The study deals with issues regarding educational relations in a family and parental aspirations in the conditions of current social changes. The contemporary social context as an implication of the transitional processes brings changes permanently in the sphere of upbringing and education. In the complex constellation of relations between the society and upbringing, there are changes of the external character - at the level of changing social educational institutions, but there are also internal changes that deeply upset the family and affect the performing of its educational function. The changes in a contemporary family reflect on the educational relations and the course of parent's educational role. In a society of a disturbed system of values, the issue of achieving motivation development in family education becomes very important. Can a school offer some solutions, what do parents think about their children's education, how do they affect the development of achievement and success motivation - are just some of the questions which we will try to answer. The study represents a part of a larger research conducted in a group of 304 children and their parents in the area of the city of Niš. The research results point out the existence of parents' high aspirations in relation to the children's achievements at school.