The educational system of Kazakhstan is now characterized by certain gradual changes of an educational paradigm. The educational paradigm is understood as framework of key provisions and the ideas which are acknowledged by the pedagogical public during the concrete time period and are the cornerstone of scientific research. Change of an educational paradigm includes transition from the education aligned on teaching to the education aligned on training. The criterions for the change of this paradigm are: the education which is more aligned on the student; change of teacher's role; the further definition of the main goal; transition from potential to result; change of the training process The competence-based approach in education also objectively meets both social expectations in education, and interests of participants of educational process. At the same time this approach conflicts too many stereotypes which developed in an education system, the existing criteria for evaluation of students' educational activity, pedagogical activity of teachers, work of administration. Practice of teaching at the higher school showed that the existing crisis in the field of education for a long time is not only overcome, but still is not even fully realized by most of participants of educational process. Explanatory and illustrative didactic approach still remains the leading model in educational process where activity is transferred as the unique content of training. Certainly, it does not meet requirements of time, moreover, contradicts new laws of practice. Now there is an urgent need to train students in the real ways of thinking (the theoretical, dialectic, logical analysis, synthesis, system approach). Developing their creative abilities (ability to apply the acquired knowledge in any situations, including also independent problem definition, and also search of new ways of tasks solution), increasing professional skills of teachers when they can freely carry out pedagogical activity in standard and unusual situations.