This article investigates a map-drawing activity in a Swedish preschool from the perspective of how children are positioned as being or becoming mathematicians by the children themselves, the teacher and the researcher. The children positioned themselves as being mathematicians, who were capable of expressing and using their own experiences and skills. The researcher also focused on the children’s expertise and so positioned them as being mathematicians. Nevertheless, there were times when the children acknowledged their need for more skills and knowledge to solve a problem and thus positioned themselves as becoming mathematicians. Similarly, some of the teacher’s questions also focussed on developing children’s mathematics skills, which thus emphasized children’s incompleteness or state as becoming mathematicians. By contrasting the teacher’s role with those of the children and the researcher, it is possible to identify how the teacher affects children’s socialisation and learning through her questioning.