This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

First language and second language learners have to learn through making mistakes. Foreign language learners do not have to learn, to anything like the same extent, in this way. Foreign language teachers should study students' mistakes in order better to understand how they are learning and mislearning. Teachers should try to avoid language…

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…