The aim of this monograph is to describe a program of research investigating the problem-solving responses of young children and to present in summary form the results of the analyses completed so far. Attention is given to characteristics of clinical studies which are thought to make the clinical method particularly useful with young children. After a brief introduction, the first section describes the research decisions that had to be made either prior to launching the study or while it was being conducted. The second section summarizes results obtained in unique problem situations involving division, space and geometry, reflections in a plane, mirror reflection, coordinates, and factors and sequences. Problem situations devised for the studies, such as cargo groups, fold-out shapes, parking grids and theater grids, are described and illustrated in color photographs and diagrams. Additionally, for most problem situations the mathematical significance of the problem is pointed out and results and conclusions or concluding statements are given. The final section of the monograph evaluates the clinical methodology employed in the studies and considers the contribution of the research to mathematics education. (Author/RH)