Insight into the Morphology of Polyhedra


Irit Wertheim


Nitsa Movshovitz-Hadar



Technion Israel Institute of Technology

Department of Education in Science and technology

Haifa 32000, ISRAEL


Abstract. The impact of visual representations on understanding, and even more so, on actively doing mathematics, has been intensively researched and is widely recognized. This is particularly true for the study of 3-d geometry. What about the role of verbal descriptions - - Are they necessarily needed? Simply redundant? Or are they inappropriate, may be even disturbing???

In this paper we attempt at demonstrating the crucial role verbalization plays as a complementary mode to visualization, for dealing with 3-d geometry tasks, understandably and insightfully. Our claim is that neither visualization alone nor verbalization in itself suffices for meaningful conceptualization.

The cognitive processes involved will be demonstrated in the context of Polyhedra.