Can Classification Criteria Constitute a Correct Mathematical Definition? Pre-service and In-service Teachers’ Perspectives

Abstract

The study reported here addresses pre-service and in-service teachers' attitudes toward mathematical-geometrical definitions. The goal of the study is to investigate whether understanding the role of definitions as classification and identification criteria will guarantee that participants: (1) accept that there may be more than one equivalent definition for particular concept; and (2) accept the minimal definitions which include necessary and sufficient attributes to be legal definitions. Fifty-three math educators participated the study, including 22 pre-service junior teachers, 19 pre-service senior teachers and 12 in-service senior teachers. The findings indicate that considering (an) attribute/s as sufficient in order to classify examples and non-examples of the concept did not guarantee considering this/ese attributes as concept definition. 56% of the participants did not accept equivalent definitions as legal definitions, 36% of them (the participants) did not accept the minimal definitions, which include necessary, and sufficient attributes to be a legal definition. For many participants, the essence of the mathematical concept is more important than the essence of the mathematical definition.