The mathematical competence of Olympiad participants as an indicator of the quality of mathematical training level

Introduction. The relevance of the research on the formation and assessment of the level of development of competencies in the mathematical educational field is due to the fact that the subject competence of the participant of the Olympiad predetermines his victory in the competition. And the Mathematical Olympiad, as a form of education, has potential not only for the formation, development, but also for determining the level of mathematical competence of its participants. The research problem is to justify the didactic potential of the mathematical Olympiad as a tool for determining the level of mathematical competence of school students. Aim of the study: to theoretically substantiate, develop and specify the content, indicators of mathematical competence of mathematical Olympiad participants Methodology and research methods. The methodological basis of the study is determined by: the activity and competence-based approaches to teaching; a retrospective analysis of psychological and pedagogical studies affecting the formation and development of key and subject competencies of schoolchildren; an analysis of the content of mathematical Olympiads; an analysis of the results of Kyrgyz Republic schoolchildren in international mathematical Olympiads; the study and generalization of the experience of juries of Olympiads. Results. The subject Olympiad forms a competence-based educational environment in which the levels of formation of key and subject competencies of its participants are most fully displayed. The competence-based approach to training in the Olympiad environment is characterized by the formulation of objectives from the point of view of the activity approach to the formed competence. Subject competence is leading in determining the quality of the student’s Olympiad activity. The mathematical Olympiad is one of the effective forms of both the formation and development, and the determination of the level of mathematical competence of its participants. The introduction of presented system for preparing schoolchildren for mathematical Olympiads, using model’s formation of mathematical, informational competencies in the experimental group, led to an increase in students' knowledge of the theory and practice of solving Olympiad problems in mathematics by 12,95%; the qualitative indicator of knowledge of the school curriculum in mathematics increased by 15,25%. The index of absolute indicators in the experimental groups in the theory of Olympiad mathematics was 53,12%, in the methods of solving Olympiad problems – 55,38%. In control groups, these indicators were 41,23% and 42,36%, respectively. The qualitative indicator of exam results of schoolchildren of the Olympic reserve turned out to be 19% higher. The results of the questionnaire survey participants of the Olympiads confirm the expediency of using technology for the development of critical thinking, the project method of teaching, ICT in the process of preparing for the Olympiads, contributing to the emergence of motivation to study an extracurricular course in mathematics in 68% of students, 42% of students showed a desire to participate in the Olympiads. The results obtained confirm our conclusions that the development of the mathematical competence of the participants of the Olympiads is successfully realized only in a situation of continuous Olympiad activity.