The cloud technologies for mathematics teachers training

This article is devoted to modern approaches to interpretations of "the cloud technology", the types of cloud computing application for teachers training are discussed. A comparative analysis of Web-SCM SAGE and The Sagemath Cloud is made.Aim: to do a theoretical analysis of pedagogical application of Web-SCM SAGE and The Sagemath Cloud.Objectives: 1) to make an analysis of contemporary approaches to the interpretation of the concept of "of cloud technology"; 2) to consider Web-SCM in terms of the cloud-based environment; 3) to compare Web-SCM SAGE and The Sagemath Cloud.Object of study: the learning process of university students with the support of cloud technologies.Purpose of the study: to reveal the features of The Sagemath Cloud use in high school.Methods: the study of the domestic scientific pedagogical publications on the problems of implementation and use of advanced cloud technology, and Web-SCM including Web-SAGE and The Sagemath Cloud.Results: advantages and disadvantages of The Sagemath Cloud application in comparison to the Web-SCM SAGE are revealed.Conclusions considered various interpretations regarding the concept of "of cloud technology", comparison of Web-SCM SAGE and The Sagemath Cloud as learning tools.