THE DEVELOPMENT OF THE STUDENTS’ RESEARCH ACTIVITY SKILLS WITH THE SPECIFIC EXAMPLE
An opening of the new specialty at the mathematical faculty poses the set of the important problems of the providing the high-quality education for the students. The generalized description of these tasks is to create and support the educational and methodological base, which will ensure the formation of the professional competencies of our graduates. The specific content of these tasks has several components. Let us single out the one that is associated with the specifics of the use of the innovative techniques in the training of the modern teacher. These techniques provide the formation of such important qualities of a specialist as creativity and flexibility of thinking, the ability to make decisions in non-standard situations, the ability to organize and effectively manage the research activities of the students. The idea of writing this article lies precisely in this plane. The article proposes an algorithm for the extracting nth root of the positive number as a generalization of the well-known algorithm for the extracting the square root without using tables and calculators. It has been shown that this algorithm is exact, while the available publications present the algorithms, which are based on the use of the numerical methods, and therefore are approximate. The article provides the justification for the algorithm, which is based on the decimal representation of the number, as well as, an example of its use. In addition to the fact that the algorithm itself is quite interesting and attractive from a mathematical point of view, it provides the possibility to solve several methodological and pedagogical problems. First of all, this example demonstrates the close relationship between elementary and higher mathematics. Further, the possibility of the formation and development of the research competence as an important component of the general professional competence of the teacher of mathematics in the modern school is emphasized. Finally, the material of the article gives an idea that the formulation of the problems for the generalization of the known problems and algorithms is a natural and, moreover, is the powerful source of the research problems.
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