The Influence of Students' Commognition in Solving Integral Problems

Abstract

This study investigates the influence of students' commognition on their ability to solve integral problems, drawing from Sfard's commognitive framework, which integrates cognition (intrapersonal thought) and communication (interpersonal discourse) as unified processes. Conducted among 60 undergraduate Mathematics Education students in Indonesia, the research utilized validated Mathematics Proficiency Test and Integral Problems tests, alongside semi-structured interviews, to assess performance across four commognition indicators: keywords, visual mediators, endorsed narratives, and routines. High-performing students excelled in all indicators, achieving 87.2% of the maximum score, reflecting a strong grasp of conceptual understanding and procedural fluency. Conversely, medium- and low-performing students demonstrated significant challenges, particularly with visual mediators and endorsed narratives, often struggling to construct and utilize mathematical representations and theorems effectively. Statistical analyses revealed a significant correlation between commognition and problem-solving ability (t-test p < 0.05; F-test p < 0.05). These findings underscore the critical role of structured pedagogical strategies, including explicit instruction in mathematical communication and visualization, to bridge gaps in mathematical discourse. The study highlights the importance of collaborative learning environments and the integration of commognitive principles in curriculum design to enhance mathematics education and equip students for advanced problem-solving tasks. Further research is recommended to evaluate long-term impacts and the potential of technology-based interventions in fostering commognitive skills.