Exploring South African high school learners problem-solving skills in Euclidean Geometry

Abstract

This study investigated the effects of South African mathematics learners’ problem-solving errors in Euclidean geometry on their performance in matric mathematics paper 2 of the National Senior Certificate (NSC) examination. The study also proposed Euclidean geometry teaching-learning continuum approach that may reduce the problem-solving errors and ultimately improve performance in the matric mathematics paper 2 examination. The study was underpinned by Newman problem-solving error analysis (Newman, 1977). To this end, the study was conducted in two phases: Phase I and Phase II. In Phase I, type of errors committed in the matric mathematics paper 2 and their effect on performance was investigated, while the Phase II of the study explored the efficacy of the teaching-learning continuum (EGPSLM-EGPSIA) approach proposed. Mixed method research approach was used in the study. This involved quasi-experimental and descriptive research designs. Quasi-experimental design used ex-post facto and pre-test post-test matching control research approach to collect data, while the descriptive research design adopted solution appraisal and classroom observation to collect data. In Phase I, 244 scripts from the 2020 mathematics paper 2 exam from three provinces and 432 scripts from the 2021 mathematics paper 2 exam from five provinces were used to collect data. In Phase II, random and convenient sampling were used to select three schools from the study population. Two of the selected schools were experimental schools and the remaining one was a control school. A total of 95 Grade 12 mathematics learners formed the study participants for the study in Phase II. There were nine itemised findings but they are summarised as but not limited to (1) problem-solving errors in Euclidean geometry significantly affected the learners’ matric mathematics paper 2 performance, (2) South African mathematics learners commit similar pattern of errors in Euclidean geometry yearly, (3) reading error was the leading error that were commonly committed in Euclidean geometry problem-solving, (4) EGPSLM-EGPSIA continuum intervention facilitate the learning of Euclidean geometry concepts, and (5) EGPSLM-EGPSIA continuum intervention has the potential to improve the learners’ performance in Euclidean geometry.