Van Hiele Theory-Based Instruction and Grade 11 Students’ Geometric Proof Competencies

Abstract

South African matric results on the National Senior Certificate indicate low success in geometry, as do other African countries such as Nigeria. This poor performance affects potential career choices for students and limits the number of students who enter the highly-needed engineering fields on the African continent. Hence, this paper reports findings from a quasi-experiment involving 186 Grade 11 students from four conveniently selected township secondary schools in the Limpopo province of South Africa. The study tested the effect of Van Hiele theory-based instruction on the students’ geometric proof competencies. Data were collected using a geometry proof test and analysed using nonparametric analysis of covariance. Results showed that there was a statistically significant difference in students’ performance between the treatment and control groups (𝑇=595.9,𝑝=.005,𝜂𝑝2 =.684). Analysis of nonparametric regression curves fitted for the treatment and control groups showed that the treatment group had higher post-test scores than the control group. It was therefore concluded that Van Hiele theory-based instruction is more effective in teaching non-routine geometric proofs than conventional instruction. The study recommends that geometry teachers in upper secondary school should consider implementing Van Hiele theory-based instruction to enhance students’ geometric proof competence.