The National Research Council (NRC), through the Center for Education (CFE), wishes to build on the work in early childhood it has already done. In particular, the NRC wishes to focus on research on young children and their learning of mathematical and scientific ideas. The workshop that is the subject of this report, one in a series of workshops made possible through a grant to the CFE from the National Science Foundation, is the starting point for that effort. The center's mission is to promote evidence-based policy analysis that both responds to current needs and anticipates future ones. This one-day workshop was designed as an initial step in exploring the research in cognition and developmental psychology that sheds light on children's capacity to learn mathematical and scientific ideas. The workshop brought experts together to discuss research on the ways children's cognitive capacities can serve as building blocks in the development of mathematical and scientific understanding. The workshop also focused on curricular and resource materials for mathematics and science found in early childhood education settings as a means to examine particular research-based assumptions that influence classroom practice. The sole purpose of this report is to describe the discussions that took place at that workshop. However, issues for further investigation are explored in two afterwords.