Grade 9 learners’ algebra performance: Comparisons across quintiles, insights from errors and curriculum implications

Keywords: learner error, linear equations, didactic cut, integers, quintile 5 maths performance


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-resourced
secondary 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.


  • 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.
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