THIS REPORT DESCRIBES THE DEVELOPMENT OF A PROGRAM IN PLANE GEOMETRY AND THE USE OF THIS PROGRAM IN EXPLORATORY RESEARCH TO GENERATE HYPOTHESES ABOUT METHODS OF PROGRAM IMPROVEMENT. AN INDUCTIVE APPROACH, BASED ON AN INTENSIVE ANALYSIS OF THE BEHAVIOR OF INDIVIDUAL STUDENTS IN A SELF-STUDY SITUATION, WAS USED TO DEVELOP PRINCIPLES OF PROGRAM DESIGN AND IMPROVEMENT. A COMMERCIALLY PRODUCED PROGRAM ON GEOMETRIC INEQUALITIES WAS GIVEN TO HIGH-SCHOOL STUDENTS IN A SERIES OF TUTORIAL SESSIONS. AS EACH STUDENT STUDIED THE MATERIALS, THE EXPERIMENTER/TUTOR MODIFIED THE PROGRAM IN VARIOUS WAYS DESIGNED TO HELP THE STUDENT OVERCOME ANY LEARNING DIFFICULTIES THAT HE ENCOUNTERED. SUCCESSIVE REVISIONS OF THE INITIAL PROGRAM WERE PRODUCED UNTIL FORMAL EXPERIMENTAL COMPARISONS SHOWED THAT THE REVISED PROGRAM WAS BOTH STATISTICALLY AND PRACTICALLY SUPERIOR TO THE ORIGINAL VERSION. DETAILED RECORDS WERE KEPT OF THE PROGRAM MODIFICATIONS THAT APPEARED MOST EFFECTIVE IN IMPROVING THE INSTRUCTION. THESE EMPIRICAL RECORDS WERE THEN USED TO DERIVE SEVERAL GENERAL PRINCIPLES OF PROGRAM DESIGN. (WB)