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The article is devoted to the formation of intellectual abilities of the students of post- graduate education. Analysis of the pedagogical, methodological, psychological sources on this issue demonstrates the need for the adaptation of existing theoretical propositions to the peculiarities of the educational process in the system of post- graduate education. The article explained the significance of the formation of intellectual abilities at training of competent specialist and considered the features of the implementation of this process in the system of post- graduate education, taking into account the specificity of this form of learning. Especially it concerns the training of teachers, because intellectual abilities are substantive components of their professional competence. From the general structure of post- graduate education of the teachers, special attention is paid least represented in the scientific literature of its elements – obtaining a new teaching or related educational specialty or supplementary education. Considering that in the training of specialists in these categories it is necessary to solve specific pedagogical, methodological, psychological, etc. objectives, the role of intellectual abilities as the ability to replenish their own knowledge and to navigate in the information flow is increasing. The author has modified and implemented in the educational process technology of the stage-by-stage providing of the educational process by O. Chemerys. The article presents a scheme of the stage-by-stage formation of the intellectual abilities of students of post- graduate education and illustrated the features of its realization in the training of teachers of mathematics at the example of study of professionally-oriented educational disciplines, providing methodological training of future teachers («School mathematics course and methods of teaching», «History and Methodology of Mathematics», «Mathematics in educational technologies», coursework on methods of teaching of mathematics, pedagogic practice). For each of the six stages of the system, depending on the levels of mastering of knowledge (according to B. Bloom’s taxonomic approach) – reproductive and productive – the basic educational goals, learning outcomes and tasks are carried out, as well as various functions of intelligence, which in this case developing. Approaches under which this system can be implemented in the system of post- graduate education are considered.
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