There now appears to be widespread agreement that early childhood mathematics education (ECME) should be implemented on a wide scale, particularly for disadvantaged children. Yet little is known about the teaching of early mathematics. The goal of this paper is to demystify the process. We analyze one early childhood teacher's work as she attempts to implement an extended activity on mapping. Her efforts reveal the myriad activities involved in teaching mathematics to young children. Her teaching entails all the processes involved in teaching mathematics to older children, including profound knowledge of the subject matter, pedagogical content knowledge, lecturing, introduction of symbolism, and connecting everyday experience to abstract ideas. Teaching early mathematics to young children is essentially the same as teaching it to older children. The implications of this observation for professional development are enormous: extensive pre-service and in-service education is necessary to train a new generation of effective teachers of early mathematics.