What About a Learning Environment Where Euclidean Concepts are Manipulated with a Mouse?

Abstract

Some decades ago the idea of microworld was born and it has been extensively used in numerous areas. A main idea with strong implications for learning is the possibility offered by microworlds which embody theoretical domains and concepts into a physical reality within which learners can freely interact. (Thompson, 1987; Edwards, 1991) The kind of learning such microworlds allows has been discussed in particular in mathematics: (1992) point to the play paradox, a tension between the free exploration of pupils playing with the computer and the intention of a teacher who aims for the development of mathematical ideas.

The development of a new kind of interface and the possibility of direct manipulation is now opening a new era. What is the impact of software based on such an interface on the meaning that learners can give to geometrical objects? This paper is an attempt to address this question in the case of Cabri-géomètre (Laborde, 1986), an intelligent microworld with direct manipulation in the field of geometry. The discussion is not confined solely to the case of Cabri-géomètre: It could also embrace other modern geometry computer-based environments, e.g., the Geometer's Sketchpad (Jackiw, 1990).

After a short presentation of principles underlying the design of the software (Section 1), die chapter presents in Section 2 two aspects of geometry which can be enhanced by the use of the software and which are absent or neglected by traditional teaching: the distinction between graphical phenomena and geometrical properties and the modeling power of geometry. In Section 3, we propose some features of the interaction between the learner and the software which are due to characteristics of the software and which may have an impact on learning. This is illustrated in Section 4 by a solution to a problem discussed at the workshop gathering the authors of this book. Finally some principles underlying the design of learning situations and deriving from the preceding analysis are proposed in Section 5.