What on earth is a straight line? What can we learn from an epistemological episode in eighth grade?

A detailed account of a spontaneous discussion in eighth grade of the nature of geometrical objects is given and related to constructivistic learning theory. The pupils were quite eager and able to discuss such subjects as infinity and more generally the process of abstraction inherent in geometrical concepts. Discussions of this type in class are advocated in order to encourage pupils to problematize concepts and procedures often regarded as self-evident, to spot and discuss pupils' misconceptions, and thus to attempt to raise the level of abstraction in mathematical communication and concept formation in class.