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The article presents the results of research work on the formation of cognitive flexibility (CF) as an essential competence of the future teachers’ multicultural personality. It has been shown that various branches of knowledge (psychology, philosophy, clinical medicine, pedagogy, and others) contribute to the scientific and theoretical substantiation of CF, which is included in the TOP-10 most requested competencies in the XXI century. Based on the analysis of the essence and nature of the future teachers’ multicultural personality, the hypothesis that the competence of CF should become a vital component of personal development was put forward. To test this hypothesis, a pedagogical experiment was organised, which covered 33 future teachers studying "Educational, Pedagogical Sciences" at the Precarpathian National University (Ivano-Frankivsk, Ukraine). The experiment was conducted in four stages: on the first preparatory stage, a defined program of experimental activities was made; on the second statement stage, the diagnosis of future teachers’ CF levels was set on the basis of the developed prognostic tools (the Questionnaire Cognitive flexibility was created to define the main features of CF as a component of multicultural competence of the future teacher, tests); on the third formative stage the approbation of our methodology for the formation of CF was carried out, which had no analogues in modern education and pedagogy (this was implemented on the basis of our own special course "Cognitive flexibility and multicultural competence of the future teacher", which was held as a training seminar); on the fourth control stage the results of the experiment were determined. They showed that the indicators of CF formation of future teachers at a high level increased from 9.1% to 41.5% (4.7 times), at the medium level they decreased from 63.6% to 53% (1.2 times). At the low level, they changed from 27% to 5.5% (4.9 times) according to four defined criteria (cognitive abilities, adaptive abilities, flexibility of thinking, and emotional flexibility). This proves the effectiveness of the authors’ methodology for the formation of CF as a basic competence of the multicultural personality of the future teacher. It can be widely used in the training of specialists in various specialities.
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