HOW THE VAN HIELE THEORY AND THE PIRIE-KIEREN THEORY CAN BE USED TO ASSESS PT’s UNDERSTANDING OF CONCEPT OF REFLECTION?

Abstract

This paper seeks to investigate how the van Hiele Theory and the Pirie-Kieren Theory can be used to assess pre-service teachers’ understanding of the concept of geometric reflection. These analyses include motivations for ultimately utilizing the van Hiele Theory and Pirie-Kieren Theory to examine how pre-service teachers can develop a mapping view of geometric reflection from a motion view of geometric reflection. Additionally, I contrast previous cases which utilized the van Hiele Theory and Pirie- Kieren Theory separately, noting that there is yet to be work done in which the Pirie- Kieren Theory is utilized in conjunction with dynamic geometry software. While this study is not inherently connected to these existing studies, the utilization of frameworks did play a role in our decisions for deciding on a particular framework, namely the van Hiele Theory. I acknowledge that both the van Viele and Pirie-Kieren frameworks offer insights into pre-service teachers’ thinking about geometric reflection (particularly when paired with a dynamic geometry software); however, due to certain characteristics of the van Hiele Theory (namely providing a clear progression in-depth of knowledge), I primarily suggest using the van Hiele Theory in teaching geometric reflection. My findings show that the emphasis on a clear path of progression and requisite knowledge is a critical factor in this change of perspective, as well as the importance of well-designed tasks that illuminate characteristics for a mapping view of geometric reflection.