The essence of the concept of critical thinking as a modern pedagogical phenomenon is disclosed in the article. It is revealed that among the most important competencies, which are relevant to the work of a modern teacher, teachers often refer to critical thinking as the ability to critically process various information, the ability to produce ideas, identify strategic issues and solve them, find convincing arguments, take responsibility, defend your position and correct it under the reasonable influence of the opponents. The theoretical foundations of the process of formation of critical thinking of future teachers in the process of professional training at the level of principles, properties, methods, stages are identified. The analysis of the project "The Higher Education Standard of Ukraine" in the field of knowledge 01 "Education" for specialty 014 "Secondary Education", subject specialization 014.04 "Secondary Education (Mathematics)", which provides for the formation of a number of competencies among students is carried out. It is found that the basis of the above listed competencies and learning outcomes is critical thinking. It is proved that geometry (in particular, constructive and projective), its methods and tasks have inexhaustible possibilities and means that can be used as an effective tool for critical thinking formation in the process of professional training of future mathematics teachers. For an example, we solve two problems of Euclidean geometry (a construction task and a proof) with the use of the Desargues theorem- one of the key statements of projective geometry.

The analysis of competences that should be formed in the future foreign language teachers by the tools of modern information and communications technologies is presented by the authors. It is been determined that generic (core) competences include: informatics, informational, organizational and methodological competences; profile (specific) competences include the abilities of information and communications technologies usage for such pupils` skills forming as: listening, speaking, reading and writing. The program of electronic study course to support the realization of abovementioned task is presented. The purpose of the program is to create a modern level of informational and computer culture, acquiring practical skills of application information technologies by teachers and philologists in order to increase the efficiency of the educational process; students of philological specialties and their preparation for the pedagogically effective use of information technology training in further professional activities. The content of the program modules has been given. Module 1. Network technologies in foreign languages, module 2. Office technologies in foreign languages, module 3. Multimedia technologies. The stages of using ICT in education have been identified, they are search, analysis and research of information, software, methodological resources for a lesson preparation with the further discussion; planning of organizational and methodological measures aimed at achieving goals and objectives of a certain lesson type; developing information materials according to the topic and type of lesson using ICT tools; assessment of future foreign language teachers readiness for the introduction of informational materials on the basis of software resources into The Modern Higher Education Review No. 2, 2017 ISSN 2518 the learning process. The usage of ICT for listening, speaking, reading and writing skills forming is demonstrated on the examples of software, on-line services and various podcasts.

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Прошкін Володимир Вадимович доктор педагогічних наук, професор кафедри інформаційних технологій і математичних дисциплін Київський університет імені Бориса Грінченка, м. Київ