Teacher-child interactions in preschool children's play may enhance mathematics learning in several ways. As teachers interact with children, they may promote more complex, independent, and symbolic play. Resulting increases in play abilities, in turn, can enhance intellectual growth, including mathematical thinking. Teachers may also facilitate math learning directly by engaging children in mathematical thinking as they play. The purpose of this study was to examine the effects on math learning of interactions that enhance play, itself, and those that directly engage children in mathematical thinking. The classroom play interactions of 47 preschoolers and their teachers were video recorded and analysed. The relationship between specific teacher-child interactions -- both enhancing play strategies and promoting math approaches -- was examined. Pre-test and post-test scores on the Test of Early Mathematics Ability, Third Edition (TEMA-3) showed that three play interactions predicted growth in math learning: 'good-fit' interactions to support play, itself, and number and math communication interactions. Findings confirm that teacher interactions in children's play can have an impact on academic performance. Interactions that are a good fit with what children are currently playing and those that prompt children's thinking about number or engage them in communicating about math enhance early math performance. (author abstract)