Semantic Services of the Digital Ecosystem Ontomath for Mathematical Education

Article Sidebar

PDF (Русский)
Published: 28.09.2023
UDC 004.4
DOI: https://doi.org/10.26907/1562-5419-2023-26-4-538–569
Issue
Vol. 26 No. 4 (2023)

Main Article Content

Olga Avenirovna Nevzorova
Kazan (Volga region) Federal University
https://orcid.org/0000-0001-8116-9446
Evgeny Konstantinovich Lipachev
Kazan (Volga region) Federal University
https://orcid.org/0000-0001-7789-2332
Konstantin Sergeevich Nikolaev
Kazan (Volga region) Federal University
https://orcid.org/0000-0003-3204-238X

Abstract

We present a set of semantic services developed by us to support the educational process in mathematics. The functionality of these services is based on the use of mathematical ontologies OntoMathEdu and OntoMathPRO. The ontology of professional mathematical knowledge OntoMathPRO is designed to classify and systematize the concepts of professional mathematics and includes several important areas of mathematics. Educational mathematical ontology OntoMathEdu systematically represents knowledge on the training course “Planimetry”. For the use of ontologies in educational applications, an approach to the design of prerequisite relations in these ontologies has been developed. To support mathematical education, we have developed: a service for semantic search by mathematical formulas, a service for semantic annotation of educational materials, a service for visualizing subgraphs of the OntoMathEdu ontology semantic network, a parallel formal/informal corpus of mathematical statements, a system for automatically generating test questions in mathematical disciplines.


We provide examples of successful application of the developed software tools.


The created software tools are built into the OntoMath digital ecosystem. This ecosystem implements the interaction of semantic services for managing mathematical knowledge.

