Examining Students' Mathematical Understanding of Patterns by Pirie-Kieren Model

Abstract

The purpose of this study is to investigate students' mathematical understanding of patterns. Three 7th grade students who enrolled in a public school solved the questions regarding the patterns. Semi-structured interviews were conducted with them about their solutions. The data were analyzed by using the Pirie-Kieren theory of mathematical understanding. The findings of this study revealed that students' mathematical understanding varied between first six levels from primitive knowing to observing and their mathematical understanding mostly occurred between Image Making and Formalising layers. In terms of theory, students were able to pass the first and second "Don't Need" boundaries but they could not progress their understanding over the third "Don't Need" boundary. The results also illustrated that all of the students had knowledge about the patterns. In order to find the general rule of the pattern, they mostly endeavored to determine a formula and check its correctness by writing initial three steps.