Under the pentagonal principle, a class is divided into groups of five (or six) to complete a discrete learning task, which is divided into five bits. Students take turns presenting the bits; if one fails, the group takes over. In this rotation, each student leads at least once in the session; the group verifies all steps. The instructor acts mainly as consultant. The principle is illustrated here with a course in math or philosophy. The outline allows for varied student interests; shows progress from strict first objectives to more flexible ones (through small group rather than lecture sessions); gives direction in the use of the textbook (Copi's SYMBOLIC LOGIC); sets up relationships among the instructor and students as individuals and as learning team members. Expected outcomes were: various interests would be generated; four to six student leaders would emerge; students would help each other; they would use the library more; their anxiety about grades would lessen; some would reach an A grade before end of term; behavior would be reinforced with little pressure from the teacher; average learning team size would stabilize at five; ten or fewer would have trouble adapting to the learning style; some would settle early for a C or B and become less attentive. At quarter's end, some groups met most expectations; some held stable and highly motivated; others were distracted by other classwork; many opted for extra sessions; students exhorted each other to study; they learned to function as group members. (HH)