Gavrilina O. Methods of forming mathematical research skills in the process of in-depth study of the elements of the integral calculus

The thesis proposes scientifically based and experimentally confirmed methodical formation system research of mathematical skills during in-depth study of mathematics in secondary schools. Structural components are identified in senior research skills, the place and role of study of integral calculus in school mathematics courses, usefulness in the development of research skills of students and ways of forming research skills pupils in learning elements of the integral calculus are determined, the system of grading students' research skills of students is offered that meets modern requirements of student achievements for the 12-point scale. Significant premises, that are conducive for forming of the research mathematic skills during in-depth studing of elements of integral calculus are: age-related and psychological features of secondary school pupils, realization of competent, personal-oriented approaches to the studing abidance of such principals of forming the search pupils skills as: wide treatment of meaning "research", independent value of general research skills,intersubject,integralness,continuity,motivation,scientific,differentiation and individualization of studing. The methodical system components are devised that form educational research skills in the process of studying integral calculus using pedagogical tool "GRAN1", "Mathematics 5-11 class. Practical work". Key words: senior research skills, pupils' research, methodical formation system of pupils' research skills.