  The article describes the advisable ways of the cloud-based systems use to
support students collaboration in the process of math disciplines learning. The
SageMathCloud-based component that aggregates electronic resources for several
math disciplines training is introduced. The learning technique of the
SageMathCloud use in the process of educational staff training is proposed. The
expediency of this technique implementation for more active take up of
innovative approaches, forms and methods of math training with the use of the
cloud-based tools is substantiated. The experimental results of the
SageMathCloud learning component introduction research along with the methods
of its use that were elaborated in the course of the study are presented. The
use of the evidence-based technique as improving the educational environment of
the univer-sity, empowering access to electronic learning resources in the
course of math training and engaging with this the educational community and
also rising their ICT competence is grounded.
