Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

Discusses solving rotation problems and shows that there is an alternative to using mental rotations or their encoding into verbal terms, namely using geometrical properties. Presents an analysis of the functionality and effectiveness of the different kinds of strategies as a function of the task's characteristics. Describes research to improve…

Several examples of concrete mathematical models are discussed along with suggested criteria for good heuristic models. (MN)

Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…