Contradictions of a mathematics didactic system in the realization of a traditional study model

Contradictions of a traditional didactic system impeding the realization of a varied higher edu­cation mission have been revealed: between the objectives – to train abilities of learners – and the content provided as status quo knowledge; between the objectives and incompatibility of teaching forms. A lecture, the main teaching form in a traditional study model does not motivate to be an active participant of the process. A student is only a listener trying to perceive what is said by a lecturer, whereas abilities are trained through intensive activities of a person itself and higher cognition goals may be achieved by allowing for expression; between the objectives and the exis­ting assessment system stimulating to reproduce knowledge, but not to demonstrate abilities and comprehension; between the experience of a learner and abstract conceptions perception of which is difficult for a mass student, thus he is not able to absorb them; between the incumbency of a lec­turer and his possibility to realize it. A lecturer is a researcher. A traditional study model provides no possibility for accessing thesauruses of students, and therefore restricts the research of students' learning; between the necessity for deep realization of learning strategies and a possibility to do it.