In this paper the authors demonstrate how play can serve as a space for assessing and promoting children's mathematical thinking. Analyzing data from a larger study of professional development to support culturally and developmentally responsive mathematics teaching in preschool, we found that through Learning Stories, a holistic narrative assessment tool, teachers describe how they explicitly identify the mathematical practices children engage with during play. The structure of Learning Stories provided teachers with a way to think about how they identify and reflect on children's mathematical practices and, based on that understanding, develop strategies for supporting children's mathematical understanding. The purpose of this paper is not to argue for play as the only space for teaching and assessing mathematics in preschools but to provide evidence of what is possible when teachers attend to children's mathematical thinking and mathematize play. (author abstract)