| Summary: | The development of the information society and technological progress are significantly influenced by the learning tools. Therefore, to the variety of tools that could be used to support the study of any discipline new ones emerging lately are continuously being added. Along with the great deal of systems of computer mathematics (SCM), web-oriented versions of SCM mathematical applications and other math learning tools the cloud-based versions of mathematical software such as MapleNet, MATLAB web-server, WebMathematica and others are now being used. These tools accomplishment becomes the essential part of training mathematics teachers. Domestic and foreign experiences of using cloud services for forming professional competences of mathematics teachers are analyzed. The place of the CoCalc within the system of mathematical disciplines learning tools is investigated. The task of improving the math teachers’ ICT competence by means of cloud services use in the process of training is considered. Among the new forms of learning rising along with the cloud services dissemination are such as collaborative learning, inquiry-based learning, person-oriented learning. At the same time, the use of the appropriate cloud service in the study of some mathematical discipline improves the assimilation of the learning material and improves the knowledge acquisition process on most topics. The analysis of current research of Ukrainian scientists on the problem in question shows that the progress is underway as for further elaboration and implementation of new learning methods and techniques of using cloud services in the higher education institutions.
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