Virtual laboratories for mathematical learning in online and face-to-face higher education environments

In an era where computers perform calculations automatically, it is essential, especially at the university level, to foster a deep understanding of mathematics and its application to real-world problems. This thesis analyzes how simulation-based education can enhance mathematical learning through interactive, experiential, and problem-centered approaches. An instructional methodology based on constructive alignment is proposed, ensuring coherence between objectives, activities, and assessment, to implement simulation in both face-to-face and online university environments. A virtual lab focused on the Vehicle Routing Problem has been developed for undergraduate and master's students, and it has been used in an empirical study conducted across several European face-to-face and online universities. The results show that the educational use of simulation through aligned methodology improves learning outcomes, fostering student engagement, collaborative work, metacognitive skills, and deep understanding. Moreover, the online results were not inferior to the face-to-face results, demonstrating the methodology's effectiveness in both settings.