Faculty of Applied Sciences

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Conjecturing an effective problem-solving heuristic instructional approach for circle geometry
(ASR Research, 2022-04-21) Abakah, Fitzgerald; Brijlall, Deonarain
Abstract- This paper reports on an investigation into finding an effective contemporary problem- solving instructional approach for circle geometry. The participants were high school learners in a South African school. This proposed instructional approach-the IPAC model, adopted four elements of this new approach, namely, the infusion approach, Polya’s approach, and APOS theory in a collaborative learning classroom. This study followed a mixed-method research design. The quantitative data was analysed by implementing descriptive statistics and inferential statistics, while content analysis was performed on data extracted from qualitative questionnaires. The research findings that emanated from this study were the following: the validity, practicality and effectiveness of the designed model were established. Based on these research findings, the researcher recommended among others: (1) the designed model, should be implemented for teaching and learning of mathematics in general and circle geometry in particular, in South African schools; (2) teaching of thinking skills and teaching effective problem-solving instructional approaches should be prioritized in mathematics classrooms in South Africa.
High school learners’ challenges in solving circle geometry problems
(PONTE, 2022-12-19) Brijlall, Deonarain; Abakah, Fitzgerald; Boschi
This paper reports on a study that investigated high school learners’ difficulties when solving circle geometry problems. This study was conducted on the premise that, if these difficulties are well-known, then the teacher will be guided, to implement appropriate instructional strategies to address them. High school mathematics learners’ poor performances in examinations (formal/informal), nationally, necessitated this study. A high school in the Northern Cape Province was purposefully sampled to serve as the research field for the study and circle geometry lessons were conducted, with the study participants. Thereafter, activities, investigation tasks, class work, home-work and standardized tests were administered to collect data. Data was also collected through classroom observations, video recordings and field notes. This was qualitative research hence, qualitative procedures were followed for data collection, analysis and interpretations. Content analysis was carried out on participants’ written responses to the standardized tests, utilising Newman’s Error Analysis model to inductively, identify participants challenges, which also served as the theoretical framework for the study. The analysed data revealed that learners do not understand circle geometry concepts, hence, their inability to make connections across geometry concepts to solve geometric problems. The researchers concluded this lack of fundamental background prevents learners from applying appropriate techniques in solving circle geometry problems.