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Psychological Science and Education
2025. Vol. 30, no. 6, 5–20
doi:10.17759/pse.2025300601
ISSN: 1814-2052 / 2311-7273 (online)

Digital educational system design for individual work on mathematical errors of primary school students

 
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Abstract

Context and relevance. Currently, the possibilities and limitations of using digital technologies, including artificial intelligence, in education are being actively discussed and researched. One of the important areas of research in this field is the development of digital tools for individualization (personalization) of the educational process in schools. Objective. The goal is to justify and develop a digital educational system for individual work with primary school students on their mathematical errors. Hypothesis. The use of a digital educational system in the learning process, which allows primary school students to monitor the process of completing a mathematical task, will allow for the prompt identification and correction of possible errors, improve the quality of subject matter acquisition, and promote the development of interest in mathematical knowledge. Methods and materials. The pedagogical foundation of the digital educational system being developed is based on research into the phenomenon of mathematical errors, identifying their types, their causes, and methods for eliminating them. The psychological foundation of the design is based on L.S. Vygotsky's theory of the zone of proximal development and J. Bruner's concept of scaffolding. Results. The concept of the proposed digital educational system, "Smart Notebook," is described as follows: it will be able to analyze students' progress in solving math problems, detect errors, compare them with a database of common mistakes, identify its causes, and tailor hints and supporting tasks to each student's needs to eliminate these causes. The Smart Notebook will consider students' abilities by offering tasks within their zone of proximal development. A peer, a virtual assistant, will aid the student according to a pre-planned scenario, with various support options. Conclusions. The digital educational system can be used in pedagogical education to prepare primary school teachers to work on subject-specific mathematical errors.

General Information

Keywords: individualization of learning, zone of proximal development, digital educational system, smart notebook, primary school students

Journal rubric: Educational Psychology

Article type: scientific article

DOI: https://doi.org/10.17759/pse.2025300601

Funding. The publication was prepared according to the project of the MSUPE Development Program “Smart Notebook: an Educational Intelligent System for Working on the Errors of Primary School Students” within the framework of the implementation of the Priority-2030 Program.

Received 20.09.2025

Revised 10.11.2025

Accepted

Published

For citation: Isaev, E.I., Margolis, A.A., Safronova, M.A., Sokolov, V.L. (2025). Digital educational system design for individual work on mathematical errors of primary school students. Psychological Science and Education, 30(6), 5–20. (In Russ.). https://doi.org/10.17759/pse.2025300601

