MATHPROGIA: A CONCEPTUAL AND METHODOLOGICAL FRAMEWORK FOR THE EVOLUTION OF MENTAL MODELS IN HYBRID LEARNING ECOSYSTEMS WITH EXPLAINABLE AI

Abstract

This longitudinal case study evaluated the evolution of the mental models of 17 non-commissioned officers who were students of Topographic Survey Technology at the School of Military Engineers (ESING). The objective was to analyze the evolution of mental models in the domain of variational and statistical-random thinking through the implementation of MathProgIA, a methodological framework developed for the design, implementation and evaluation of hybrid learning ecosystems. Its structure integrates fundamentals from Knowledge  Space Theory (KST), knowledge state modeling, competency-based learning, continuous assessment and teacher auditing processes supported by explainable artificial intelligence (XAI). From this perspective, artificial intelligence is not the axis of the training process, but a methodological mediator whose function is to strengthen the construction of knowledge through the critical validation of information and the monitoring of the evolution of mental models. In the implementation developed in this research, explainable artificial intelligence (XAI) was incorporated into the design of the analog and digital learning experiences that made up the hybrid ecosystem. Longitudinal evaluations allowed us to observe the progression of students' mental models from elementary levels to more inclusive levels. The research was carried out over six months with a sample of 15 men and 2 women, using a longitudinal design with a mixed approach, supported by linear regression analysis and multivariate analysis. The results showed a progressive evolution of the mental models and a high explanatory power of the regression model (adjusted R² = 0.983). An original contribution of the study consists of the identification of the Evaluative Discrepancy Effect, understood as the systematic difference between the answers generated by artificial intelligence tools and the information verified in original sources through teacher auditing processes. This process favored the critical reconstruction of knowledge, metacognition, and the development of critical thinking. Overall, the findings provide empirical evidence that MathProgIA constitutes a conceptual and methodological framework with the potential to promote the evolution of mental models in hybrid learning ecosystems based on explainable artificial intelligence principles.