Mathematical Model of an Automated System for Learning to Play the Piano

Purpose of research. Nowadays, the automation of the distance learning process or self-study is relevant. However, to increase its effectiveness, there is a need for a personality-oriented approach to the student. The creation of adaptive learning technologies is becoming a priority. Development of a mathematical model of an automated system for learning to play the piano was the purpose of this work.

Methods. The article discusses one of the approaches to modeling educational processes and systems - the cybernetic approach. The use of this approach allows us to consider the model of the educational system from the point of view of internal blocks and their functions, it allows us to identify sets of input and output data and internal relationships of various components of the system. The mathematical model is based on the operations of the algebra of logic and set theory.

Resalts. Based on the cybernetic approach, the article provides a functional diagram of the system, which clearly demonstrates the sequence of actions performed, as well as the flow of various sets of input and output data. The functionality of the blocks is described in the terminology of operators, which determine the sequence and the required number of questionnaire questions to determine the initial knowledge, skills, and abilities of the trainee and his goals, select the most optimal initial training plan, assess progress and adjust the initial training plan depending on the results of the student. For each operator, sets of inputs and outputs are defined. The description of the data shows what information the system must operate in order for it to work correctly and efficiently. Another significant result of the work was the mathematical model of the system obtained as a result of research, which determines the relationship between input and output data.

Conclusion. The cybernetic approach to modeling educational activities, including in the system of additional education, allows you to structure complex logical connections in the educational system, to determine the sequence and options for the system. The model will form the basis of the information system for piano playing teaching.

1. Zaidullina S.G., Safronov A.M. Rol' sovremennykh sistem adaptivnogo obuche-niya v obrazovanii [The role of modern systems of adaptive learning in education]. Prepodavanie informatsionnykh tekhnologii v Rossiiskoi Federatsii [Teaching information technologies in the Russian Federation] 2018; 227-228.

2. D'yachkov D.B., D'yachkova E.V. Obzor i analiz tekhnologii dlya adaptivnogo obucheniya [Overview and analysis of technologies for adaptive learning]. E-Scio. 2022; no.12 (75). Available at: http://e-scio.ru/wp-content/uploads/2022/12/D'yachkov-D.-B.-D'yachkova-E.-V.-Golubnichii-A.-A.pdf.

3. Andrade A.I., Nasuro E.V. Sredstvo muzykal'noi transkriptsii pri pomoshchi metodov mashinnogo obucheniya [Means of musical transcription by means of machine training methods]. BIG DATA and Advanced Analytics. 2019; №5: 386-390.

4. Korukhova Yu.S., Mytrova M.V. Poisk not v elektronnykh bibliotekakh po fragmentu melodii [Search for notes in electronic libraries by melody fragment]. Biomashsistemy = Biomachsistems. 2018; no.3: 101-108.

5. Sviyazova E.R. Problema avtomaticheskoi muzykal'noi transkriptsi [Musical transcription using neural network technology]. Molodezhnyi vestnik Ufimskogo gosudarstvennogo aviatsionnogo tekhnicheskogo universiteta = Molodezhnyj Vestnik UGATU (scientific journal of Ufa State Aviation Technical University). 2019; no.1: 159-162.

6. Zhao W., Zhou Y., Tie Y. and Zhao Y. Recurrent Neural Network for MIDI Music Emotion Classification, 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing, China, 2018; 2596-2600. doi: 10.1109/IAEAC.2018.8577272.

7. Ostrenko A.A., Ryzhkova M.N. Obzor i analiz tekhnologii postroeniya komp'yuternykh sistem obucheniya igre na fortepiano. [Review and analysis of technologies for building computer systems for teaching piano playing]. Algoritmy, metody i sistemy obrabotki dannykh = Algorithms, Methods and Data Processing Systems. 2020; no.1: 21-32.

8. Ostrenko A.A., Ryzhkova M.N. [Review and analysis of automated systems for learning to play the piano]. Nauka i obrazovanie v razvitii promyshlennoi, sotsial'noi i ekonomicheskoi sfer regionov Rossii. XII Vserossiiskie nauchnye Zvorykinskie chteniya. [Science and education in the development of industrial, social and economic spheres of Russian regions. XII All- Russian Scientific Zworykin Readings]. Murom, 2020: 388 (In Russ.).

9. Zvereva N.A. [Multi-level and differentiated learning as a factor in improving the efficiency of the educational process in secondary vocational education]. Molodoi uchenyi. VIII Mezhdunarodnaya nauchnaya konferentsiya «Pedagogicheskoe masterstvo». [Young scientist. VIII International Scientific Conference "Pedagogical Excellence"]. Kazan’, 2016; 35-37 (In Russ.).

