Harnessing the power of programming to support explorations in Euclidean geometry

The development of a Logo–like microworld tuned to a specific domain (Euclidean geometry) is reported, together with the educational experience gained. The importance of a specialised programming language in the pursuit of improved learning is considered. A case is made that in order to be educationally powerful, the learning environment should provide flexible tools for defining notions as well as expressing, articulating and experimenting with new ideas. These tools should facilitate problem–solving, promote student and teacher individualisation, and support clear communications. Some representative examples are considered in the context of the latest version of Geomland – a mathematical laboratory in Logo style, designed, developed and experimented on by Bulgarian researchers. The style of guided explorations and discoveries tested in both a school and a university setting is discussed.