Mitigating errors and misconceptions among Grade 11 learners in algebra through error analysis

Abstract

Background: A good command of algebra concepts is vital for proficiency and success in higher mathematics and related disciplines. However, students are beset by conceptual challenges which require consistent attention because errors and misconceptions hinder learning and understanding.

Aim: With the aim of mitigating the problem of errors and misconceptions in school mathematics learning, a qualitative descriptive-interpretative research study was conducted.

Setting: The study involved 30 ordinary-level learners purposively sampled from one rural boarding high school in Zimbabwe.

Methods: Focus group discussions in which learners scrutinised illustrative sketches of erroneous worked examples were used as means to raise informants’ awareness of common errors and misconceptions in school algebra. Task-based interviews were used to elicit data in the form of participants’ written responses to tasks involving school algebra concepts. Content analysis informed by Biggs and Collis’ model and Kiat’s taxonomy of errors was applied to the textual data.

Results: With respect to basic ideas in algebra such as notions of coefficients, operators and variables and simplifying algebraic fractions, Grade 11 learners reached the extra-extended and relational levels of the SOLO model and solutions were free from conceptual and procedural areas. With regard to solving quadratic equations, lower levels of the SOLO model manifested with solution attempts marred with conceptual errors.

Conclusion: It can be concluded that error analysis has a potential to mitigate the problem of errors and misconception among Grade 11 learners depending on the nature of content involved.

Contribution: These findings have important implications for mathematics education and research in school algebra in the sense that it has contributed to efforts intended to find strategies that can provide solutions to the persistent problem of errors and misconceptions in mathematics education.