In this paper we 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. We describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles.
Pessia Tsamir, Dina Tirosh and Esther Levenson (all from Tel Aviv University, Israel) have written an article about concept formation in kindergarten children in Educational Studies in Mathematics. The article is entitled: Intuitive nonexamples: the case of triangles. Here is the abstract: