This document focuses on research on the relation between children's use and understanding of counting as a symbol system for number and the development of number conservation concepts. An underlying assumption is that a better match between mathematics curricula and the educational needs of children will be facilitated by learning more about the factors which influence the formation of numerical skills. The research completed is presented in six sections; however section one containing overview articles has been removed from this document due to copyright restrictions. Section two reports on research on counting/number conservation relations. The third portion concerns developmental changes in children's conceptions of conventional counting properties. Section four presents studies of developmental changes in children's use of counting to represent numerical information. Section five discusses research on number concepts in Papu, New Guinea on topics other than conservation. The final portion presents planned research. Also included is a list of conference presentations, articles, chapters, and manuscripts disseminated during the funding period, and a list of additional research proposed during the support time of the projects. (MP)