Enhancing students' geometrical thinking levels through Van Hiele's phase-based Geometer's Sketchpad-aided learning

Abstract

The content order of geometric components in the mathematics curriculum and the teaching process in a geometry class are said to be in contrast with the existing level of geometric thinking among secondary school students in Malaysia. Van Hiele (1986) proposed that directions should be given at the same level as the students' ability and therefore recommended phases of learning geometry in order to address this issue. The present study investigates the effectiveness of activities based on Van Hiele's phases of learning geometry by using the Geometer's Sketchpad (GSP) software which researchers claim is in line with the approach of Van Hiele's model. A quasi-experimental design was used in this study. The study was conducted for six weeks and involved 94 students and two teachers from a secondary school. The students were divided into control and treatment groups, with each group consisting of 47 students. Van Hiele's geometry test was given to both groups before and after the treatment. Five students from each group were randomly selected to identify the early and final levels of their geometric thinking in greater depth. Wilcoxon signed-rank test analysis showed that, although both groups showed significant differences between the early and final levels of their geometric thinking, the students' final thinking levels in both groups were significantly different. The findings from the analysis of the interview data also support the findings of the statistical analysis. Therefore, it is demonstrated that the Van Hiele phases of learning geometry should be used as a reference in arranging the geometric curriculum and content. In addition, the Van Hiele model and the GSP software can be used as an approach to teaching and learning geometry in the classroom to help students improve their level of geometric thinking.