Objective: The purpose of this study is to form the arithmetic musical competency of students on the basis of Al-Farabi's theoretical musical heritage. In this context, the work "The Great Book of Music" is of great importance. In this work, he gives not only a scientific explanation of the origin of sounds as properties of matter but also gives an idea of the arithmetic principles of the emergence of harmony and musical melodies.Background: Musical competence is described as an ability and an aptitude to adequately perceive and emotionally respond (react) to music, to transfer musical perception into the ability to think using artistic images. In school, its formation occurs during the study of a discipline "Music", among special subject competencies that form within this subject an arithmetic musical competence can be distinguished.Method: Judging from the musical theory composition method, Al-Farabi suggests an innovative method to improve the musical development of students with intellectual disabilities which consists of the individual preparation of a training plan.Results: As a result of this study, it was determined that the problem of the formation of arithmetic musical competence in the learning process is relatively new and insufficiently studied. Arithmetic musical competence can be formed on the basis of teaching the method of the musical theory of composition Al-Farabi. Conclusion:The experiment results allows for the conclusion about the advantages of the formation of musical competence of students via knowledge of music theory.
The purpose of the study is to identify the main problems and prospects of the education system in the context of innovative development, as well as the intellectualism of future teachers. The authors of the article conducted a factor analysis of the ongoing reforms in the education system. The transition of the economy to the innovative way of development and the overall socio-economic situation in Kazakhstan and other countries requires a rethinking of some priorities prevailing in politics and focusing on building a new type of society based on the development and mutual integration of three main elements such as education, innovation, and research. These elements are impossible without intellectualism and critical thinking. The formation of innovation policy should contribute to the development of a set of measures in the system of higher professional pedagogical education that organize and stimulate innovative activities and promote the integration of education in the scientific and technical space. This integration process will serve as the basis for the formation of the strategy and tactics of innovative development based on intellectualism and critical thinking.
Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve non-standard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the course of teaching computational informatics, elaboration of constructive computational solution algorithms of inverse problems for differential equations, during which the bachelors and graduate students develop own professional competencies. The research conducted a review of previous literature on the topic. Formulation of the inverse problem for differential equations for the investigation of which the computational mathematics finite difference methods are applied, is presented. In the course of investigation, it was revealed that at elaborating the constructive computational algorithms of its solution, the bachelors and graduate students develop not only fundamental knowledge in the field of applied and computational mathematics, computational informatics methods, but also develop the professional competences, including computational thinking. Key words: professional competence; computational informatics; computational mathematics methods; non-standard.
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