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The article makes the attempt of the theoretical understanding of the essentiality and peculiarities of situational tasks out of methods of teaching mathematics, defining their place and role in the scheme of training future teachers of mathematics, typing them for various signs. The absence of the tough conditionality of the content of methods of teaching mathematics (unlike the science of mathematics itself) as one of the basic professionally oriented courses in pedagogical universities, situational and multivariate methods, which are inherent for it, allow the wide implementation of the method of concrete situations in the scheme of the teacher training. It was concluded that on the basis of generalization of many years of authors’ experience in the training of the teachers of mathematics, that the systematic use of situational tasks out of the methods of teaching mathematics has significant advantages in comparison to the traditional reproductively informative angle to the situation. It is shown that situational tasks out of the methods of teaching mathematics is a specialized way for creating the competency oriented learning environment for the establishment, development and self-identity of the student as a future teacher of mathematics. It is emphasized the effectiveness of using the situational tasks in the modeling creative activity and independence of the students, skills of interpersonal communication, enhancing motivation and emotional factors in the acquiring the profession by them. (Authorial practical manual out of the methods of teaching mathematics, which offer more than 1,000 situational tasks and exercises have been tested for over twenty years.) Examples illustrated that in the process of quasi-professional practice in this environment the student receives the product of education, the essence of which is primarily in the acquiring by the future teacher of mathematics the subjectively new professionally-relevant knowledge and initial experience of practical implementation of leading professional ways of varying degrees of generality, forming of readiness and capability to found a systematic way to solving problems that arise in the practice in work of mathematics teacher. Soundly, that the expediency of creation and use of the scheme of situational tasks out of methods of teaching mathematics as a productive foundation of dynamic combination of theoretical and practical components of methodological training of the specialists.
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