The use of Van Hiele theory to address BED foundation phase students’ misconceptions in transformation geometry.

Abstract

The purpose of this study was to explore South African student teachers’ misconceptions in transformation geometry and address these through the lens of the Van Hiele theory. It has been observed that students have weak knowledge of geometry is attributed to, among other factors, teachers’ incompetence in geometric knowledge. Teachers’ inability to communicate geometry content to students in ways that allow construction of students’ own conceptual knowledge, has been identified as a problem. Literature suggests that the Van Hiele theory of geometric reasoning has a potential to enhance students’ conceptual understanding of geometry, bridge the communication gap between teachers and students and help towards addressing the misconceptions that students have with the learning of geometry. Eighty-two bachelor of education foundation phase teachers’ trainees were involved in the qualitative research study. An action research approach was used, and data were collected firstly through pre-tests, followed by interviews with selected students, to get insight into the causes of the errors identified in the students’ test scripts. A Van Hiele phase-based intervention programme was then designed and implemented, in order to address the students’ misconceptions and associated errors, as well as improve the researcher’s own practice. Students then wrote a post-test to determine the extent to which the Van Hiele phase-based instruction helped address the misconceptions. Data was analysed using a thematic analysis approach. Various codes and patterns were formulated into themes that addressed the research questions. Findings indicated that students displayed some errors with transformation geometry and their misconceptions were exposed as they worked through the various phases of Van Hiele phase-based instruction. The errors fell under two main categories. Firstly, there were non-systematic errors, where, for example, students carelessly read instructions or wrote words or numbers without paying attention. Secondly, there were systematic errors, such as cases where students confused the properties of translations, reflections or rotations, as well as failing to recognise, describe or perform these transformations. The Van Hiele phase-based instruction provided opportunities for students to confront their errors and address them as the programme continued over time. The results of the post-test showed that students improved their performance in general, but still struggled with problems that were set at higher Van Hiele levels. Implications of the findings are discussed and then some recommendations are provided.