Van Hiele theory-based instruction, geometric proof competence and grade 11 students' reflections

Abstract

This study sought to (a) investigate the effect of Van Hiele theory-based instruction on Grade 11 students’ geometric proofs learning achievement, (b) explore students’ views on their geometry learning experiences, and (c) develop a framework for better teaching and learning of Grade 11 Euclidean geometry theorems and non-routine geometric proofs. The study is based on Van Hiele’s theory of geometric thinking. The research involved a convenience sample of 186 Grade 11 students from four matched secondary schools in the Capricorn district of Limpopo province, South Africa. The study employed a sequential explanatory mixed-methods design, which combined quantitative and qualitative data collection methods. In the quantitative phase, a non-equivalent groups quasi-experiment was conducted. A Geometry Proof Test was used to assess students’ geometric proof construction abilities before and after the teaching experiment. Data analysis using non-parametric analysis of covariance revealed that students from the experimental group of schools performed significantly better than their counterparts from control group schools. In the qualitative phase, data were collected using focus group discussions and students’ diary records. Results revealed that the experimental group students had positive views on their geometry learning experiences, whereas students from the control group of schools expressed negative views towards the teaching of Euclidean geometry and geometric proofs in their mathematics classes. Based on the quantitative and qualitative data findings, it was concluded that in addition to organizing instruction according to the Van Hiele theory, teachers should listen to students’ voices and adjust their pedagogical practices to meet the expectations of a diverse group of students in the mathematics class. A framework for better teaching and learning of Grade 11 Euclidean geometry theorems and non-routine geometric proofs was thus developed, integrating students’ views and Van Hiele theory-based instruction. The study recommends that teachers should adopt the modified Van Hiele theory-based framework to enhance students’ mastery of non-routine geometric proofs in secondary schools.