Enming Zhang

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.

Subject (e.g., math) problems often have deep rationales and concepts underlying them. Accordingly, when students solve these problems, they are prone to making errors that expose their misunderstandings and are difficult to correct. Previous research has shown the benefits of teacher feedback in learning from errors, but the effectiveness of specific feedback elements and their underlying mechanisms remain unclear. Drawing on educational psychology theories, this study aims to compare the isolated and combined effects of principle-based feedback, which targets understanding of underlying concepts, and procedure-based feedback, which focuses on the correct application of steps. The study also examines the mediating effects of cognitive load and learning speed. A total of 135 eighth-grade students participated in the experiment, randomly assigned to one of four groups in a 2 (principle-based feedback: yes or no) × 2 (procedure-based feedback: yes or no) design. Between-subjects analysis of covariance (ANCOVA) was conducted to test the intervention effects, while path analysis was used to examine the mediating effects. Results indicated that principle-based feedback significantly helped students correct more errors, but combining both types of feedback did not yield additional benefits. Furthermore, cognitive load did not mediate the effects of the intervention as anticipated, suggesting other factors may play more significant roles. Notably, exploratory analysis suggested that learning speed may play a mediating role, implying that principle-based feedback could help students achieve "desirable difficulty." This study confirms the effectiveness of principle-based feedback in helping students learn from their errors and provides corresponding theoretical explanations and educational implications.

Recently, learning from errors has gained significant attention worldwide in educational psychology. Both theoretical and practical issues are emerging regarding how to design instructional conditions regarding learning from errors to facilitate deep learning. By examining four research contexts, including simulation of the human thinking process by computational modeling, retrieval process of memorization, conceptual change, and meta-cognition and self-regulation, this study identified learning from errors as a higher-order learning and self-regulated learning activity and introduced the error-learning and error-reaction models as supportive reference. The study also analyzed and compared various related elements in research fields, including generating effect, problemsolving prior to instruction, example-based learning, conceptual change, self-addressing errors, and language learning. Results indicated error source and the timing, method, form, process, and outcome of learning from errors as crucial instructional conditions to moderate the effects of existing instructional modes. These findings can provide a guide for future research on learning from errors. Practically, the discussion on integrating the research findings into existing instructional designs offers implications for improving classroom practices that leverage errors more effectively.= 近年来，从错误中学习逐渐受到国际教育心理学界的关注。如何设计从错误中学习的教学条件促进深度学习，成为理论与实践共同关注的议题。本文通过梳理计算模型模拟人类思维过程、记忆提取过程、概念转变和元认知与自我调节四条研究脉络，明确从错误中学习作为高阶学习活动和自我调节学习活动的内涵，并引入错误学习模型和错误反应模型作为支持证据。本文还通过分析与比较生成效应、问题解决为先、样例学习、概念转变、错误的自主处理和语言学习六个领域的研究，从理论层面指出错误的来源和从错误中学习的时机、方法、形式、过程与结果等教学条件，或是调节既有教学模式效果的重要因素，从而为未来研究提供指南，以及从实践层面讨论如何将从错误中学习的理论成果嵌入既有教学设计，为创设利用错误学习的课堂提供启示。