Abstract:
Acquiring conceptual understanding, procedural knowledge, and adaptive reasoning is imperative for developing problem-solving proficiencies in learners. However, while there are a few studies on mathematical proficiencies in South Africa, there is a lack of research on learners’ proficiencies in Euclidean geometry (EG) that combine conceptual understanding, procedural knowledge, and adaptive reasoning in the same study. The purpose of the current study was to explore the problem-solving proficiencies of learners in EG in terms of conceptual understanding, procedural knowledge and adaptive reasoning. The current study was underpinned by a five-strand mathematical proficiency framework consisting of conceptual understanding, procedural knowledge, strategic competence, adaptive reasoning, and productive disposition. Based on an interpretivist philosophical stance, the study used a qualitative approach. Specifically, using convenience sampling strategy, a sample of 200 learners was selected from 10 schools in the Vhembe East District in Limpopo, South Africa. A Euclidean geometry proficiency test (EGPT) was used as a starting point towards the acquisition of qualitative data for this project. The current study used the Oregon Mathematics Problem Solving Rubric and the Rubric of Mathematical Adaptive Reasoning as its framework for analysing the learners’ solutions to the problems in the EGPT. The findings show that on questions of predominantly conceptual knowledge, 87% of the participants were ranked novice problem solvers; on questions of predominantly procedural knowledge, 85% of the participants were classified as novice problem solvers. In addition, 89% of the participants were ranked poor in adaptive reasoning. Future research in South Africa should examine the mathematics proficiencies of learners in various districts throughout several provinces to uncover the general trend in the mathematical proficiency of learners.
