Abstract:

University education has increasingly integrated Information and Communication Technologies (ICT), especially in mathematics instruction, where computational tools and numerical simulations have redefined the learning process. From a pedagogical perspective, an in-depth study of practical teaching is essential to improve instructional approaches. Recent literature highlights that practice-based and real-world problem-solving learning are effective strategies. Studies have shown that students retain concepts better when they can experiment with them through problem-solving and interactive simulations. Additionally, gamification and computational challenges have been shown to improve student motivation and engagement. For the authors, classroom practices dedicated to problem-solving are vital, as they help students understand complex ideas and stay motivated.

The Mathematics course for the Bachelor's Degree in Geology at the University of Oviedo provides students with an introduction to integral and differential calculus, linear algebra, as well as probability and statistics.

The present research performed a qualitative study with 28 first-year students of the Bachelor of Geology at the University of Oviedo during the 2024-2025 academic year. These students, who regularly attended the Mathematics course’s practical sessions, constituted a group of intact individuals, as they were not randomly assigned for the research. They were asked to anonymously write down the qualities they considered most important for effective problem-solving practices. The analysis of their responses, which was carried out by calculating word frequency and creating a word cloud, allowed for the identification of the most repeated concepts.

The results identified four key dimensions that students value for their learning: clear main concepts, available materials, teacher methodology, and teacher-student interaction and autonomy.

Regarding session structure, students prefer an initial part with a teacher explanation followed by a second part of individual work. They also value the teacher providing a review of theoretical concepts and a final summary. For instructional materials, the priority is having access to practice guides, exercises with detailed solutions, and self-assessment questionnaires for individual practice.

In terms of methodology, students emphasize the importance of guided explanations, application examples in real-world problems, and in-class exercise correction. Also, interaction and autonomy are reflected in the need for sufficient time to complete exercises, the ability to ask questions during the session, and to receive feedback.

Finally, it can be stated that this study provides a solid foundation for improving Mathematics instruction in Geology degrees, suggesting that teachers should prioritize clarity in session structure, the provision of complete study materials with detailed solutions, and the implementation of methodologies that foster active student participation. The study underscores the need to continue adapting teaching strategies to maximize learning effectiveness and respond to the evolving needs of students.

Keywords:

Mathematics instruction, problem-solving learning, student engagement, instructional materials, qualitative study, educational trends and experiences, enhancing learning and the undergraduate experience.