Abstract
It is well known that learners’ performance in mathematics in under-resourced secondary schools in South Africa is poor. However, little is known about the performance of learners in top-performing well-resourcedsecondary schools apart from their good results in Grade 12. In this study, the performance of Grade 9 learners in top-performing quintile 5 (i.e. well-resourced) schools was compared with that of learners in quintile 1–3 (i.e. poorly resourced) schools using a 45-item test. While the quintile 5 learners obtained higher test scores, the performance pattern across the test items was very similar for both quintile groupings. A detailed error analysis of 89 quintile 5 learners’ responses to equation items revealed difficulties in applying the standard equation-solving procedure, and in operating with negatives and subtraction, particularly on like terms. These problems may be related to a poorly conceived curriculum in the areas of integers and equations. It is recommended that Grade 8 and 9 teachers pay regular attention to all four arithmetic operations on integers. Furthermore, the teaching of equations should give greater attention to the cognitive shifts required in solving equations with letters on both sides of the equal sign.
 Significance:
 
 Learner performance patterns on a test were similar for learners from top-performing quintile 5 schools and learners from lower quintile schools, although the quintile 5 learners obtained higher test scores.
 Quintile 5 learners’ ability to solve linear equations correctly is substantially impacted by their difficulties in simplifying two algebraic terms to a single term, particularly when negatives and/or subtraction are involved.
 Particular aspects of the curriculum may partly be responsible for the difficulties learners experience with integers and equations.
Highlights
Research suggests that Grade 9 learners in quintile 5 schools, which are well resourced, are approximately 4 years ahead of their counterparts in poorly resourced quintile 1–3 schools.[1]. This tells us about the relative performance of the two quintile groupings in South African schools and we know only too well about the poor mathematics performance of learners in under-resourced schools[2] but we still do not know much about what is happening at Grade 9 level in well-resourced quintile 5 schools
As the ability to solve equations is fundamental for future success in mathematics, quintile 5 learners’ responses to three linear equation items were investigated to gain insight into their fluency in solving equations and into their fluency in algebraic manipulation
Equation error codes Six sub-codes were identified for equation errors: 1. Move term with letter – a term involving a letter is moved unchanged across the equal sign
Summary
Research suggests that Grade 9 learners in quintile 5 schools, which are well resourced, are approximately 4 years ahead of their counterparts in poorly resourced quintile 1–3 schools.[1]. While many quintile 5 schools produce excellent results at Grade 12 level, research conducted on the mathematics performance of high performers writing the National Benchmark Tests[3] has shown that these learners have difficulties with apparently basic ideas such as percentage and inequalities. Many of these learners will come from quintile 5 and high-fee independent schools. We knew the quintile 5 learners would obtain higher marks but we wanted to compare performance patterns over the entire test, i.e. the trends in which items had a higher/lower number of correct responses. What are the most common errors made by quintile 5 learners on linear equation items?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
