Play-based preschool pedagogy usually relies on informal teaching while policy trends and some research call for increased formalisation of the pedagogy. Using Bernstein's concepts of classification and framing, this article characterises mechanisms that link evaluation of preschool to the push towards the formalisation of teaching in preschool. Moreover, it is suggested how preschool teaching of mathematics can be conceptualised in a way that widens the pedagogical responsibilities of the teachers to include a broader range of social activities than typically expected. These responsibilities concern how teachers are involved in pedagogical situations, if situations are planned and if the mathematics is a pedagogical goal in the situation or instrumental in some other activity. It is argued that a practice built on these principles could both honour well-developed play-based preschool practices and provide a structure for teaching preschool mathematics in which using traditional child-teacher interaction is only one of many options. (author abstract)