Enhancing Students’ Level of Geometric Thinking Through Van Hiele’s Phase-based Learning

Abdul Halim Abdullah

doi:10.17485/ijst/2013/v6i5.13

Abstract

The purpose of this study was to test the effectiveness of Van Hiele’s phase-based learning on students’ levels of geometric thinking. Quasi-experimental design was used in this study. The six-week study was conducted in a secondary school involving 94 students and two teachers. The students were divided into two groups, with 47 in a control group and the other 47 in a treatment group. Van Hiele’s Geometry Test (VHGT) was given to both groups before and after the treatment. Ten students were randomly selected to further determine their initial and final levels of geometric thinking. Wilcoxon-t tests were conducted to test the developed hypotheses. The results showed that there was no significant difference between the initial levels of geometric thinking in both groups. However, the analysis showed significant difference between the final levels of geometric thinking in both groups. Furthermore, qualitative analysis revealed that, in initial levels of geometric thinking, the majority of students in both groups obtained the first Van Hiele levels with complete acquisition, a low acquisition of level two and no acquisition of level three. In the post interview, most of the students in the control group showed an increment of geometric thinking from level one to level two, but no one in this group achieved level three. In contrast, all the students in the treatment group showed a complete acquisition of Van Hiele level one and almost all of them indicated a complete acquisition of level two. As for level three, only one student did not achieve this level, whereas the rest showed a complete and high level of acquisition. This demonstrates that Van Hiele’s phase-based learning can be applied in classrooms in order to help students achieve better level of geometric thinking. Keywords: Van Hiele’s Phase-based Learning, Students’ Levels of Geometric Thinking, Van Hiele Model, Learning Geometry

Highlights

In the Malaysian education system, geometry-r elated topics are emphasised in the syllabus at secondary school level. 42% of the 60 topics in the Integrated Curriculum for Secondary School (KSBM) of Mathematics from Form One to Form Five consist of geometry topics [9]
A quasi-experimental non-e quivalent pretest-posttest control group design was used in this study. Ninety-four Form Two students were involved in this study, and they were divided into two groups, namely the control group and the treatment group
Ho2: There is no significant difference between the students’ initial levels of geometric thinking in the treatment group and control group

Summary

Introduction

In the Malaysian education system, geometry-r elated topics are emphasised in the syllabus at secondary school level. 42% of the 60 topics in the Integrated Curriculum for Secondary School (KSBM) of Mathematics from Form One to Form Five consist of geometry topics [9]. 42% of the 60 topics in the Integrated Curriculum for Secondary School (KSBM) of Mathematics from Form One to Form Five consist of geometry topics [9]. Students are exposed formally to the geometry concepts for two- and three-d imensional shapes as early as Year One in these topics [11]. Current teaching and learning practice in the classroom does not reflect the importance of geometry in the lives of students, and the emphasis that is placed on it in the mathematics curriculum. According to Wan Mohd Rani [37], in terms of teacher training and attitude, more often teachers who teach mathematics use the blackboard to explain theorems, definitions, and concepts, and to show the solutions for the related problems. Mathematics teachers’ practice in Malaysia can be seen from the research done by TIMSS conducted in 1999, 2003, and 2007 [21, 22, 23]

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