The Role of Cognitive Feedback in Correcting Students’ Conceptual Misconceptions During Error-Based Learning: A Study in Teaching Derivatives

Background and Objectives: In contemporary mathematics education, errors are no longer regarded merely as indicators of learners’ weaknesses. Instead, they can provide opportunities for identifying students’ ways of thinking and correcting misconceptions. Cognitive feedback helps students reconsider their reasoning and strategies, thereby facilitating conceptual change. This study aimed to examine the role of cognitive feedback in correcting students’ conceptual misconceptions within error-based learning in the teaching of derivatives. Methods: This descriptive–analytical study was conducted as an instructional intervention involving 57 twelfth-grade science students. The intervention was implemented over four 70-minute sessions during a two-week period. Instructional activities focused on the analysis of erroneous responses, comparison of problem-solving strategies, and the provision of cognitive feedback. Data were collected through three instructional tests, analysis of students’ responses, and identification of recurring error patterns. Findings: The findings indicated that many student errors in learning derivatives were rooted in conceptual misconceptions and the algorithmic use of differentiation rules. The most frequent errors were associated with continuity and differentiability, piecewise-defined functions, absolute value functions, the chain rule, and distinguishing between a zero derivative and a vertical tangent. Comparison of pre-test and post-test results revealed substantial reductions in the frequency of errors across all investigated categories. Conclusion: The findings suggest that cognitive feedback in an error-based learning environment can guide students toward analyzing their reasoning, reconsidering their thinking processes, and correcting conceptual misconceptions. Therefore, instructional activities based on error analysis and cognitive feedback may enhance students’ conceptual learning of derivatives.