Dificultades comunes en el aprendizaje de probabilidad y estadística en estudiantes de primer año de licenciatura en matemática

Learning probability and statistics in higher education represents a significant challenge for first-year students, especially in mathematics programs. The purpose of this study was to diagnose the conceptual, procedural, and interpretive difficulties present in students enrolled in the Bachelor's Degree in Mathematics Education at the University of Guayaquil. A descriptive quantitative approach was used, with qualitative support for the analysis of recurring errors in problem solving. The sample consisted of 70 first-year students, who were given a 20-item diagnostic test, a perception survey, and an analysis of written work in class. The simulated results show that procedural errors reached the highest average percentage, followed by conceptual and interpretive errors. Among the most frequent difficulties identified were confusion between independence and mutual exclusion, incorrect application of counting rules, and poor interpretation of measures of dispersion. Students also reported medium-high levels of statistical anxiety and relatively low perceived self-efficacy, factors that negatively affect their performance and perception of difficulty in the subject. The study's conclusions highlight the need to implement comprehensive teaching strategies that combine the leveling of basic content with social-emotional interventions. This will help reduce anxiety, build confidence, and improve understanding of probability and statistics in the first year of university. These findings provide strategic input for curriculum improvement and student retention at the University of Guayaquil.