Abstract
The relevance of the problem under consideration. In the process of training at the pedagogical university, the educational activities of future mathematics teachers should acquire the features of his professional activity, so in addition to mastering knowledge, must have the ability to control mental processes, justify, identify problems and find their own solutions, be able to defend their opinions, choice of elements of educational content and teaching methods in lesson design. These provisions intensify the problem of developing critical thinking of future mathematics teachers in the process of their professional training. The purpose of the study is to reveal ways to organize the process of professional training of future teachers of mathematics, which will contribute to the effective formation of their critical thinking in the study of professional mathematical disciplines. Research methods: theoretical: analysis, systematization and generalization of pedagogical and psychological research. Critical thinking is the most important component of the training of future mathematics teachers. Critical thinking of the teacher is generally defined as a type of evaluative thinking activity, based on the formed skills of a certain type, which contributes to the understanding of theoretical knowledge, translating them into practical activities and predicting results. Methods of training future teachers of mathematics, focused on the formation of critical thinking skills, includes the organization of the educational process based on involving students in active cognitive activities using various methods of working with information and development of specially designed sets of tasks.
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