Category: Geometry

In this paper the authors examine the possibility of differentiating between two types of
nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are
intuitively accepted as such. That is, children immediately identify them as nonexamples.
The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. They describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles.

Although different theories exist regarding the formation of geometrical concepts, in this study they use the van Hiele model as basic framework. Van Hiele theorized that students’ geometrical thinking progresses through a hierarchy of five levels, eventually leading up to formal deductive reasoning. The focus of the study is on the beginning of this development.

According to the van Hiele theory, at the most basic level, students use visual reasoning, taking in the whole shape without considering that the shape is made up of separate components. Students at this level can name shapes and distinguish between similar looking shapes. At the second level students begin to notice that different shapes have different attributes but the attributes are not perceived as being related. At the third level, relationships between attributes are perceived. At this level, definitions are meaningful but proofs are as yet not understood.

Authors: Pessia Tsamir & Dina Tirosh & Esther Levenson

Published online: 25 June 2008
# Springer Science + Business Media B.V. 2008

Books by the Authors

1. The Handbook of Mathematics Teacher Education: Volume 2 (International Handbook of Mathematics Teacher Education)
2. Preschool Geometry: Theory, Research, and Practical Perspectives
3. Implicit & Explicit Knowledge: An Educational Approach (Human Development)