The growing heterogeneity of mathematical knowledge, generated, in particular, by the introduction of concepts of an ever higher level of abstractness, creates local insurmountable obstacles for students at all stages of education that stop thought. To actively get students out of such dead ends, special personally oriented teaching methods are required. The article provides examples of such methods and techniques and shows that they can give a lasting positive effect.

mathematical education, nonlinear models of educational processes, impulse learning methods, synergetics