Building the Language of Geometry Through the Use of Examples and Non-Examples

In this study we examine definitions of seven geometric concepts constructed by\ud groups of pre-service elementary school teachers through the use of examples and nonexamples. The structure of the analysis consists of correctness, completeness, generality, and minimality of the definitions. The results of this study provide some insight on what the participants consider a definition to require. This thesis demonstrates how having participants distinguish between examples and non-examples of a concept can be used as an effective teaching tool. The teaching approach presented in this thesis will allow students to be creative in understanding definitions as they are deriving these definitions on their own