An Analysis on Male and Female Junior High School Students’ Van Hiele Levels of Geometric Thinking from Mathematical Ability

Abstract

The purposes of this research were to examine the students’ levels of thinking based on gender differences by investigating the students’ levels of geometric thinking and making learning examples to improve the students’ levels of thinking. Mathematical ability differences in this research referred to high, medium, and low mathematical abilities. This research was explorative research using a naturalistic qualitative approach. The use of the naturalistic qualitative approach was based on the consideration that the analysis for Van Hiele levels of thinking needed to be done by observing the students’ thinking process characteristics. The research subjects consisted of 3 male students and 3 female students which were grouped based on mathematical abilities. In order to collect information about the students’ levels of thinking, each research subject was interviewed with six activities which included: (1) Drawing quadrilaterals, (2) Identifying and defining quadrilaterals, (3) Sorting quadrilaterals, (4) Determining a mystery shape, (5) Equivalence of two definitions of a parallelogram, and (6) Application of quadrilaterals. The results of each activity were analyzed and the levels of thinking of each research subject were determined. It was found that there were five students at level 1 and only one student at level 0. All subjects had several weaknesses, among others using improper properties to distinguish, identify, and sort geometrical structures. All subjects still ignored class inclusion in quadrilaterals, although they were able to identify geometric shapes based on the properties of their components. From the analysis of the students' levels of thinking, learning examples were made based on Van Hiele five learning phases, i.e.: (1) Information Phase, (2) Guided Orientation Phase, (3) Explicitation Phase, (4) Free Orientation Phase, and (5) Integration Phase. The results showed that there was no difference between male and female students' levels of thinking since both male and female students were at level 1. It was different from the students' levels of thinking viewed from their mathematical abilities. All students in the high- and medium-scored groups were at level 1, while only one student was at level 1 and the others were at level 0 in the low-scored group. The learning examples were made in the form of Lesson Plan (Rencana Pelaksanaan Pembelajaran, RPP) and Student Worksheets (Lembar Kerja Siswa, LKS). It was hoped that the students could progress from level 1 to level 2 with these lesson plan and student worksheets.

Keywords: Van Hiele Levels of Geometric Thinking, Mathematical Ability