Examining Students’ Mathematical Understanding of Geometric Transformations Using the Pirie-Kieren Model

Author/s: Hilal Gülkılık, Hasan Hüseyin Uğurlu, Nejla Yürük

DOI: 10.12738/estp.2015.6.0056 

Year: 2015 Vol: 15 Number: 6


Students should learn mathematics with understanding. This is one of the ideas in the literature on mathematics education that everyone supports, from educational politicians to curriculum developers, from researchers to teachers, and from parents to students. In order to decide whether or not students understand mathematics we should first identify how mathematical understanding occurs. The purpose of this research is to analyze 10th-grade students’ mathematical understanding of geometric transformations as developed in an environment enriched with multiple representations. Four 10th-grade students were observed during their lessons on translation, rotation, reflection, and dilation; semi-structured task-based interviews were then conducted with them after the lessons. The findings of this study reveal that although students’ levels of mathematical understanding developed from informal to formal, this development was not unidirectional and students showed a tendency to use informal understandings. Students’ primitive knowledge of geometric transformations was at the core of their understanding, whereas activities in the understanding levels of Image Making and Property Noticing directly affected the growth of their mathematical understanding. The folding back movements, activities in the forms of acting and expressing within the different levels of understanding, and multiple representations of concepts in the learning environment guided their process of mathematical understanding.

Mathematical understanding, Pirie-Kieren Model, Geometric transformations, Representations, High school students

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