10. Muranova N.P. Modelirovanie fiziko-matematicheskoi podgotovki starsheklassnikov k obucheniyu v tekhnicheskom universitete kak didakticheskoi sistemy [Modeling of physical and mathematical training of senior school pupils for studying at a technical higher school as a didactic system]. Izvestiya VGPU = Ivzestia of the Volgograd State Pedagogical University. 2015; no.1 (96): 56-63.

11. Vanyagina M.R. Kompleksnaya model' sistemy inoyazychnogo obucheniya v vysshei voennoi shkole. [Comprehensive model of foreign-language teaching system in higher military school]. Vestnik Tambovskogo universiteta. Seriya: Gumanitarnye nauki = Tambov University Review. Series: Humanities. 2023; no.1: 122-133 (In Russ.).

12. Kuntsevich O.Yu. Modelirovanie protsessa obucheniya v kontekste adaptivnykh obrazovatel'nykh tekhnologii (na primere distsipliny «Bazy dannykh») [Modeling the learning process of adaptive educational technologies (on the example for discipline «Databases »)]. DM = Didactics of mathematics: Problems and Investigations. 2022; no.55: 76-80.

13. Goncharov D.I., Gerashchenkova T.M. Modelirovanie protsessa obucheniya v kontekste adaptivnykh obrazovatel'nykh tekhnologii (na primere distsipliny «Bazy dannykh») [Algorithm for making recommendations in electronic educational environments based on stochastic Markov models]. Sovremennye tekhnologii upravleniya = Modern Management Technology. 2022; no.1 (97). Available at: https://sovman.ru/article/9713/ (In Russ.)

14. Avgustova Yu.V. Vektornaya model' praktiko-orientirovannogo obucheniya v podgotovke budushchikh yuristov v sisteme SPO [Vector Model of Practice-Oriented Learning in the Training of Future Lawyers in the System of Secondary Vocational Education]. Obshchestvo: sotsiologiya, psikhologiya, pedagogika = Society: Sociology, Psychology, Pedagogics. 2022; no.12 (104): 342-348 (In Russ.).

15. Domuzhneva K.E. Modelirovanie podkhodov k obucheniyu informatike studentov sistemy srednego professional'nogo obrazovaniya putem ikh klasterizatsii na didakticheskie gruppy [Modeling of approaches to teaching computer science for vocational students by clustering them into didactic groups]. Vestnik KGPU im. V.P. Astafyeva = Bulletin of the KSPU named after V.P. Astafyev. 2022; no.2 (60): 190-199.

16. Nadezhdin E. N., Fedotenko I. L., Smirnova E. E. Metodologiya imitatsionnogo modelirovaniya pedagogicheskikh sistem [Methodology of simulation modeling of pedagogical systems]. Chebyshevskii sbornik. 2022; №5 (86): 291-304. 17. Shaporeva A.V., Kukharenko E.V., Grigorenko O.V. Primenenie infologicheskogo modelirovaniya pri razrabotke avtomatizirovannoi sistemy otsenki kachestva obespecheniya i organizatsii uchebnogo protsessa pri distantsionnoi tekhnologii obucheniya [Application of infological modeling in the development of the automated system of assessment of the quality of security and organization of the educational process in distance technology of training]. Evraziiskii Soyuz Uchenykh = Eurasian Union of Scientists. 2019: no.3-3 (60): 63-68.

17. Kurzaeva L.V., Chusavitina G.N., Musiichuk M.V. Razrabotka bazy znanii intellektual'noi sistemy podderzhki obucheniya IT-spetsialistov s ispol'zovaniem ontologicheskogo modelirovaniya [The development of a knowledge base of intellectual system of support of training of it-specialists with the use of ontological modeling]. Mir nauki. Pedagogika i psikhologiya = World of Science. Pedagogy and Psychology. 2017; no.6. Available at: https://mir-nauki.com/PDF/99PDMN617.pdf.

18. Tulokhonova I.S. Modelirovanie sistemy obucheniya na osnove tezaurusnogo podkhoda [Simulation learning system on the basis of thesaurus approach]. Vestnik evraziiskoi nauki = The Eurasian Scientific Journal. 2017; no.4 (41). Available at: https://naukovedenie.ru/PDF/86TVN417.pdf. (In Russ.)

19. Ostrenko A.A., Ryzhkova M.N. [Algorithm for constructing an individual learning path]. Nauchnyi potentsial molodezhi – budushchee Rossii. XII Vserossiiskie nauchnye Zvorykinskie chteniya. [Scientific potential of youth - the future of Russia. XII All-Russian Scientific Zworykin Readings]. Murom, 2020 (In Russ.).