The relevance of the research: For the fourth decade, Russian education system has undergone constant changes at various levels: from preschool to higher education. Accordingly, the process of teacher's professional training is being modernized, including state educational standards, which assume significant strengthening of the role of practical training. In this regard, it becomes urgent to find a balance between the theoretical and practical training of the future mathematics teacher. The purpose of the study is to identify the optimal balance between theoretical and practical teaching in the process of professional training of the future mathematics teacher. The research was carried out based on the regularities of the methodological problems of pedagogical forecasting, including the expert evaluation method, historical analysis, practical methods (questionnaire surveying).
The research objective is to show new possibilities for understanding cognitive interest as one of the indicators of personality development. Based on a systematic analysis, the authors clarified the content of the category of “cognitive interest”. A conceptual model of the dialectic of interest in knowledge was proposed. The principles that are the foundation of the process of its learning were revealed. On this ground, educational technology was developed. Long-term observations of the subjects of the educational process, conducted by the authors, allowed determining the dialectical connections of cognitive interest with thinking, attention, memory, speech, and emotions. The pro-posed model of the dialectic of interest in knowledge is conceptual, since based on it, the process of raising interest is built as a didactically thought-out system for managing children’s development, contributing to their personal growth, one of the components of which is educational technology.
The article considers the necessity, importance and practicability of the digital technologies used in the math education. The purpose of the analysis is to identify the advantages, disadvantages and risks of using digital technologies in the math education. The article includes a review of publications on using digital technologies in education. It is emphasised that in recent years the students' culture of mathematical speech, especially oral, has deteriorated. The students were interviewed to identify the influence of information technology on the math education. The survey was organised among the students and graduates of Yelets State University named after I.A. Bunin and Orel State University named after I.S. Turgenev. According to the survey results, digital learning will have a positive effect on students' motivation, but just for a moment. The comparison of the survey results demonstrates that the students are not interested in the subject of math, but in the form of material presentation, not in the content of the material presented, but in the dynamics of the presentation, i.e. in what is not related to the math education. Key\words-e-learning tools, digital technologies, math education, student training.
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