Article Details

References

1. Moodle – Open-source Learning Platform. URL: https://moodle.org/?lang=ru.
2. Технология решения планиметрических задач. https://edu.kpfu.ru/course/view.php?id=2652.
3. Муромцев Д. И. Модели и методы индивидуализации электронного обучения в контексте онтологического подхода // Онтологии проектирования. 2020. Т. 10. № 1. С. 34–49. https://doi.org/10.18287/2223-9537-2020-10-1-34-49.
4. Anderson J. Q. Individualisation of Higher Education: How Technological Evolution can Revolutionise Opportunities for Teaching and Learning // International Social Science Journal. 2013. V. 64. No. 213–214. P. 305–316. https://doi.org/10.1111/issj.12046.
5. Абрамский М. М., Батырова Э. Ф., Марданова А. Р., Ахметзянова Т.А. Генерация индивидуальных образовательных траекторий и расписания обучения в парадигме индивидуализации образования // Электронные библиотеки. 2018. Т. 21. № 3–4. С. 129–145. URL: https://rdl-journal.ru/article/view/466.
6. Jakus G., Milutinović V., Omerović S., Tomažič S. Concepts, Ontologies, and Knowledge Representation. Series: SpringerBriefs in Computer Science. Springer New York, NY, 2013. https://doi.org/10.1007/978-1-4614-7822-5. URL: https://link.springer.com/book/10.1007/978-1-4614-7822-5.
7. Елизаров А. М., Кириллович А. В., Липачёв Е. К., Невзорова О. А., Шакирова Л. Р. Семантические технологии в математическом образовании: онтологии и открытые связанные данные // Ученые записки ИСГЗ. 2018. Т. 16. № 1. С. 222–227.
8. Tzoumpa D., Mitropoulos S. Semantic Web Technologies for Ontologies Description: Case study in Geometry Education // In: 2020 5th South-East Europe Design Automation, Computer Engineering, Computer Networks and Social Media Conference (SEEDA-CECNSM), Corfu, Greece. 2020. P. 1–5. https://doi.org/10.1109/SEEDA-CECNSM49515.2020.9221781.
9. Tzoumpa D., Karvounidis T., Douligeris C. Circle’s Ontology Extended: Circumference and Surface Area of a Circle // Advances in Intelligent Systems and Computing. 2020. Vol. 916. P. 120–132.
10. Elizarov A., Kirillovich A., Lipachev E., Nevzorova O. Digital Ecosystem OntoMath: Mathematical Knowledge Analytics and Management // L. Kalinichenko, S. Kuznetsov, and Y. Manolopoulos (Eds.). Revised Selected Papers of the XVIII International Conference on Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2016), Ershovo, Moscow, Russia, October 11–14, 2016. Communications in Computer and Information Science. Springer, 2017. Vol. 706. P. 33–46. https://doi.org/10.1007/978-3-319-57135-5_3.
11. Elizarov A. M., Zhiltsov N. G., Kirillovich A. V., Lipachev E. K., Nevzorova O. A., Solovyev V. D. The OntoMath ecosystem: Ontologies and applications for math knowledge management // Semantic Representation of Mathematical Knowledge Workshop, Fields Institute, Toronto, Canada, February 5, 2016. URL: https://video-archive.fields.utoronto.ca/view/4698.
12. Елизаров А. М., Липачев Е. К. Цифровая библиотека Lobachevskii-DML в научном пространстве математических знаний // Научно-техническая информация. Серия 1: Организация и методика информационной работы. 2023. № 1. С. 32-37. https://doi.org/ 10.36535/0548-0019-2023-01-3.
13. Елизаров А. М., Кириллович А. В., Липачёв Е. К., Невзорова О. А. Цифровая экосистема OntoMath как подход к построению пространства математических знаний // Электронные библиотеки. 2023. Т. 26. № 2. С. 154–202. https://doi.org/10.26907/1562-5419-2023-26-2-154–202. URL: https://rdl-journal.ru/article/view/771.
14. Nevzorova O., Zhiltsov N., Kirillovich A., Lipachev E. OntoMathPRO Ontology: A Linked Data Hub for Mathematics // P. Klinov and D. Mouromstev (Eds.). Proceedings of the 5th International Conference on Knowledge Engineering and Semantic Web (KESW 2014), Kazan, Russia, September 29 – October 1, 2014. Communications in Computer and Information Science. Springer, Cham, 2014. Vol. 468. P. 105–119. https://doi.org/10.1007/978-3-319-11716-4_9.
15. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEDU: Towards an Educational Mathematical Ontology // E. Brady et al. (Eds.). Workshop Papers at 12th Conference on Intelligent Computer Mathematics (CICM-WS 2019), Prague, Czech Republic, 8–12 July 2019. CEUR Workshop Proceedings. CEUR-WS, 2020. Vol. 2634. URL: https://ceur-ws.org/Vol-2634/WiP1.pdf.
16. Елизаров А. М., Кириллович А. В., Липачёв Е. К., Невзорова О. А. Цифровая экосистема OntoMath: взаимодействие семантических сервисов и математических онтологий // Научный сервис в сети Интернет: труды XXIV Всероссийской научной конференции (19–22 сентября 2022 г., онлайн). М.: ИПМ им. М.В. Келдыша, 2022. С. 167–178. https://doi.org/10.20948/abrau-2022-40. URL: https://keldysh.ru/abrau/2022/theses/40.pdf.
17. Kirillovich A. V., Nevzorova O. A., Lipachev E. K. OntoMathPRO 2.0 Ontology: Updates of Formal Model // Lobachevskii J. Math. 2022. Vol. 43. No 12. P. 3504–3514. https://doi.org/10.1134/S1995080222150136. URL: https://link.springer.com/article/10.1134/S1995080222150136.
18. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Dyupina A., Shakirova L. Prerequisite Relationships of the OntoMathEdu Educational Mathematical Ontology // J.C. Figueroa-García et al. (Eds.). Proceedings of the 8th Workshop on Engineering Applications (WEA 2021), Medellín, Colombia, October 6–8, 2021. Communications in Computer and Information Science. Springer, 2021. Vol. 1431. P. 517–524.
