This article addresses the question of what is considered possible – desirable – plausible in preschool mathematics. On the one hand, there is a growing consensus that preschool mathematics matters, on the other hand, there are different opinions about how it should be designed and what constitutes an appropriate content. In the article we provide an overview of similarities and differences found in eight articles published in a thematic issue of NOMAD on preschool mathematics. The overview is based on Bernstein’s notions vertical and horizontal discourses, and how content for learning is described as basic or advanced mathematics. The aim is not to evaluate or rate the articles but to illustrate diversity regarding possible – desirable – plausible in current research of preschool mathematics.