The article deals with the problem of psychological mechanisms of development of students’ mathematical research abilities in the process of solving mathematical creative tasks. It is indicated on the growing role of mathematical knowledge in connection with the implementation of a new, broader approach to the social functions of the school. Therefore, the formation of creative, research thinking, high level of need for achievements of schoolchildren is, of course, an important task of modern education, in particular its intermediate level. In order to develop the flexibility of thinking, developed and proposed to students of the upper classes, three types of problems with gradually increasing complexity: analytical and synthetic problems, problems with different degrees of assistance, tasks of self-research orientation. The results of recent researches and publications on psychology of creative activity, specifics of the process of formation of mathematical abilities are analyzed. The definition of concepts of research abilities, research mathematical abilities is given. The relationship between research abilities and the development of the problem of creativity psychology has been established. It was created the methodology for the development of components of mathematical research abilities of pupils in the process of carrying out special classes, which was focused on the development of separate components of mathematical research abilities. It has been confirmed that specially organized training positively influenced the development of structural components of mathematical research abilities of senior pupils. It is indicated on certain differences in the definition of research abilities in psychological and pedagogical literature, in revealing the essence, structure of research abilities, which affects the absence of valid methods of their detection. This is precisely why we can explain the inadequate development of this problem in methodological, theoretical and practical plans. It is proved that the senior school age is the age of development of the pre-professional scientific orientation of the person, in particular research abilities. The research mathematical orientation of high school students is manifested in the ability to quickly and easily find original, non-standard ways of solving problems, to investigate problems for compatibility and sufficiency of data, to establish cause and effect patterns. It is confirmed that the role of the motivational-personal component of mathematical research abilities is increasing among the high school students, namely: the interest in mathematical thinking is increasing, the desire to learn new is growing, showing persistence, determination, commitment and so on.
Junior high school mathematics teachers’ knowledge in calculators