Automated Teaching System “Sets” (Research for Organizing the 1st Part of the Project)

The issues of building an automated learning system “Sets” which will allow students to master one of the important topics of the discipline “Discrete Mathematics” and to develop logical and mathematical thinking in this direction are studied. The corresponding topic of the 1st part of the project includes materials related to the concept of a set, operations on sets, algebra of sets, proofs of statements for sets, and the derivation of formulas for the number of set elements. The system is based on a construction of the statements proof editor for a set and of the formulas derivation editor for the number of set elements, both editors are to be used for teaching. The first of these allows students to split the original statement into a number of simpler statements, taken together equivalent to the original statement, to choose a method of proving each simple statement and to conduct their step-by-step proof. The second editor allows (using the inclusion-exclusion principle and the formula of the number of complement elements) to derive a step-by-step formula for the number of set elements through the specified numbers of elements for sets from which the resulting set is constructed. An important part of the system is to monitor the correctness of all actions of students, and on this basis the entire learning system is developed. The logical supervision over the correctness of the selected action in the first editor is performed by a Boolean function created by the system and corresponding to this action and by checking it for identical truth. In the second editor, invariants such as characteristic strings of the set and of its number of elements are used for verification. The rest of the system is related to learning of set algebra and to preparation to editors usage. The main focus here is on the learning strategy in which testing the understanding of the learned material is rather rigorous and eliminating the random choice of answers. The division of the material into sections with verification of the success of teaching not only by tests, but also by exercises and tasks, allows students to master the complex logical and mathematical techniques of proving statements for sets and derivation of formulas for the number of set elements.

1. A. Buchner, Moodle 3 Administration. Third Edition. Packt Publishing, 2016.

2. S. K. Udaya and T. V. Vamsi Krishna, “E-Learning: Technological Development in Teaching for school kids”, International Journal of Computer Science and Information Technologies, vol. 5, no. 5, pp. 6124–6126, 2014.

3. M. Kerres, D. Meister, F. von Gross, and U. Sander, Enzyklopadie Erziehungswissenschaft. 2012.

4. S. Clark and J. Baggaley, “Assistive Software for Disabled Learners”, The International Review of Research in Open and Distributed Learning, vol. 5, no. 3, 2004. [Online]. Available: https://doi.org/10.19173/irrodl.v5i3.198.

5. A. Nagy, “The Impact of E-Learning”, in E-Content: Technologies and Perspectives for the European Market, Berlin: Springer-Verlag, 2005, pp. 79–96. [Online]. Available: https://doi.org/10.1007/3-540-26387-X_4.

6. I. E. Allen and J. Seaman, Changing Course: Ten Years of Tracking Online Education in the United States. Babson Survey Research Group, 2013.

7. D. Burgos et al., Eds., Higher Education Learning Methodologies and Technologies Online, Springer, 2019, pp. 6–7.

8. A. Holzinger et al., Eds., Machine Learning and Knowledge Extraction. Springer, 2019.

9. Y. Zhang and D. Cristol, Handbook of Mobile Teaching and Learning. Springer, 2019.

10. S. Kong and H. Abelson, Computational Œinking Education. Springer Nature, 2019.

11. G. Hanna, D. Reid, and M. de Villiers, Proof Technology in Mathematics Research and Teaching. Springer, 2019.

12. M. England and other, Eds., Computer Algebra in Scientific Computing, Springer, 2019.

13. J. H. Davenport, Y. Siret, and E. Tournier, Computer algebra: systems and algorithms for algebraic computation. Academic Press, 1988.

14. J. Gathen and J. Gerhard, Modern Computer Algebra. Cambridge University Press, 2013.

15. V. B. Taranchuk, The main functions of computer algebra systems, in Russian. Minsk: BSU, 2013.

16. A. V. Ermilova and V. S. Rublev, “Problems of mathematical thinking development for students basing on example of teaching system to the course “Algorithms and computational complexity analysis””, in Russian, in Proceedings of IX International theoretical and practical conference Information Technologies and IT-Education, Moscow: INTUIT.RU, 2014, pp. 297–304.

17. V. S. Rublev and M. T. Yusufov, “Automated system for teaching computational complexity analysis of algorithms”, in Russian, Modern Information Technologies and IT-Education, vol. 12, no. 1, pp. 135–145, 2016.

18. V. S. Rublev and M. T. Yusufov, “Automated teaching system “Analysis of algorithms computational complexity” (research for organizing the 1st part of the project)”, in Russian, Modern Information Technologies and IT-Education, vol. 13, no. 2, pp. 170–178, 2017.

19. V. S. Rublev and M. T. Yusufov, “Automated System for Teaching Computational Complexity of Algorithms Course”, in Russian, Modeling and Analysis of Information Systems, vol. 24, no. 4, pp. 481–495, 2017.

20. V. S. Rublev and M. T. Yusufov, “Models for teaching analysis of algorithm computational complexity”, in Russian, in 3rd International on Computer Algebra and Information Technologies, Odessa: ONSU, 2018, pp. 157–160.

21. V. S. Rublev and D. R. Vakhmyanin, “Automated system for teaching «Proof of statements for sets»”, in Russian, Modern Information Technologies and IT-Education, vol. 15, no. 4, pp. 1014–1027, 2019.

22. V. S. Rublev, Boolean functions (individual work #4 and #5 for the course “Discrete Mathematics”), in Russian. Yaroslavl: YSU, 2018.

23. V. S. Rublev, Sets (individual work #1 for the course “Discrete Mathematics”), in Russian. Yaroslavl: YSU, 2018.