Educational Projection Systems, Levels And Prerequisites Of Mathematical Ontology OntoMathEdu
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Abstract
The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMathEdu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.
Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.
The OntoMathEdu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.
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References
2. Nahhas S., Bamasag O., Khemakhem M., Bajnaid N. Added Values of Linked Data in Education: A Survey and Roadmap // Computers. 2018. V. 7, No. 3. https://doi.org/10.3390/computers7030045.
3. Lange Ch. Ontologies and languages for representing mathematical knowledge on the Semantic Web // Semantic Web. 2013. V. 4, No. 2. P. 119–158. URL: https://doi.org/10.3233/SW-2012-0059.
4. Kohlhase M. A Data Model and Encoding for a Semantic, Multilingual Terminology of Mathematics // In: Watt S.M., et al. (Eds.) Proceedings of the International Conference on Intelligent Computer Mathematics (CICM 2014). Lecture Notes in Computer Science. . Springer, Cham. 2014. V. 8543. P. 169–183. URL: https://doi.org/10.1007/978-3-319-08434-3_13.
5. Nevzorova O., Zhiltsov N., Kirillovich A., Lipachev E. OntoMathPRO Ontology: A Linked Data Hub for Mathematics // In: Klinov P., Mouromstev D. (Eds.) Proc. of the 5th Int. Conf. on Knowledge Engineering and Semantic Web (KESW 2014). Communications in Computer and Information Science. Springer, Cham. 2014. V. 468. P. 105–119. https://doi.org/10.1007/978-3-319-11716-4_9.
6. Кириллович А.В., Жильцов Н.Г., Иваньшин П.Н., Каюмова А.В., Каюмов И.Р., Липачев Е.К., Матвейчук М.С., Невзорова О.А., Соловьев В.Д., Уткина Е.А. Онтология профессиональной математики «OntoMathPRO» // Свидетельство о регистрации базы данных RU 2018622131, 25.12.2018.
7. Ginev D., Iancu M., Jucovshi C., Kohlhase A., Kohlhase M., Oripov A., Schefter J., Sperber W., Teschke O., and Wiesing T. The SMGloM Project and System: Towards a Terminology and Ontology for Mathematics // In: Greuel G.M. et al. (Eds.) 5th International Conference on Mathematical Software (ICMS 2016). Lecture Notes in Computer Science. Springer, Cham. 2016. V. 9725. P. 451–457. https://doi.org/10.1007/978-3-319-42432-3_58.
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. 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.
10. 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.
11. 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.
12. Галеев Р.Д., Гильманшин И.Р., Кашапов Н.Ф., Гильманшина С.И. Применение индивидуальных образовательных траекторий и адаптивного контента в инженерном образовании // Перспективы и приоритеты педагогического образования в эпоху трансформаций, выбора и вызовов. сборник научных трудов VI Виртуального Международного форума по педагогическому образованию. Казань, 2020. С. 120–129.
13. Абрамский М.М. Управление данными в современных цифровых образовательных средах // Информационное общество. 2019. № 1–2. С. 82–91.
14. Абрамский М.М. Модели, методы и программные средства управления данными цифровых образовательных сред. Дис.к.т.н…. Казань, 2019. 160 с.
15. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu:Towards an Educational Mathematical Ontology // In: Edwin B. 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. 2020. V. 2634. http://ceur-ws.org/Vol-2634/WiP1.pdf, last accessed 2020/11/21.
16. Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.
17. Loukachevitch N., Komissarov A., Dobrov B., Shternov S. Using Ontology for Natural Sciences and Technologies for Vacancies Analysis // DTTL-2021: International Workshop on Digital Technologies for Teaching and Learning, March 22-28, 2021, Kazan, Russia. 2021 (in press).
18. Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu: a New Linguistically Grounded Educational Mathematical Ontology // In: Benzmüller C. and Miller B. (Eds.) Proc. of the 13th International Conference on Intelligent Computer Mathematics (CICM 2020). Lecture Notes in Artificial Intelligence. Springer. 2020. V. 12236. P. 157–172.
19. Шакирова Л.Р., Фалилеева М.В., Кириллович А.В., Липачев Е.К. Проектирование образовательной математической онтологии: проблемы и методы решения на примере курса планиметрии // XV Международная конференция по компьютерной и когнитивной лингвистике TEL 2018. Сборник трудов: в 2-х томах. Т. 1. Казань: Изд.-во АН РТ. 2018. С. 393–405.
