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.