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This book is a thoroughly revised result, updated to mid-1995, of
the NATO Advanced Research Workshop on "Intelligent Learning
Environments: the case of geometry", held in Grenoble, France,
November 13-16, 1989. The main aim of the workshop was to foster
exchanges among researchers who were concerned with the design of
intelligent learning environments for geometry. The problem of
student modelling was chosen as a central theme of the workshop,
insofar as geometry cannot be reduced to procedural knowledge and
because the significance of its complexity makes it of interest for
intelligent tutoring system (ITS) development. The workshop centred
around the following themes: modelling the knowledge domain,
modelling student knowledge, design ing "didactic interaction", and
learner control. This book contains revised versions of the papers
presented at the workshop. All of the chapters that follow have
been written by participants at the workshop. Each formed the basis
for a scheduled presentation and discussion. Many are suggestive of
research directions that will be carried out in the future. There
are four main issues running through the papers presented in this
book: * knowledge about geometry is not knowledge about the real
world, and materialization of geometrical objects implies a
reification of geometry which is amplified in the case of its
implementation in a computer, since objects can be manipulated
directly and relations are the results of actions (Laborde,
Schumann). This aspect is well exemplified by research projects
focusing on the design of geometric microworlds (Guin, Laborde).
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