The paper deals with the problem of out-of-class students’ independent work in information and communication learning environment based on cloud technologies. Results of appropriate survey among students of pedagogical university are discussed. The students answered the questions about systematicity of their learning activity and propositions for its improving. It is determined that the leading problems are needs in more careful instruction according to features of the task completing, insufficient experience in self-management, the lack of internal motivation. Most of all, students recommend to provide the tasks with detail instruction (oral or written) and to pay attention to careful planning the time that is necessary for full completion of the task. It is pointed that such complicated requirements can be satisfied only by complex use of information and communication technologies as well as the automated system of pedagogical diagnostics. Some requirements for management of students’ out-of-classroom independent work are formulated as a result of this discussion.

The announcement of the 2020/2021 academic year as the Year of Mathematical Education in Ukraine and the adoption of the Concept for the Development of Natural and Mathematical Education (STEM-education) until 2027 were a response to the systemic crisis of mathematical training in general secondary education and training of mathematics teachers in Ukraine. The World focus on the integration of natural and mathematics, informatical and engineering education requires rethinking of the role and place of Informatics as a science, as a study discipline and as a basis of computer engineering in training future mathematics teachers. Nowadays, the teacher of mathematics should be capable for effective professional activity in a rapidly changing technology, educational paradigms and catastrophic educational disruptions, such as the current COVID-19 pandemic.

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