This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of…

Attempts to express a group of children's understanding of inversion, retrograde, and retrograde-inversion as it applies to musical composition and color schemes. The children, ages six to nine, displayed idiosyncratic approaches to the problems. Discusses the possible implications for symbolic language and cognitive development. (MJP)