The process of notion formation in mathematics is a series of qualitative changes in which the quantity of life experiences brings about a change in quality represented by the level of abstraction of knowledge. Disregarding this mechanism (e.g. when the teacher introduces new notions by definitions) leads to a formal knowledge of notions. This is a source of misunderstanding in communication between the teacher and the pupil as well as a source of strategic and world outlook misinformation of the pupil. The article contains the description of a teaching method (we have called it the method of combined discussion) by means of which a new notion is introduced in spontaneous classroom discussion. Each pupil actively mobilizes his own experiences, confronts them with the views of his classmates, and thus arrives, in a creative way, at an informal knowledge of the notion.
Examples are given of the method being experimentally tested at Secondary Vocational Training Schools. A pedagogical analysis of this method is made on three levels: the pupil, the class, and the teacher. It is believed that the method can be used in other subjects as well.