The aim of this paper is to show how preschool teachers interpret the goals set for mathematics in the Swedish curriculum. A didactic perspective has been used to understand what mathematics for young children is according to preschool teachers’ interpretations and how the goals are transformed according to the examples preschool teachers use to illustrate their points. In relation to the interpretation of the curriculum and the didactical questions, I will try to highlight the expectations that preschool teachers have of children and mathematics. To define and understand what these expectations are, I will introduce to my study the concept of didactic contract as a metaphor. My use of a didactic contract does not imply that I am importing the general theoretical framework of the theory of didactical situations. Instead I use some of the elements of the didactic contract in order to focus on expectations.