This dissertation reports the results of a one-year pilot study conducted to determine the feasibility of a small group-discovery method with a class of college freshmen studying calculus. The class consisted of twelve volunteer students who had A or B grades in their high school mathematics courses. The pilot class scored slightly better on a final exam than a control section taught by the lecture-discussion system. The pilot class also had a positive or non-negative effect upon students' interest in mathematics and estimate of problem solving skill. A number of problems were stated for further investigation. Contents include: background, the small group-discovery method, classroom organization and social climate, the interaction between the students and the mathematics content, and data analysis. (MP)