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

Year 2022, Issue: 90, 363 - 376, 28.03.2022

Murat Akarsu

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.

Keywords

van Hiele theory, Pirie-Kieren Theory, Geometric reflection, Dynamic geometry software, Motion view, Mapping view.

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