Works towards a synthesis of metacognitive theories that are implicit in the works of van Hiele and Piaget. Provides greater detail on those theories after describing two features of a good theory of metacognition that prefigure the contrast between van Hiele and Piaget. Contains 17 references. (ASK)

Discusses students' use of visual considerations in doing geometrical proofs. Studies ninth-grade students (n=17) in an academically-selective high school in Jerusalem. Concludes that only three out of 16 students who turned in their papers chose symmetry considerations when working on a proof. Contains 16 references. (ASK)

Investigates the development of shape concepts within an instructional unit on geometric paths, including the role of noncomputer and computer interactions in that development. Concludes that the computer environment and the activities facilitated students' development of their conceptualizations of the properties of geometric shapes and their…

Discusses the issue of proof in school geometry and views dynamic software as an excellent tool for exploration in geometry classes, mathematical practice, and for helping students see that a theorem is true. Argues that justification without proof would be untrue to the theory and practice of mathematics. Contains 32 references. (ASK)

The focus of this article is on the verification processes children use when assessing the equality of parts produced by them when partitioning geometric shapes. Different processes and children's verbal proofs of equality are presented. Activities for mathematics instruction are suggested. (YP)

Describes the typical eighth-grade geometry curriculum (with regard to teacher emphasis on content, time allocations, instructional methodologies, the use of manipulatives, and compared to current research models) of typical (n=109) and enriched (n=23) mathematics classrooms in the United States based on data from the IEA Second International…