Discusses an activity-based, exploratory-centered model of instruction based on the Piagetian theory of developmental learning that bridges the gap between the expected and actual levels of student reasoning. Applies the method to learning the mathematical concepts of circumference, area and volume, and division by zero. (22 references) (MDH)

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

Uses small axiom systems to teach logic and reasoning to first year mathematics students. Incorporates a collaborative technique to train students to write formal arguments in a nonintimidating atmosphere by applying logic informally to small axiomatic systems. Provides examples of student-designed systems. (MDH)