Using erroneous examples for teaching Grade 9 Algebraic Linear Equations at a School in Johannesburg Central District

Abstract

The importance of mathematics is well known the world over, and its applications in commerce, science, technology and everyday life situations cannot be emphasised. Algebra is an abstract and challenging branch of mathematics to teach and learn. Teachers struggle to teach it, and learners struggle to understand it, hence they develop a plethora of misconceptions and associated errors. Passing mathematics at FET is a prerequisite for admission into tertiary institutions to study science, engineering, technology and mathematics. To pass mathematics, one has to have a comprehensive understanding of algebra at an early stage of learning. This study’s purpose was to explore the impact and effectiveness of erroneous examples for teaching Grade 9 algebraic linear equations. Learners’ performance in mathematics in Grade 9 is crucial because, in South Africa, learners use their results to choose the subject combination they will take at FET. This study was underpinned by constructivism, which recognises the role of the individual in making knowledge. This study followed an explanatory embedded mixed-methods research design. Qualitative data for this study was collected through lesson observations and semi-structured interviews with two Grade 9 mathematics teachers. A pre-test was used to collect quantitative data from both the experimental and control groups (N=31) and (N=28) respectively. A post-test was also administered to both the experimental group (N=12) and the control group (N=24). Excel was used for data management. Statistical data analysis was done using IBM SPSS version 28. The experimental and control groups were compared using a t-test at the 95% confidence limit (2-sided). The results were declared statistically and significantly different for all p-values of 0.05 or less. The post-test results after the intervention showed an improvement in performance for the two study groups, with the experimental group improving from 𝑥𝑥̅=1.12903 in the pre-test to 𝑥𝑥̅=18.83333 in the post-test, an increase of 𝑥𝑥̅=17.7043. In contrast, the control group improved from 𝑥𝑥̅=12.82143 in the pre-test to 𝑥𝑥̅=23.00000 in the post-test an increase of 𝑥𝑥̅=10.17857. The greater increase in the mean differences by the experimental group suggests that the intervention positively impacted learners’ performance. Qualitative data obtained from semi-structured interviews and lesson observations were coded and identified according to different themes. Erroneous examples positively impacted the TEG’s teaching practice and improved the learners’ performance.