Errors in trigonometric proof-related reasoning tasks: Insights from Grade 10 learners at a rural Eastern Cape school

Background: This study explored Grade 10 learners’ errors and their perceptions of the errors they made in solving trigonometric proof-related reasoning (PrR) tasks. Aim: This embedded case study follows a qualitative approach to examine learners’ errors in written responses to trigonometric PrR tasks and their perceptions to illuminate the misconceptions that often hinder the development of PrR skills. Setting: A secondary school in the rural area of Nkozo in the Eastern Cape province, South Africa. Methods: A custom-designed test was administered to 40 Grade 10 learners. Purposive sampling was used to select 30 learners’ scripts for analysis of written responses. Following this analysis, 10 learners were purposively selected for semi-structured interviews. Guided by cognitive constructivism adaptation processes, the study employed Newman’s Error Analysis Model as an analytical tool. Results: Process-skill (50%) errors were dominant, followed by comprehension errors (30%), transformation errors (14%), encoding errors (6%) and reading errors (0%). Learners encountered challenges with incorrect formula application, misinterpretation of angle constraints and difficulty coordinating multiple representations. The written responses indicated a tendency to rely on procedures with minimal understanding, defaulting to surface-level strategies and superficial reasoning even when tasks required conjecturing and evaluating mathematical claims. The interviews supported these findings, revealing limited metacognitive awareness and misconceptions about quadrant-based trigonometric ratios that are considered invariant, which hindered effective reasoning. Conclusion: The study highlights the significance of instructional strategies that foster conceptual understanding, multiple representational fluency and reflective reasoning. Contribution: This research deepens the existing understanding of common error patterns in trigonometry and learner perceptions. It offers insights for developing PrR skills in trigonometry.