20. Кириллович А.В., Липачев Е.К., Невзорова О.А., Фалилеева М.В., Шакирова Л.Р. Онтология образовательной математики «OntoMathEDU» // Свидетельство о регистрации базы данных RU 2019622208, 28.11.2019.
21. Elizarov A.M., Lipachev E.K. Lobachevskii DML: Towards a Semantic Digital Mathematical Library of Kazan University // CEUR Workshop Proceedings. 2017. V. 2022. P. 326–333.
22. Елизаров А.М., Жильцов Н.Г., Кириллович А.В., Липачев Е.К., Невзорова О.А. Экосистема OntoMATH и проект Всемирной цифровой математической библиотеки // Труды международной конференции по компьютерной и когнитивной лингвистике. Сер. "Интеллект. Язык. Компьютер" 2016. С. 25–28.
23. Elizarov A.M., Kirilovich A.V., Lipachev E.K., Nevzorova O.A. Mathematical Knowledge Management: Ontological Models and Digital Technology // CEUR Workshop Proceedings. 2016. V. 1752. P. 44–50. URL: http://ceur-ws.org/Vol-1752/paper08.pdf.
24. Elizarov A.M., Kirillovich A.V., Lipachev E.K., Zhizhchenko A.B., Zhil’tsov N.G. Mathematical Knowledge Ontologies and Recommender Systems for Collections of Documents in Physics and Mathematics // Doklady Mathematics. 2016. V. 93, No. 2. P. 231–233. https://doi.org/10.1134/S1064562416020174.
25. Elizarov A., Kirillovich A., Lipachev E., Nevzorova O. Semantic Formula Search in Digital Mathematical Libraries // Proc. of the 2nd Russia and Pacific Conf. on Comp. Technology and Applications (RPC 2017). IEEE. 2017. P. 39–43. https://doi.org/10.1109/RPC.2017.8168063.
26. Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.
27. Федеральные государственные образовательные стандарты. Основное общее образование (5–9 кл.). URL: https://fgos.ru/#b3ac23ba5e3cfc8ef, https://fgos.ru/LMS/wm/wm_fgos.php?id=osnov.
28. The national curriculum. URL: https://www.gov.uk/national-curriculum.
29. National curriculum in England: mathematics programmes of study. URL: https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study.
30. Standards for Mathematical Practice.
URL: http://www.corestandards.org/Math/Practice/.
31. Cummins J., Carter J.A., Cuevas G.J., Day R, Malloy C. Glencoe Geometry, Virginia Student Edition. McGraw-Hill/Glencoe, 2012. 810 p.
32. Gantert A.X. Amsco's Geometry. AMSCO School Publications, Incorporated, 2008. 643 p.
33. Larson R.L., Boswell L., Stiff L. Heath Geometry an Integrared Approach. Teacher’s Edition, 1998. 876 p.
34. KS2 Maths SATs Study Book: For the 2021 Tests (Collins KS2 SATs Practice). Collins KS2, 2015. 112 p.
35. KS3 Maths Complete Revision & Practice - Higher (with Online Edition) (Paperback). CGP Books, 2014. 171 p.
36. Joinson R. Exercises in KS3 Mathematics Levels 5-6 (Spiral bound). 2001. 101 p.
37. Pereira C.K., Matsui Siqueira S.W., Nunes B.P., Dietze S. Linked Data in Education: A Survey and a Synthesis of Actual Research and Future Challenges // IEEE Transactions on Learning Technologies. 2018. V. 11, No. 3. P. 400–412.
https://doi.org/10.1109/TLT.2017.2787659.
38. D’Aquin M. On the Use of Linked Open Data in Education: Current and Future Practices // In: Mouromtsev D. and D’Aquin M.(Eds.) Open Data for Education: Linked, Shared, and Reusable Data for Teaching and Learning. Lecture Notes in Computer Science, Springer, Cham. 2016. V. 9500. P. 3–15.
https://doi.org/10.1007/978-3-319-30493-9_1.
39. Borgo S., Masolo C. Ontological Foundations of DOLCE // In: Poli R., Healy M., Kameas A. (Eds.) Theory and Applications of Ontology. Computer Applications. Dordrecht: Springer, 2010. P. 279–295.
40. Gangemi A., Mika P. Understanding the Semantic Web through Descriptions and Situations // In: Meersman R., Tari Z., Schmidt D.C. (Eds.) On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE. OTM 2003. Lecture Notes in Computer Science, Berlin, Heidelberg: Springer. 2003. V. 2888. P. 689–706.
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