The urgency of the problem stated in this paper results from the fact that willingness of students to organize future professional activities requires the correction of contents, forms and methods of practical classes on techniques of teaching mathematics, as well as the improvement of programs of all types learning and teaching practices. The leading methods to the problem of the study were: theoretical analysis and familiarization of studies, questionnaire surveys, overt observations, design methods, analysis of creative activity products. The study involved about 1,000 students, 50 young teachers, and 15 university teachers. The main purposes of the study are to identify the means of training future math teachers to enhance learning and cognitive activities of students, to identify the main difficulties of students and young teachers in the organization and in enhancement of learning and cognitive activities of students, and to determine the level of willingness of students to enhance learning and cognitive activities (reproductive, functional, creative).
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