Gamified Learning and Learning Analytics to Improve Mathematical Competence in University Students

Abstract

Improving mathematical competence in higher education requires combining active pedagogical strategies with learning analytics models capable of detecting risk profiles and participation trajectories. This pilot study analyzes a dataset of 64 Ecuadorian university students using a 20-item Likert questionnaire and sociodemographic variables. The aim was to explore the latent structure of affective indicators related to readiness for mathematical learning in gamified contexts and to propose a multivariate framework for educational decision-making. Reliability analysis, KMO and Bartlett tests, principal component analysis (PCA), HJ-Biplot representation, K-means and hierarchical clustering, linear regression, and Random Forest were applied. The global scale showed high internal consistency (Cronbach’s alpha = 0.857); KMO was 0.623, and Bartlett’s test was significant, supporting factorial exploration. PCA revealed a first dimension associated with general affective distress and a second dimension linked to anxious reactivity. Clustering identified differentiated profiles of affective readiness, ranging from students with higher tension and lower learning availability to students with lower emotional load. The HJ-Biplot helped interpret students and items simultaneously, whereas Random Forest identified the most relevant indicators explaining the affective readiness index. The findings suggest that gamification should be supported by affective learning analytics to personalize feedback, academic support, and mathematical learning interventions.