Exploring visible mathematics with IMAGINE: Building new mathematical cultures with a powerful computational system

Abstract

In our paper we explore how programmable pictures together with events, parallel independent processes and direct manipulation tools can be used for building powerful interactive visual elements and provide rich environments for exploring basic mathematical concepts. To visualize the concepts we use IMAGINE turtles, the shapes of which are specified by the Logo language. Thus we achieve high interactivity in the resulting microworlds. Children can easily create such objects, control them, combine, move, group, match, etc. We hope that new features of IMAGINE will inspire math teachers and developers to create new visible math educational materials. © 2003 by Springer Science+Business Media New York.