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

Abstract

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.