaev, M. A. (2025). Problemy ispolzovaniya iskusstvennogo intellekta pri napisanii vypusknykh kvalifikatsionnykh rabot [Problems of using artificial intelligence in writing graduation theses]. Pedagogicheskoe obrazovanie v Rossii, 19(3), 23–30. DOI: 10.31161/1995-0659-2025-19-3-23-30. (In Russian).
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Муханов Сергей Александрович, Архангельский Александр Игоревич, Архангельская Мария Владимировна, Берков Николай Андреевич (Автор)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright in their published work and grant The System Technologies a non-exclusive right of first publication, including the right to publish the article on the Journal’s electronic platform, assign a DOI, distribute, and archive the work.
All articles published in The System Technologies are distributed under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/
The CC BY 4.0 licence permits others to read, download, copy, distribute, reproduce, adapt, and use the article for any lawful purpose, including commercially, provided that appropriate credit is given to the author(s), article title, Journal, DOI, and licence, and any changes made are indicated.
