The essay on thinking of thinking. The article is motivated by the 80-th birth anniversary of outstanding psychologist and pedagogue V.V. Davydov who was engaged, in collaboration with D.B. Elkonin, in elaboration of psychological foundations and pedagogical practices of developing education. The program he has devised focused on the advance of schoolchildren’s capacity for theoretical thinking and formation of readiness, inclination and capacity for conceptual thinking. An attempt to apply V.V. Davydov’s ideas to analysis of the thinking per se is made. Special attention is given to reflexion and intuition.