The purpose of the scientific article is aimed at studying the features of students’ competenceformation at tertiary educational institutions by practical training aids. To reveal the purpose of a scientific article, methods of theoretical analysis and synthesis have been used (to study the theoretical framework of students’ competence formation at tertiary educational institutions by practical training aids) and methods of comparison, grouping and concretization (to analyze and assess the practical results of students’ competence formation at tertiary educational institutions by practical training aids). The practical results of the study are presented through: the results of assessing students’ knowledge of Mathematics, Reading and Science, according to the PISA program; dynamics and structure of the number of students enrolled in tertiary education; the proportion of undergraduate students in% of the population at the age of 20-24 years old. According to the results of the PISA program, developed by the Organization for Economic Cooperation and Development (OECD), it has been found that Austria, Belgium and Germany have the highest average scores in Mathematics, Reading and Science, compared to the average scores in OECD countries. It has been established that in Ukraine the average students’score in Mathematics in 2018 is lower than the average score in OECD countries by 21 points, in Reading - by 36 points, and in Science - by 20 points. In the course of the study it hasbeenestablished that currentlyeducators use the following practical training aids for the formation of students’ competence in the learning process, namely: introduction of a modular academic program in the educational process, providing the necessary level of theoretical basis, implementation of introductory,educational, training, undergraduate practices, work experience internship in the educational process of students’ training, application of information, innovation and interactive technologies in the educational process, teaching and training of students in accordance with the requirements of the labor market and employers, ensuring cooperation between tertiary educational institutionsin the framework of student exchange programs.

The phenomenon of talent and giftedness is the driving force of innovative progress, but the lack of a clear definition of this concept hinders the development of a clear system of training and upbringing of capable children, which has led to the relevance of the study. The purpose of the scientific work is to compare foreign views on the interpretation of the concept of “giftedness” for further borrowing of educational methods of training in the Ukrainian scientific space. General research methods, in particular structural and comparative analysis, including the synthesis method, allow achieving this goal. The article highlights the main theoretical concepts of giftedness in foreign and Ukrainian discourse. In this context, the problem of identifying the concepts of “giftedness”, “talent”, and “abilities” is considered. The views of foreign scientists on the interpretation of the phenomenon of giftedness are presented. It is found that many scientists consider certain aspects of giftedness in relation to related humanities, including history, anthropology, psychology and cultural studies. Examples of the main models of the structure of giftedness in the context of historical development are given. Based on the conducted categorical analysis, the author’s definition of the concept of “giftedness” is suggested, which is identified through such structural elements as the basis and factors of giftedness, experience, and favourable environmental conditions. The concepts of giftedness considered in the article allow stating that they have not only a theoretical but also a practice-oriented character since they are aimed not only at interpreting the phenomenon of giftedness and mechanisms of its development but are the theoretical and methodological basis for systematic activities with gifted children