The article describes the problem of awakening the cognitive activity of students, arising due to revolutionary transformations in teaching technologies. It shows the need to study the factors that affect cognitive activity and assesses the information content of those factors. Based on the method of pair comparisons, a technology for ranking the factors affecting cognitive activity has been developed. A mathematical model of the formation and processing of expert assessment results and an example of calculations are given, and the feasibility of including the subsystem for evaluating factors affecting cognitive activity in the computer control system of the university is shown. The structure of an adaptive e-learning system based on the technology of taking into account the factors that form the cognitive independence of students is described Experiments carried out in 3 universities of Ukraine have shown that the use of the developed mathematical model and information technology allows to increase significantly academic performance and to decrease the frequency of refusals from independent work of students using the e-learning environment.