Diagnostic Analysis of Grade 11 Learners’ Errors in Trigonometric Function Graphs: A Mixed-Methods Investigation.
(1) University Of Pretoria
(*) Corresponding Author
Abstract
Trigonometric function graphs are a central component of the secondary mathematics curriculum and underpin further learning in STEM disciplines. Yet learner performance in this area remains persistently weak, with errors commonly observed in examination contexts. This study investigated the types and underlying causes of errors made by Grade 11 learners when solving tasks on trigonometric function graphs. A mixed-methods design was adopted. Data were gathered from 150 learners through a researcher-developed Trigonometric Achievement Test, from which 30 scripts were subjected to detailed analysis, and semi-structured interviews with 15 learners provided complementary insight. Errors were classified using Newman’s Error Analysis Framework, and Radatz’s cognitive model was used to identify underlying causes. Findings revealed that comprehension errors (33%) and misconceptions (31%) were most common, followed by encoding errors (17%). Learners experienced difficulty with horizontal shifts, determining range and asymptotes, and reasoning graphically from symbolic expressions, often relying on procedural rather than conceptual strategies. The study concludes that reducing error prevalence requires diagnostic, concept-focused instruction that integrates visual and algebraic representations. It recommends use of error-analysis frameworks in classroom practice and professional support for teachers. Future research should examine the effects of conceptual intervention and technological tools on learners’ understanding of trigonometric graphs.
Keywords
References
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DOI: http://dx.doi.org/10.30738/indomath.v0i0.188
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