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Abstract: The purpose of this work is to offer an active form of training, using the network cognitive information technology which allows to develop the competences determined by the Federal state educational standard of Bachelors in the course of teaching of mathematics. Based on the results of the work of American authors, it is shown that the effectiveness of training depends on the active participation of students in the learning process, as well as the number of students in the group. A brief review of scientific works on the convergent approach in learning is given. It is concluded that the convergence in learning should be understood more widely; it should include the results of the achievements of neuropsychology and philosophy of pedagogy. That is, convergent technologies in learning should include neuropsychology, pedagogical and cognitive information technology. To implement the convergent approach in training, it is proposed to create an internal network e-learning environment based on information technology. The development of such an environment is possible when using the learning management system software — LMS, which can be used as an open-source SOFTWARE, for example, Moodle, GoogleClass, as well as a free cloud service GoogleCloud. It is possible to use the MediaWiki or DokuWiki engines, distributed as free software, to fill the content with didactic materials and to create one’s own wiki-base of knowledge. Thus, on the basis of the convergent approach, the algorithm of curriculum development is proposed, in which the lecture part should be combined with the practice of mastering the educational material within the electronic learning environment, containing a bank of tasks of different levels and contributing to the development of cognitive and metacognitive thinking abilities.