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)

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)

Refutes the assumption that large classes must be impersonal, characterized by lecture style, and presented in a theorem-proof-example format. Discusses successful strategies for space use, classroom management, and collecting student feedback. (DDR)

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…