Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

A study was conducted in Israel to determine effects of external similarity in problem structure on students' responses. Fifty students from each of the 7th, 8th, 10th, and 12th grade levels were presented with three problems involving successive divisions that were similar in structure. The problems asked separately whether the processes of…

The main thesis of the paper is that geometry deals with mental entities (the so-called geometrical figures) which possess simultaneously conceptual and figural characters. The paper analyzes the internal tensions which may arise in figural concepts because of their double nature, developmental aspects, and didactical implications. (Author/MDH)