This set of papers was selected from presentations made at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics because of their pertinence to classroom teachers. The papers concern: (1) "Research and Development Related to Learning about Numerals for Whole Numbers: Implications for Classroom/Resource Room/Clinic" (Ashlock); (2) "Levels of Maturity in Diagnosis and Instruction" (Engelhardt); (3) "Teaching Arithmetic: A Diagnostic Approach" (Hopkins); (4) "Using Manipulative Aids to Model Algorithms in Remedial Situations" (Hynes); (5) "A Theoretical Study of the Organization of Basic Addition Facts for Memorization" (Heddens); (6) "How Do You Get Children to Quit Using Their Fingers to Add and Subtract?" (Rathmell); (7) "But I Have 42 Students in My Class" (Connelly); (8) "Implementing Diagnosis in the Classroom" (Inskeep); and (9) "The Role of Dual Programming in Diagnostic and Prescriptive Mathematics" (Wyer). (MNS)