Intellectual Growth and Understanding Mathematics. Mathematics Education Reports

This review of recent Piagetian research in mathematics education is divided into three parts. In the first part the author states the assumptions upon which the remainder of the paper rests. These assumptions are based on Piaget's theory of cognitive development and he presents six relevant points. The second part is a review of recent research on pupil's understanding of mathematical ideas. In the research devoted to students in elementary school he examines the child's understanding of number and the growth of spacial and geometric concepts--perspective, measurement in 2 and 3 dimensions, and time concepts. In secondary school research he examines the understanding of proportion, probability, function, and proof. The third part of the paper is devoted to the implications of the first two parts for teaching. The author suggests that elementary schools should be less formal, have more manipulative materials, and provide for more peer interaction. In the secondary school the author suggests more active learning by students, utilization of concrete materials, and provision of time for student initiated questions and answers. An extensive bibliography is included. (CT)