Unravelling the quality of processes of learning from errors: Insights from students' written error reflections in factoring tasks

Background

Errors can provide valuable opportunities for deep learning outcomes, but these opportunities are often missed when the quality of processes of learning from errors is low. This quality can be inferred from students' level of cognitive engagement indicated by their written error reflections; however, research directly analyzing such reflections remains limited.

Aims

This study identifies patterns in students' error reflections and explores their relationship with academic achievement.

Sample

Participants were 118 eighth-grade students.

Methods

Students wrote reflections on presumed errors in two factoring problems with minimal prompts. Reflections were counted for frequency (involving categories of error detection, error correction, and out of scope) and scored for depth (involving descriptors of transferability, awareness, and correctness). These six coded features were used for clustering analysis to identify reflection patterns, and analysis of variance was used to explore their relationship with academic achievement.

Results

Overall, students produced moderate-frequency but low-depth reflections. Clustering analysis revealed five distinct patterns, labeled as ineffective thinker, disengaged learner, error detector, informative classifier, and insightful reflector, inferring a range from low-to high-quality processes of learning from errors. Low-quality-related patterns typically included superficial reflections like vague, overly general, or meaningless thoughts, while high-quality-related ones demonstrated required reflections on error detection and correction, with some including transferable insights about when or why to use specific knowledge. Patterns associated with higher-quality processes were also linked to higher academic achievement.

Conclusions

This study enhances our understanding of how students learn from errors, providing implications for improving relevant instructional strategies.