A holistic framework to model student's cognitive process in mathematics education through fuzzy cognitive maps

Abstract

This study introduces a pioneering framework for modeling students' cognitive processes in mathematics education through Fuzzy Cognitive Maps (FCMs). By integrating key educational theories—Duval's Semiotic Representation Theory, Niss's Mathematical Competencies, Marton's Variation Theory, and the broad Engagement, Motivation, and Participation framework— the model offers a comprehensive and holistic understanding of students' cognitive landscapes. This research underscores the necessity of a multidimensional approach to capturing the intricate interplay of cognitive, affective, and behavioral factors in students' mathematical learning experiences. The novelty lies in its methodological innovation, employing FCMs to transcend traditional qualitative analyzes and facilitate quantitative insights into students' cognitive processes. This approach is particularly relevant in the current era dominated by digital learning environments and artificial intelligence, where real-time, automated analysis of student interactions is increasingly vital. The proposed FCM has been developed over the years with a data-driven approach; the concepts and relationships in it have been derived from the literature and refined by the author's experience in the field. Illustrated through case studies, the framework's utility is demonstrated in diverse contexts, highlighting how the quantitative data obtained are confirmed by qualitative approach: analyzing the impact of remote learning during the Covid-19 pandemic on student engagement and exploring Augmented Reality's role in enhancing mathematical conceptualization. These applications show the framework's adaptability and its potential to integrate new technologies in educational practices. However, the transition from qualitative to quantitative methodologies poses a challenge, given the prevalent use of qualitative approaches in mathematics education research. Additionally, the technological implementation of the FCM model in educational software presents practical hurdles, necessitating further development to ensure ease of integration and use in real-time educational settings. Future work will focus on bridging these methodological gaps and overcoming technological challenges to broaden the FCM model's applicability and enhance its contribution to advancing mathematics education.