The Role Of Representations In Middle School Preservice Teachers’ Conceptions Of Real Numbers

The purpose of this study was to investigate the role of the representations in 158 middle school preservice teachers’ conceptions of real numbers. The distinction of the transperant and opaque representations was used as a theoretical framework. Participants were asked to define rational and irrational numbers, to show real numbers system in a diagram and to identify the type of the given numbers. Moreover, 10 preservice teachers were interviewed. The results showed that participants had difficulty in determining whether a number is rational or irrational even in case of transparent representation (i.e. 1/3). In addition, praticipants’ responses were significantly influenced by the type of representations and some believed that as the representation change, so was the number.