The Effectiveness of Deep Learning and Productive Errors in Developing Mathematical Cognitive Flexibility and Cognitive Engagement among Middle School Students

This study aimed to investigate the effectiveness of deep learning and productive errors strategies in developing mathematical cognitive flexibility and cognitive engagement among first-grade intermediate students. The study adopted an experimental design with equivalent groups. A sample of (120) female students was randomly assigned into three groups: two experimental groups (deep learning and productive errors) and one control group taught using the traditional method . Two instruments were used: a mathematical cognitive flexibility test consisting of (35) items and a cognitive engagement scale consisting of (25) items. Both instruments were validated and tested for reliability using appropriate statistical methods . The results revealed statistically significant differences in favor of the experimental groups in both cognitive flexibility and cognitive engagement compared to the control group. However, no significant differences were found between the deep learning and productive errors strategies, indicating their comparable effectiveness . The study concludes that employing modern teaching strategies based on deep understanding and learning from errors enhances the quality of mathematics learning, promotes flexible thinking, and increases students’ cognitive engagement. These findings support contemporary educational trends that emphasize a shift from surface learning to deep learning .