Research on the characteristics of individuals who have demonstrated a high level of ability in mathematics is presented. The importance of structure in mathematical thinking is stressed and implications for teaching are detailed. (MNS)

This brief report focuses on the cognitive level of decimal problems in 16 textbooks. Activities at the application level are included, but seldom are higher-order intellectual behaviors found in the books. (MNS)

Research on when and how geometric concepts are learned is briefly discussed. Several teaching suggestions are included. (MNS)

Research on fractions and decimals is reviewed. Understanding is vital, and thus children need experiences with concrete materials for the various interpretations of rational numbers. (MNS)