Contemporary authors emphasise the importance of viewing the family as a specific educational context and of studying its role in the cognitive development. In this paper, we tested the model that postulates the way in which the different ways of parental mediation and various means of the family cultural-supportive system affect the development of formal operations. We assumed that the education of parents and financial status of the family form a wider context that influences the general dimensions of family interaction (emotional exchange and democratism), but also the cultural-pedagogical status of the family, and that their connection with formal operations is mediated by the above-mentioned variables. We expected the education of parents and general dimensions of family interaction to influence the parental mediation characteristic for the development of formal operations, operationalised by CSS scale, and to mediate, via this variable, the development of that form of thinking. The direct link with formal operations is postulated in the case of variables of cultural-pedagogical status and CSS scale. The sample consists of 305 pupils aged 15 to 19. The Structural Equation Modeling was used for testing the postulated model. The results show that there is a direct influence of cultural-pedagogical status and CSS scale on formal operations, but of mother's education as well. Some relations between other predictors were confirmed, and some not, which suggests that the proposed explanatory model must be revised to some degree.