Organizing adaptive learning with the help of a cognitive-activity matrix: mathematics in a university

In an era of rapid progress in modern technology, there is an urgent need for effective exchange of knowledge, experience and skills. The catalyst for social, economic and cultural development is the transformation of the structure and content of higher professional education, which is aimed at developing its fullness and diversity. In turn, new information needs arise that determine the configuration of the modern information environment.At the same time, the development of new training formats, for example, mobile and distance learning, contributes to the need to create innovative training systems and tools for their development. Modern higher education institutions have high potential for introducing ad-vanced forms and methods of education. Such resources include not only the material and technical base, qualified engi-neering and pedagogical personnel, but also the possibility of promptly developing new approaches to teaching various disciplines, in particular, mathematics.It is worth noting that not all methods are fully aimed at taking into account the peculiarities of the level of training of students in higher educational institutions. As a result, an urgent task is to develop innovative principles for building adaptive training programs.We propose to use an informative - activity matrix when solving mathematical problems at a university, in particular, when studying the topic "Derivative of a function and its applications." We have presented problems of various levels of complexity for calculating derivatives using an cognitive-action matrix, and also consider the solution of a professionally directed problem.