The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for conservation and summarizes results of some experiments from which this theory evolved. Fuson, Richards, and Briars review the state of knowledge of children's counting systems. In the chapter by Hoemann and Ross, the literature on children's probability concepts is reviewed. Siegel considers how children's linguistic competence interacts with the assessment of logical-mathematical competence. Recent findings from his ongoing studies of mathematical cognition among the Oksapmin tribes in Papua New Guinea are reported by Saxe. Finally, Brainerd outlines a general learning system for certain concepts that is based on a rule-sampling interpretation of a family of Markovian processes. (MNS)