Malygina O.A.

A concept of modernizing the Russian science and education constitutes education of a new quality, which comprises developing competencies which help acquire experience of independent work, personal responsibility, self-development, raising qualification independently, ability to coordinate his/her own activity with partners - activities, and being competitive. The active use of modern technologies in education help develop such competencies. The system and activity-based approach ensures achievement of goals of teaching. This approach is based on psychological theory of human activity and concepts of system investigations. How the system and activity-based technology is implemented is demonstrated on a higher mathematics discipline for students studying high technology sciences. The experimental model is realized at the Moscow State Institute of Radio-Engineering, Electronics and Automatics. The experimental model is built on the following principles: a system attitude to working out the content of the higher mathematics course; description of a discipline of higher mathematics as a whole of general, specific and particular; optimal combination of fundamental knowledge and professional skills of teaching higher mathematics in a technical university. Also demonstrated here is a principle of differential attitude to the subject-s activities when studying higher mathematics; developing nature of teaching; integration of modern technologies in teaching; a single experimental program for training the teacher and student taking into account differences of the subjects involved. The article also shows the results of implementation of the system and activity-based approach for students who study higher mathematics within the advanced sciences discipline. A system is presented here of qualitative and quantitative parameters of estimation of the developed competencies of today-s certificated specialists, bachelors and masters of science. The qualitative parameters include form of development, generalized character, widespread of procedures, sphere of realization, and acquiring actions; worthiness of application, conscious perception, abstract nature, durability; content of approximate basis of activities. The teaching results revealed that it is important to check understanding of mathematical and methodological components of the teaching process (a method of system analysis, a synthesis method, a method of mathematical modeling, ability to put forward hypotheses, checking and proving those hypotheses). The most important criteria of learning efficiency include ability to use general scientific and mathematical methods in solving applied tasks, tasks of graduation project design work and diploma paper; ability to obtain independently new knowledge from different fields of knowledge; and development of thinking