Creation and analysis of errors as a strategy for mathematical learning

Abstract

The creation and analysis of errors in mathematics teaches students to deepen their understanding of concepts by discovering why they made mistakes, thereby strengthening their comprehension. This strategy develops critical thinking and fosters metacognition, as it requires reflection on one’s own mental processes. It integrates cognitive, metacognitive, and affective components. On the cognitive level, it enables a thorough grasp of mathematical concepts and procedures by identifying what went wrong and why. It can face several threats. Among them is the fear of making mistakes, which limits student participation, especially in contexts where failure is penalized. Misinterpretation of errors can also arise if their analysis is not properly guided. Furthermore, without careful teacher guidance, students can lose confidence. Finally, superficial use of this strategy can turn it into a mere correction of exercises, losing its value as a reflective tool and promoter of critical thinking. On the metacognitive level, it promotes self-reflection and encourages self-regulated learning. It also ties into mathematical communication, since it involves clearly arguing and explaining ideas, and supports collaboration by sharing and discussing errors with others. This is a comprehensive strategy that enhances meaningful learning from multiple dimensions. Moreover, it encourages mathematical communication by explaining errors in a clear and logical way. Rather than punishing mistakes, it turns them into valuable opportunities for learning, thus reducing fear of error. This approach fosters a positive classroom environment and encourages active student participation.