The paper is concernedwith the attitudes of teachers of mathematics to the sharing of educational competencees between school and family. It is based on the analysis of interviews with 60 teachers of mathematics at basic (elementary) schools and the lower level of gymnasia (academic secondary schools) with early entry, which were conducted as part of the research project “Critical Points in the Teaching of Mathematics”. Across a range of areas the teachers spoke about different aspects of the family background of pupils, and expressed their views on the existing and ideal relationshp between teachers and parents. Qualitative analysis of the interviews focused on the teachers’ conceptualisation of “home preparation” and its connection to the school success of children. The paper shows the expectations of teachers with regard to pupils’ parents and the role of parents in the degree of success of pupils in mathematics. The view “over” the boundary of school teaching (i.e. what happens and should happen in home preparation), also reveals what is happening inside the boundary, i.e. what teachers see as the core of school mathematics and their educational approach.