Mathematics with Component-Oriented Exploratory Software

In this paper we discuss a component-oriented architecture which we are employing to develop programmable exploratory software for mathematics. We argue that the architecture can be used to provide synergy between end-user programming and efficient behavior of components, i.e. Computational objects of a wide range of technical complexity and functionalities. We give examples of components with mathematics in their behavior and components which in themselves embody mathematical relations. Through both formal language and visual means, users can link them to form creative configurations with interesting functionalities and use the resulting environments for exploratory activity. We conclude that this architecture enables a more efficient collaboration between technical and educational expertise in developing exploratory software. This revised version was published online in July 2006 with corrections to the Cover Date.