In the article the author discusses problems connected with reflection understood as: a scientific reflection (related to a specific issue), a critical reflection and self-reflection leading to self-discovery and self-correctness, i.e. inner transformation. The author reveals the significance of reflection in the phylo- and ontogenetic development of the human being, in the modification of human behavior, especially in the properly conducted educational process. The analysis of the concept of reflection, as known in the humanities and social sciences, reveals the differences between the reflection and thinking, contemplation, introspection and concentration of attention. The author also points out the present-day problem of reflexivity insufficiency (understood as a mental disposition), related to such factors as information technology expansion, disturbances of the emotional, moral and spiritual harmony in children, youth and the adults, and with the incompetence in using the cultural output. Fully aware of the necessity to counteract the unfavorable phenomena, the author put forward her own proposal for shaping reflexivity of pupils/students in the familial and institutional environments.