© Isaev E.I., Margolis A.A., Safronova M.A., Sokolov V.L., 2025

License: CC BY-NC 4.0

References

  1. Александрова, Э.И. (2023). Математика. Учебник для 1 класса в 2-х кн. М.: Просвещение-Союз.
    Aleksandrova, E.I. (2023). Mathematics. Textbook for grade 1 in 2 books. Moscow: Prosveshchenie-Soyuz. (In Russ.).
  2. Выготский, Л.С. (1991). Педагогическая психология. М.: Педагогика.
    Vygotsky, L.S. (1991). Pedagogical Psychology. Moscow: Pedagogy. (In Russ.).
  3. Давыдов, В.В. (1996). Теория развивающего обучения. М.: Интор.
    Davydov, V.V. (1996). Theory of developmental learning. Moscow: Intor. (In Russ.).
  4. Заседание Совета при Президенте по науке и образованию от 06 февраля 2025 г. (2025). М. URL: http://kremlin.ru/events/president/news/76222 (дата обращения: 17.09.2025).
    Meeting of the Presidential Council for Science and Education on February 6, 2025 (2025). Moscow. (In Russ.). URL: http://kremlin.ru/events/president/news/76222 (viewed:17.09.2025).
  5. Исаев, Е.И., Марголис, А.А. (2023). Трудности в обучении: диагностика, профилактика, преодоление. Психологическая наука и образование, 28(5), 7–20. https://doi.org/10.17759/pse.2023280501
    Isaev, E.I., Margolis, A.A. (2023). Difficulties in Learning: Diagnostics, Prevention, and Overcoming. Psychological Science and Education, 28(5), 7–20. https://doi.org/10.17759/pse.2023280501
  6. Исаев, Е.И., Марголис, А.А., Сафронова, М.А. (2023). Психологический анализ компетентности учителя начальной школы в работе над предметными ошибками обучающихся. Психологическая наука и образование, 28(1), 5–24. https://doi.org/10.17759/pse.2023000002
    Isaev, E.I., Margolis, A.A., Safronova, M.A. (2023). Psychological Analysis of the Competence of a Primary School Teacher in Working on Students' Subject Mistakes. Psychological Science and Education, 28(1), 5–24. (In Russ.). https://doi.org/10.17759/pse.2023000002
  7. Комплексный план мероприятий по повышению качества математического и естественно-научного образования до 2030 года: распоряжение Правительства Российской Федерации от 19 ноября 2024 года № 3333-р. (2024). М. URL: http://government.ru/docs/53427 (дата обращения: 06.11.2025).
    Comprehensive action plan to improve the quality of mathematics and natural science education until 2030: Order of the Government of the Russian Federation of November 19, 2024 No. 3333-r. (2024). Moscow. (In Russ.). URL: http://government.ru/docs/53427 (viewed: 06.11.2025).
  8. Котляр, И.А., Сафронова, М.А. (2011). Три понятия о реальности детского развития: обучаемость, зона ближайшего развития и скаффолдинг. Культурно-историческая психология, 7(2), 74–83. URL: https://psyjournals.ru/journals/chp/archive/2011_n2/44482 (дата обращения: 17.09.2025).
    Kotliar, I.A., Safronova, M.A. (2011). Three Concepts Reflecting the Reality of Child Development: Ability to learn, Zone of Proximal Development and Scaffolding. Cultural-Historical Psychology, 7(2), 74–83. (In Russ.). URL: https://psyjournals.ru/en/journals/chp/archive/2011_n2/44482 (viewed: 18.09.2025).
  9. Марголис, А.А. (2020). Зона ближайшего развития (ЗБР) и организация учебной деятельности учащихся. Психологическая наука и образование, 25(4), 6–27. https://doi.org/10.17759/pse.2020250402
    Margolis, A.A. (2020). Zone of Proximal Development (ZPD) and Organization of Students Learning Activity. Psychological Science and Education, 25(4), 6–27. (In Russ.). https://doi.org/10.17759/pse.2020250402
  10. Марголис, А.А. (2020). Зона ближайшего развития, скаффолдинг и деятельность учителя. Культурно-историческая психология, 16(3), 15–26. https://doi.org/10.17759/chp.2020160303
    Margolis, A.A. (2020). Zone of Proximal Development, Scaffolding and Teaching Practice. Cultural-Historical Psychology, 16(3), 15–26. https://doi.org/10.17759/chp.2020160303
  11. Марголис, А.А. (2021). Новая научная грамотность: проблемы и трудности формирования. Психологическая наука и образование, 26(6), 5–24. https://doi.org/10.17759/pse.2021260601
    Margolis, A.A. (2021). New Science Literacy: Problems and Difficulties of Formation. Psychological Science and Education, 26(6), 5–24. (In Russ.). https://doi.org/10.17759/pse.2021260601
  12. Об утверждении федерального государственного образовательного стандарта начального общего образования: приказ Министерства просвещения Российской Федерации от 31 мая 2021 г. № 286. (2021). М. URL: https://www.garant.ru/products/ipo/prime/doc/400807193/ (дата обращения: 17.09.2025).
    On approval of the federal state educational standard for primary general education: Order of the Ministry of Education of the Russian Federation of May 31, 2021 no. 286. (2021). Moscow. (In Russ.). URL: https://www.garant.ru/products/ipo/prime/doc/400807193/ (viewed: 18.09.2025).
  13. Об утверждении федеральной образовательной программы начального общего образования: приказ Министерства просвещения Российской Федерации от 18.05.2023 № 372. (2023). М. URL: http://publication.pravo.gov.ru/document/0001202307130044 (дата обращения: 17.09.2025).
    On approval of the federal educational program for primary general education: Order of the Ministry of Education of the Russian Federation dated May 18, 2023 No. 372. (2023). Moscow. (In Russ.). URL: http://publication.pravo.gov.ru/document/0001202307130044 (viewed: 18.09.2025).
  14. Работа с детьми младшего школьного возраста, испытывающими трудности при изучении учебных предметов: методическое пособие для учителя начальной школы. (2024). Н.Ф. Виноградова, М.И. Кузнецова, О.А. Рыдзе / под ред. Н.Ф. Виноградовой. 2-е издание, перераб. и доп. М.: ФГБНУ «Институт содержания и методов обучения».
