The article is dedicated to the possibility of constructing a system of development of mathematical abilities of students of technical profile in the modern University. The components of the mathematical education in the technical University are defined. The necessity of building the concept of monitoring and assessment system development of students, as one of the strategic components of the directions of development of mathematical disciplines is proved. This task must be solved within the framework of individually oriented education, since the distribution of the parameters of cognitive abilities and adaptive capacity of the person is individual. In the context of the competence approach the personality-oriented optimal mathematical strategy of education with an appropriate system of monitoring and evaluation aimed at forming abilities of the student preparedness for further educational-professional activity must be well organized. One of the main objectives of fundamental based mathematical education is the development of cognitive abilities of students. Modern researchers in the field of psychology recognize the need of introduction not only of the parameters of cognitive abilities such as speed of learning, memory, intellectual abilities, but also the criteria by which to determine the level of human intelligence. It is proved that with systematic training to develop the cognitive abilities: speed of learning, memory, intellectual ability, increases cognitive potential of the individual. At the technical University the basic mathematical disciplines contribute to the development of cognitive capacities: memory improvement, increase in speed of acquiring knowledge, the identification of intellectual capabilities. Accumulated qualitative leap in the development of cognitive abilities provides favorable conditions for the formation of mathematical and professional culture of the future specialists in a complex modern society. In the technical University discipline “Higher mathematics” students obtaining bachelor’s degree study during the first two years. It gives the possibility of constructing the system for the development of mathematical abilities, as a component of cognitive potential of the individual. To ensure orderly development of cognitive abilities the system of monitoring and evaluation of the degree of improving memory, increasing speed of learning, identifying intellectual capabilities is necessary. In our opinion, there is a real need for building the concept of monitoring and evaluation of the development of the abilities of students, as one of the strategic components of the modernization of mathematics education in the system of continuous professional education.