19. Николаев К. С., Невзорова О. А. Метод автоматической семантической разметки математических образовательных текстов // Информационные технологии в образовании и науке (ИТОН–2022) и II International Workshop “Digital Technologies for Teaching and Learning” (DTTL). Материалы III Международного форума по математическому образованию: Международной научно-практической конференции и II Международного научного семинара. Казань, 2022. С. 181–190.
20. Kirillovich A., Nevzorova O., Nikolaev K., Galiaskarova K. Towards a Parallel Informal-Formal Corpus of Educational Mathematical Texts in Russian // Zhengbing Hu et al. (Eds.). Proceedings of the 2019 International Symposium on Computer Science, Digital Economy and Intelligent Systems (CSDEIS 2019), Moscow, Russia, on 4–6 October 2019. Advances in Intelligent Systems and Computing. Springer, 2020. Vol. 1127. P. 325–334. https://doi.org/10.1007/978-3-030-39216-1_29.
21. Nikolaev K., Kirillovich A., Nevzorova O. A Corpus-Based Approach to Elementary Geometry Knowledge Test Generation // L. Gómez Chova et al. (Eds.). Proceedings of the 14th International Technology, Education and Development Conference (INTED 2020), Valencia, Spain, 2–4 March 2020. IATED, 2020. P. 6342–6348.
22. Nevzorova O., Zhiltsov N., Kirillovich A., Lipachev E. OntoMathPRO Ontology: A Linked Data Hub for Mathematics // P. Klinov and D. Mouromstev (Eds.). Proceedings of the 5th International Conference on Knowledge Engineering and Semantic Web (KESW 2014), Kazan, Russia, September 29 – October 1, 2014. Communications in Computer and Information Science. Springer, Cham, 2014. Vol. 468. P. 105–119. https://doi.org/10.1007/978-3-319-11716-4_9.
23. Елизаров А. М., Кириллович А. В., Липачёв Е. К., Невзорова О. А. Онтология математического знания OntoMathPRO // Доклады Российской академии наук. Математика, информатика, процессы управления. 2022. Т. 507. № 1. С. 29–35. https://doi.org/ 10.31857/S2686954322700011.
24. Nevzorova O. A., Falileeva M. V., Kirillovich A. V., Lipachev E. K., Shakirova L. R., Dyupina A. E. OntoMathEdu Educational Ontology: Problems of Ontological Engineering // Pattern Recognition and Image Analysis. 2023. Vol. 33. No. 3. P. 460–466.
25. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEDU: Towards an Educational Mathematical Ontology // E. Brady et al. (Eds.). Workshop Papers at 12th Conference on Intelligent Computer Mathematics (CICM-WS 2019), Prague, Czech Republic, 8–12 July 2019. CEUR Workshop Proceedings. CEUR-WS, 2020. Vol. 2634. URL: https://ceur-ws.org/Vol-2634/WiP1.pdf.
26. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEDU: A Linguistically Grounded Educational Mathematical Ontology // C. Benzmüller and B. Miller (Eds.). Proceedings of the 13th International Conference on Intelligent Computer Mathematics (CICM 2020), Bertinoro, Italy, July 26–31, 2020. Lecture Notes in Computer Science. Springer, 2020. Vol. 12236. P. 157–172. https://doi.org/10.1007/978-3-030-53518-6_10.
27. Loukachevitch N., Komissarov A., Dobrov B., Shternov S. Using Ontology for Natural Sciences and Technologies for Vacancies Analysis // CEUR Workshop Proceedings. CEUR-WS, 2021. Vol. 2910. P. 30–38. URL: http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-2910/short2.pdf.
28. Фалилеева М. В., Кириллович А. В., Hевзорова О. А., Шакирова Л. Р., Липачёв Е. К., Дюпина А. Э. Системы образовательных проекций, уровней и пререквизитов математической онтологии OntoMathEDU // Электронные библиотеки. 2021. Т. 24. № 3. С. 505–530. https://doi.org/10.26907/1562-5419-2021-24-3-505-530. URL: https://rdl-journal.ru/article/view/691.
29. Fréchet M. Sur les fonctionelles continues // Acc. Ec. Norm. 1910. 27 (3). P. 193–216. URL: http://www.numdam.org/article/ASENS_1910_3_27__193_0.pdf.
30. Gateaux R. Sur les fonctionnelles continues et les fonctionnelles analytiques // Comptes Rendus Acad. Sci. Paris. Sér. I. Math. 1913. Vol. 157. P. 325–327. URL: https://gallica.bnf.fr/ark:/12148/bpt6k31103/f325.image.
31. Канторович Л. В., Акилов Г. П. Функциональный анализ. М.: Наука. Гл. ред. физ.-мат. лит., 1984. 752 с.
32. Колмогоров А. Н., Фомин С. В. Элементы теории функций и функционального анализа. М.: Наука. Гл. ред. физ.-мат. лит., 1989. 624 с.
33. OntoMath Semantic Formula Search. URL: https://lobachevskii-dml.ru/mathsearch.
34. Elizarov A., Kirillovich A., Lipachev E., Nevzorova O. Semantic Formula Search in Digital Mathematical Libraries // Proceedings of the 2nd Russia and Pacific Conference on Computer Technology and Applications (RPC 2017), Vladivostok, Russia, 25–29 September, 2017. IEEE, 2017. P. 39–43. https://doi.org/10.1109/RPC.2017.8168063.
35. MatJax. Beautiful and accessible math in all browsers. URL: https://www.mathjax.org/.
36. Николаев К. С. Сервис генерации учебных карточек математических понятий для дистанционного курса по геометрии // Электронные библиотеки. 2023. Т. 26. № 3. С. 365–377. https://doi.org/10.26907/1562-5419-2023-26-3-365-377. URL: https://rdl-journal.ru/article/view/785.
37. The OpenMath Standards. URL: https://openmath.org/standard/.


Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Presenting an article for publication in the Russian Digital Libraries Journal (RDLJ), the authors automatically give consent to grant a limited license to use the materials of the Kazan (Volga) Federal University (KFU) (of course, only if the article is accepted for publication). This means that KFU has the right to publish an article in the next issue of the journal (on the website or in printed form), as well as to reprint this article in the archives of RDLJ CDs or to include in a particular information system or database, produced by KFU.

All copyrighted materials are placed in RDLJ with the consent of the authors. In the event that any of the authors have objected to its publication of materials on this site, the material can be removed, subject to notification to the Editor in writing.

Documents published in RDLJ are protected by copyright and all rights are reserved by the authors. Authors independently monitor compliance with their rights to reproduce or translate their papers published in the journal. If the material is published in RDLJ, reprinted with permission by another publisher or translated into another language, a reference to the original publication.

By submitting an article for publication in RDLJ, authors should take into account that the publication on the Internet, on the one hand, provide unique opportunities for access to their content, but on the other hand, are a new form of information exchange in the global information society where authors and publishers is not always provided with protection against unauthorized copying or other use of materials protected by copyright.

RDLJ is copyrighted. When using materials from the log must indicate the URL: index.phtml page = elbib / rus / journal?. Any change, addition or editing of the author's text are not allowed. Copying individual fragments of articles from the journal is allowed for distribute, remix, adapt, and build upon article, even commercially, as long as they credit that article for the original creation.

Request for the right to reproduce or use any of the materials published in RDLJ should be addressed to the Editor-in-Chief A.M. Elizarov at the following address: amelizarov@gmail.com.

The publishers of RDLJ is not responsible for the view, set out in the published opinion articles.

We suggest the authors of articles downloaded from this page, sign it and send it to the journal publisher's address by e-mail scan copyright agreements on the transfer of non-exclusive rights to use the work.