Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

Discusses a new approach to mathematics education that moves away from methods that tell students what to do and toward methods that help students build mental representations of mathematical concepts. Contrasts the previous and emerging views and examines aspects of the new approach. (26 references) (MDH)