Adaptive e-Learning for Number Theory: A Mixed Methods Evaluation of Usability, Perceived Learning Outcomes, and Engagement

This study developed and evaluated an adaptive e-learning environment for selected number theory topics using a mixed-methods research design, conducted over an eleven-month period across secondary and early tertiary education contexts. The evaluation focused on three primary outcome domains: (1) learning-related outcomes (problem-solving accuracy and task success rate), (2) learner engagement and activity indicators (daily logins and tasks completed per day), and (3) system usability, assessed according to Jakob Nielsen’s usability dimensions. Quantitative data were collected through student and teacher questionnaires (N = 264 students; N = 52 teachers) and large-scale logfile analytics comprising more than 825,000 recorded system interactions. Qualitative feedback from students and teachers complemented the quantitative analyses. The results indicate statistically significant increases in learner activity, task completion rates, and problem-solving success following the introduction of the adaptive system, as demonstrated by inferential statistical analyses with confidence intervals. Post-use evaluations further indicated high levels of learner motivation and self-confidence, along with positive perceptions of system usability. Teachers evaluated the system positively in terms of learnability, efficiency, and instructional integration. Logfile analyses also revealed sustained growth in daily engagement and task success over time. Overall, the findings suggest that adaptive e-learning environments can effectively support engagement, usability, and learning-related performance in number theory education, although further research is required to examine the sustainability of learning-related outcomes over extended periods and to further refine error-handling mechanisms.