    Working with Primary School-Age Children Who Have Difficulties in Learning Subjects: A Methodological Handbook for Primary School Teachers. (2024). N.F. Vinogradova, M.I. Kuznetsova, O.A. Rydze / edited by N.F. Vinogradova. 2nd edition, revised and enlarged. M.: Federal State Budgetary Scientific Institution “Institute of Content and Methods of Teaching”. (In Russ.).
  15. Санина, С.П., Соколов, В.Л. (2021). Подходы к типологии основных ошибок младших школьников при освоении математических понятий. Современная зарубежная психология, 10(4), 138–146. https://doi.org/10.17759/jmfp.2021100413
    Sanina, S.P., Sokolov, V.L. (2021). Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts. Journal of Modern Foreign Psychology, 10(4), 138–146. (In Russ.). https://doi.org/10.17759/jmfp.2021100413
  16. Сиротюк, А.Л. (2004). Дифференцированное обучение младших школьников с учетом индивидуально-психологических особенностей: Дис. ... д-ра психол. наук. М.
    Sirotyuk, A.L. (2004). Differentiated teaching of primary school students taking into account individual psychological characteristics: Diss. Dr. Sci. (Psychol.). Moscow. (In Russ.).
  17. Соколов, В.Л. (2023). Психолого-педагогические приемы работы над ошибками младших школьников при освоении математических понятий. Вестник практической психологии образования, 20(1), 46–60. https://doi.org/10.17759/bppe.2023200105
    Sokolov, V.L. (2023). Psychological and Pedagogical Methods of Working on the Mistakes of Younger Schoolchildren in the Development of Mathematical Concepts. Bulletin of Practical Psychology of Education, 20(1), 46–60. (In Russ.). https://doi.org/10.17759/bppe.2023200105
  18. Яндекс Учебник. URL: https://education.yandex.ru/uchebnik/main (дата обращения: 17.09.2025).
    Yandex Textbook. URL: https://education.yandex.ru/uchebnik/main (viewed:17.09.2025).
  19. Aleven, V., McLaughlin, E.A., Glenn, R.A., Koedinger, K.R. (2017). Instruction based on adaptive learning technologies. In R.E. Mayer, P. Alexander (Eds.), Handbook of Research on Learning and Instruction (2nd ed., pp. 522–560).
  20. Ashlock, R.B. (2010). Error patterns in computation (10th ed.). Boston: Allyn & Bacon.
  21. Bernacki, M.L., Greene, M.J., Lobczowski, N.G. (2021). A Systematic Review of Research on Personalized Learning: Personalized by Whom, to What, How, and for What Purpose(s)? Educational Psychology Review, 33, 1675–1715.
  22. Brown, J., Skow, K. Mathematics: Identifying and Addressing Student Errors. [Nashville, TN]: Iris center, 2016. 34 p. URL: https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_case_studies/ics_matherr.pdf (viewed: 17.09.2025).
  23. Fiori, C., Zuccheri, L. (2025). An experimental research on error patterns in written subtraction. Educational Studies in Mathematics, 60, 323–331. DOI:10.1007/s10649-005-7530-6
  24. Gligorea, I., Cioca, M., Oancea, R., Gorski, A.T., Gorski, H., Tudorache, P. (2023). Adaptive Learning Using Artificial Intelligence in e-Learning: A Literature Review. Education Sciences.
  25. Jangra, A., Mozafari, J., Jatowt, A., Muresan, S. (2025). Navigating the landscape of hint generation research: From the past to the future. Transactions of the Association for Computational Linguistics, 13, 505–528. https://doi.org/10.1162/tacl_a_00751
  26. Kakoma, L., Themane, K.M. (2021). Misconceptions and associated errors in the learning of mathematics place value in south african primary schools: a literature review, Preprints, 24 p. DOI:10.20944/preprints202105.0456.v1
  27. Khan Academy. URL: https://www.khanacademy.org/ (viewed: 17.09.2025).
  28. Khalil, M., Wong, J., Wasson, B., Paas, F. (2024). Adaptive support for self-regulated learning in digital learning environments. British Journal of Educational Technology, 55(4), 1281–1289. https://doi.org/10.1111/bjet.13479
  29. Liu, T. (2022). Knowledge tracing: A bibliometric analysis. Computers and Education: Artificial Intelligence, 3, Article 100090. https://doi.org/10.1016/j.caeai.2022.100090
  30. Martin, F., Chen, Y., Moore, R.L., Westine, C. (2020). Systematic review of adaptive learning research designs, context, strategies, and technologies from 2009 to 2018. Educational Technology Research & Development, 68(4), 1903–1929. DOI:10.1007/s11423-020-09793-2
  31. Munshi, A., Biswas, G., Baker, R., Ocumpaugh, J., Hutt, S., Paquette, L. (2023). Analysing adaptive scaffolds that help students develop self-regulated learning behaviours. Journal of Computer Assisted Learning, 39(2), 351–368. https://doi.org/10.1111/jcal.12761
  32. Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163–172. https://doi.org/10.5951/jresematheduc.10.3.0163
  33. Shen S. et al. (2024). A Survey of Knowledge Tracing: Models, Variants, and Applications. IEEE Transactions on Learning Technologies, 17, 1858–1879. DOI:10.1109/TLT.2024.3383325
  34. Stephens-Martinez, K., Fox, A. (2018). Giving hints is complicated: Understanding the challenges of an automated hint system based on frequent wrong answers. In Proceedings of the 23rd Annual ACM Conference on Innovation and Technology in Computer Science Education (pp. 45–50). Association for Computing Machinery. https://doi.org/10.1145/3197091.3197102
  35. Tan, L.Y., Hu, S., Yeo, D.J., Cheong, K.H. (2025). Artificial Intelligence-Enabled Adaptive Learning Platforms: A Review. Computers and Education: Artificial Intelligence.
  36. Watson, S.M.R., Lopes, J., Oliveira, C., Judge, S. (2018). Error patterns in Portuguese students’ addition and subtraction calculation tasks: Implications for teaching. Journal for Multicultural Education, 12(1), 67–82. https://doi.org/10.1108/JME-01-2017-0002
  37. Wood, D., Bruner, J., Ross, G. (1976). The role of tutoring in prob­lem solving. Journal of Child Psychology and Psychiatry, 17, 89–
  38. Zerkouk, M., Mihoubi, M., Chikhaoui, B. (2025). A comprehensive review of AI-based intelligent tutoring systems: Applications and challenges. arXiv preprint arXiv:2507.18882. https://doi.org/10.48550/arXiv.2507.18882

