Abstract
South African learners’ mathematics performance is poor across all topics, but especially in algebra. There are several reasons for this, not least the extensive use of variables in the topic. Learners commit many different types of errors when solving algebraic equations, and the teacher’s responsibility is to identify and address these errors.
This study aimed at investigating Grade 9 learners’ errors and misconceptions in their solving of algebraic equations from a Johannesburg high school. The paradigm employed in this study is interpretivism and the qualitative approach in investigating the research questions of this study. Purposive and convenient sampling was employed, and learners were able to provide rich data about the research problems and questions. Data collection instruments which were used in this study were in the form of learners’ assessments (tests) and semi-structured mathematics teacher interviews.
The learners’ responses were inductively analysed, and the errors they committed were categorised into groups. Some misconceptions were also inferred. The errors included (among others): learners’ difficulties with addition and subtraction of like and unlike terms; challenges when dividing terms and when solving for 𝑥; incorrect application of the distributive rule (including operation error); poor conceptual understanding of the lowest common denominator when simplifying fractions; errors when transposing terms; equals sign error; and misapplication of exponential laws.
Two mathematics teachers were interviewed, and their knowledge of learner errors, when working with algebraic equations, was elicited. The researcher sought to find a relationship between the learners’ errors and the teachers’ declarative mathematical knowledge for teaching.
It was recommended that teachers should intervene by teaching the basic concepts of algebra thoroughly for learners to acquire deeper conceptual understanding. It also suggested that teachers would do well to encourage discussion among learners, in the hope that this verbal engagement improves mathematical understanding. Teachers and learners should talk openly about errors and
misconceptions, to create an awareness of the possibility of using these as learning opportunities.