This document contains 14 papers selected from those presented at the Seventh Annual Conference of the Research Council for Diagnostic and Prescriptive Mathematics. Categorized as interdisciplinary studies are reports on "Mathematics as an Activity of Our Intelligence" by Skemp and a study on "The Brain Basis of Developing Mathematical Skills: Application to Learning Disabilities" by Kinsbourne. Studies related to young children include one paper on predicting achievement from first-grade interviews by Callahan and Boller and a review of research on young children's interpretation of mathematics pictures by Campbell. Studies of testing and validation include papers by Englehardt, Van Wagenen, and Thomas; McGregor; and Beattie and Harley. Studies on errors and understanding are reported by Rees, Hart, Crawford, DeVincenzo, and Bright and Harvey. Young presents a study on the effects of instruction and field experience with preservice elementary teachers. Finally, Rising discusses "Diagnosis and Prescription for the Research Council on Diagnostic and Prescriptive Mathematics." (MNS)