Information About the Authors

Evgeny I. Isaev, Doctor of Psychology, professor, Professor, Chair of Pedagogical Psychology named after Professor V.A. Guruzhapov, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-4652-5780, e-mail: isaevei@mgppu.ru

Arkadiy A. Margolis, Candidate of Science (Psychology), Professor, Rector, Professor, Chair of Pedagogical Psychology, Moscow State University of psychology and education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0001-9832-0122, e-mail: margolisaa@mgppu.ru

Maria A. Safronova, Candidate of Science (Psychology), Dean of the Faculty of Psychology of Education, Research fellow of the laboratory of Theoretical and experimental issues in cultural-historical psychology, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-3597-6375, e-mail: safronovama@mgppu.ru

Vladimir L. Sokolov, Candidate of Science (Psychology), Associate Professor, Chair of Pedagogical Psychology named after Professor V.A. Guruzhapov, Department of Psychology of Education, Moscow State University of Psychology & Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-6180-7567, e-mail: sokolovvl@mgppu.ru

Contribution of the authors

Evgeny I. Isaev — annotation; literature review; manuscript writing.

Arkadiy A. Margolis — ideas; literature review; manuscript writing.

Maria A. Safronova — literature review; digital systems analysis; writing and design of the manuscript.

Vladimir L. Sokolov — literature review; manuscript writing; model description.

All authors participated in the discussion of the results and approved the final text of the manuscript.

Conflict of interest

The authors declare no conflict of interest.

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