Describes the behavior of five calculus professors and their students based on observations of calculus classes. Results showed that the dominant mode of instruction was lecture and students were usually not actively engaged in doing mathematics. (14 references) (Author/MKR)

Analyzes the results of an experimental study of a nontraditional style of teaching, a combination of lecture and group discovery methods. Concludes that students in the study performed better than those in traditional sections, their attitudes towards mathematics improved, and they were positive about the instructional approach. (Author/ASK)

The crisis confronting calculus and mathematics education generally results from a number of failed assumptions implicit in the dominant lecture-homework-exam methodology used in teaching mathematics. Positive resolution of this crisis can be found in adopting a noncompetitive, collaborative approach to mathematics education. (Author)

Reports the results of five contrasts between small-group learning and a more teacher-centered instructional style employed in junior high, high school, and college mathematics classes. In no case did the small-group class perform more poorly than the one led by a teacher; in one case, measuring long-term retention, the small-group class performed…