The article gives an account of psychological content and peculiarities of problem solving by an individual, and the role of problems in instruction is determined. It contains an analysis of the dependency between the problematic level of instructional tasks and the extent of productivity of students thinking. A theoretical model of the levels of problem solving by the students which covers both actual and approximate development zones (L. V. Vygotsky), is suggested. Within the framework of the model four structurally and functionally different levels of problem solving are shown, basing on two grounds: the extent of novelty and originality (correlation of productive and reproductive processes), and the level of extension of thinking process (interaction of intuitive and discourse processes). Psychological and pedagogical demands to selection of a system of problems for instruction, which arise from analysis of the model, are described in the article.