Pan-Art Pedagogy. Theory & Practice Philology. Theory & Practice Manuscript

Archive of Scientific Articles

ISSUE:    Pedagogy. Theory & Practice. 2026. Volume 11. Issue 5
COLLECTION:    Digital Education

All issues

License Agreement on scientific materials use.

Intelligent tutoring systems and digital mathematics services: opportunities and limitations

Anna Evgenevna Shpak
Mari State University, Yoshkar-Ola

Dina Alekseevna Semenova
Mari State University, Yoshkar-Ola

Olga Vasiljevna Rebko
Mari State University, Yoshkar-Ola

Natalia Vladimirovna Matrosova
Mari State University, Yoshkar-Ola
Submitted: May 27, 2026
Abstract. The aim of the study is to develop a functional typology of intelligent services for digital mathematics, which makes it possible to determine their pedagogical capabilities, limitations, and selection criteria for use in school, secondary vocational, and higher education. The article addresses the problem of integrating intelligent services into the educational process under the conditions of the “digital paradox” of mathematics education, in which the growing number of technological tools does not automatically lead to improvements in the quality of learning outcomes or student motivation. Within the framework of the proposed systemic approach, the concept of “digital mathematics” is refined as a three-component domain (the content‑related, activity‑based, and instrumental‑didactic components), and five functional groups of intelligent services are identified: automated step‑by‑step solvers, adaptive trainers, dynamic visualization and modelling environments, tutors and assistants powered by artificial intelligence, and analytical modules for pedagogical decision support. The scientific novelty of the study lies in clarifying the meaning of “digital mathematics” in a pedagogical context and in developing a criteria‑based system for selecting intelligent services (the didactic, ergonomic, adaptivity, analytical, security criteria) taking into account the specific features of schools, secondary vocational education, and universities. As a result of the study, it is established that the effectiveness of using intelligent services is determined by a methodologically grounded distribution of functions between the teacher and the digital tool, which ensures support for conceptual understanding, the development of computational thinking, and the individualization of learning. In the absence of a clear methodological framework, digital tools may act as a factor of cognitive offloading, replacing students’ independent cognitive activity with automated algorithms.
Key words and phrases:
цифровая математика
интеллектуальные сервисы
интеллектуальные обучающие системы
математическое образование
digital mathematics
intelligent services
intelligent tutoring systems
mathematics education
Reader Open the whole article in PDF format. Free PDF-files viewer can be downloaded here.
References:
  1. Алешева Л. Н. Интеллектуальные обучающие системы // Вестник университета. 2018. № 1. https://doi.org/10.26425/1816-4277-2018-1-149-155
  2. Бесшапошников Н. О., Дьяченко М. С., Леонов А. Г., Матюшин М. А., Орловский А. Е. Использование машинного обучения и нейронных сетей для автоматической верификации заданий в текстовом и графическом представлении и помощи преподавателю // Успехи кибернетики. 2020. Т. 1. № 2. https://doi.org/10.51790/2712-9942-2020-1-2-4
  3. Гриншкун В. В., Краснова Г. А. Современная цифровая образовательная среда: ресурсы, средства, сервисы: монография. М.: Проспект, 2021.
  4. Ковалева М. Л. Проблемы и перспективы внедрения онлайн-курсов в систему высшего образования // Современные проблемы науки и образования. 2022. № 1.
  5. Семенов А. Л., Поликарпов С. А. Цифровая трансформация школы и роль математики и информатики в ней. Проблемы и парадоксы математического образования и их цифровое решение // Информатизация образования и методика электронного обучения: цифровые технологии в образовании: труды IV Международной научной конференции (г. Красноярск, 06-09 октября 2020 г.). Красноярск: Сибирский федеральный университет, 2020.
  6. Токтарова В. И. Адаптивная система математической подготовки студентов в условиях информационно-образовательной среды вуза: дисс. … д. пед. н. Йошкар-Ола, 2019.
  7. Anderson J. R., Corbett A. T., Koedinger K. R., Pelletier R. Cognitive Tutors: Lessons Learned // Journal of the Learning Sciences. 1995. Vol. 4. № 2. https://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/129CogTut_Lessons.pdf
  8. Boaler J. Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. Stanford: Youcubed, Stanford University, 2015. https://www.youcubed.org/evidence/fluency-without-fear/
  9. Buchberger B., Craciun A. Distance Teaching of Mathematics Using Theorema. 2001. https://www.researchgate.net/profile/Bruno-Buchberger/publication/255737487_Distance_Teaching_of_Mathematics_Using_Theorema/links/00b7d5209e06c45d9b000000/Distance-Teaching-of-Mathematics-Using-Theorema.pdf
  10. Buchberger B., Jebelean T., Kutsia T., Maletzky A., Windsteiger W. Theorema 2.0: Computer-Assisted Natural-Style Mathematics // Journal of Formalized Reasoning. 2016. Vol. 9. № 1. https://doi.org/10.6092/issn.1972-5787/4568
  11. Clark-Wilson A., Robutti O., Thomas M. Teaching with digital technology // ZDM – Mathematics Education. 2020. Vol. 52. № 7. https://doi.org/10.1007/s11858-020-01196-0
  12. Marakshina J., Pavlova A., Ismatullina V., Adamovich T., Mironets S., Sitnikova M. A., Lobaskova M., Malykh S. The Russian version of the Abbreviated Math Anxiety Scale: psychometric properties in adolescents aged 13-16 years // Frontiers in Psychology. 2023. Vol. 14. Article 1275212. https://doi.org/10.3389/fpsyg.2023.1275212
  13. Mullis I. V. S., Martin M. O., Foy P., Kelly D. L., Fishbein B. TIMSS 2019 International Results in Mathematics and Science. Boston: TIMSS & PIRLS International Study Center, Boston College, 2020. https://timss2019.org/reports/download-center/index.html
  14. Papert S. Mindstorms: Children, Computers, and Powerful Ideas. N. Y.: Basic Books, 1980.
  15. Roschelle J. New Research Compendium Addresses Productivity & Transformation When Applying Technology in Learning Math // Digital Promise. 2017. September 25. https://digitalpromise.org/2017/09/25/new-research-compendium-addresses-productivity-transformation-applying-technology-learning-math/
  16. Roschelle J., Shechtman N., Tatar D., Hegedus S., Hopkins B., Empson S., Knudsen J., Gallagher L.Integration of technology, curriculum, and professional development for advancing middle school mathematics: Three large-scale studies // American Educational Research Journal. 2010. Vol. 47. № 4. https://doi.org/10.3102/0002831210367426
  17. VanLehn K. The Behavior of Tutoring Systems // International Journal of Artificial Intelligence in Education. 2006. Vol. 16. № 3. https://cs.uky.edu/~sgware/reading/papers/vanlehn2006behavior.pdf
  18. Wing J. M.Computational thinking // Communications of the ACM. 2006. Vol. 49. № 3. https://doi.org/10.1145/1118178.1118215
All issues


© 2006-2025 GRAMOTA Publishing