Investigation of the Development of van Hiele Levels of Geometric Thinking in a Computer Supported Collaborative Learning (CSCL) Environment

Emre Özkan,Diler Öner

doi:10.17860/mersinefd.522491

Abstract

This study investigated the use of a well-designed computer-supported collaborative learning environment, namely Virtual Math Teams (VMT), to develop middle school students’ geometric thinking. It also looked into students’ VMT discourse to better understand factors leading to higher van Hiele levels of geometric thinking. The participants of the study were selected from middle school students who were at the visual geometric thinking level. For treatment, students were presented with a set of activities on quadrilaterals, which were developed based on van Hiele’s phases of learning geometry, within the VMT environment. The data were collected by using the van Hiele Geometry Test. The VMT chat logs were qualitatively analyzed using the three-core collaborative problem-solving competencies used in the Programme for International Student Assessment (PISA) 2015. The results showed that the participants significantly developed their van Hiele Geometry Test scores after the intervention. Qualitative results pointed out that collaborative competencies could be essential in developing students’ geometric thinking levels within the VMT environment. Considering that Turkish students score lower than the international average in geometry and the lowest in collaborative problem solving area in international assessments, it becomes even more important to integrate CSCL environments into Turkish curricula.

Highlights

While geometry is a crucial sub-discipline in the field of mathematics, most students have difficulties with school geometry (Köseleci-Blanchy & Şaşmaz, 2011)
One of the explanations for these difficulties with learning geometry is the lack of instruction that is designed based on students’van Hiele levels of geometric thinking, proposed by the two Dutch mathematics educators (Dina van Hiele-Geldof & Pierre van Hiele) in the late 1950s (Usiskin, 1982)
The development of the van Hiele levels of geometric thinking and van Hiele Geometry Test (VHGT) scores After the intervention, of the 24 participants who started at Level 1, 11 of them increased their level to Level 2, and one participant to Level 3 (Table 4)

Summary

Introduction

While geometry is a crucial sub-discipline in the field of mathematics, most students have difficulties with school geometry (Köseleci-Blanchy & Şaşmaz, 2011). One of the explanations for these difficulties with learning geometry is the lack of instruction that is designed based on students’van Hiele levels of geometric thinking, proposed by the two Dutch mathematics educators (Dina van Hiele-Geldof & Pierre van Hiele) in the late 1950s (Usiskin, 1982). The van Hielemodel described five sequential levels of geometric thinking (visual, analysis, informal deduction, deduction, and rigor) that students go through when becoming proficient in geometry (van Hiele, 1999). Instruction that supports the development of the van Hiele levels of geometric thinking should consist of five learning phases, which are inquiry, direct orientation, explication, free orientation, and integration. Students can pass through one level to the if instruction based on these phases is provided (Usiskin, 1982)

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Methods

Conclusion