Using Van Hieles's geomentric model to improve grade 11 learners reasoning when solving circle riders

Abstract

In this study, I am reporting on the use of Van Hiele’s model to improve Grade 11 learners’ reasoning when solving circle riders. Studies have shown that geometry concept is deemed challenging for many learners in the country and abroad, as a result this study adopted Van Hiele’s model to improve the learners’ challenges when solving circle riders. A qualitative research approach was found suitable for this study because the findings of this study were reported using learners responses to given tasks. The learners’ responses gave an in-depth understanding of their challenges which cannot be generalised like with statistical data. A case study research design was used, following Merriam’s perspective; this was adopted because the study reports on findings from different sources of data. A sample for this study comprised a group of 34 Grade 11 learners from a technical school, in Sekhukhune District in Limpopo Province, South Africa. Data were collected using a pre-intervention activity, participant observations, and a post-intervention activity. Participants were given a pre-intervention activity to establish the level at which they operated before intervention. They were also given activities to complete during intervention lessons while I observed what transpired and how they reasoned when responding to the given activities. Later they were given a post-intervention activity, which was used to check if there was an improvement in their reasoning. The data were analysed using content analysis in three phases. This was done by scrutinising learners’ responses to pre-intervention activity, participants’ observations and post-intervention activities. Findings have shown that the use of Van Hiele’s model significantly enhanced the performances of learners when solving circle riders. The findings also revealed significant changes in learners’ reasoning, with the majority of learners’ post-intervention operating at a higher level of Van Hiele’s Model as compared to prior intervention. This shows that the use of Van Hiele’s model in teaching plays an important role in geometry learning and allows learners a chance to think critically, which helps in their conceptualisation of the knowledge area and improves their reasoning. From the findings it is recommended that there is a need for more studies that use Van Hiele’s model in all the grades and using large population of learners or more than one school for attainment of results that can be easily generalise Additionally, implementation of Van Hiele’s model within all mathematics content knowledge areas in which learners can be taught from lower level (𝑛−1) before they can be introduced to questions at higher level (𝑛). Furthermore, I recommended a need for studies that focus on how Van Hiele’s model can be used in improving teachers’ pedagogical content knowledge when teaching Euclidean geometry in all the grades. I am also of the view that there is a need for geometry content in Mathematics textbooks to be aligned and written in a way that allows learners to progress through different levels of Van Hiele’s Model. Lastly there must be more research focusing on vocabulary that learners encounter when giving reasons when dealing with the concept of geometry.