Exploring Topology in Secondary Education through Game-Based Learning

Introduction
Topology is rarely included in secondary mathematics curricula, yet it offers strong potential to foster abstract reasoning and spatial thinking. Its visual and conceptual nature makes it particularly suitable for exploratory learning. This study presents an educational proposal that introduces basic topological ideas in Secondary Education through practical and game-based experiences. By using interactive digital environments, students are encouraged to discover properties of shapes and spaces in an intuitive and meaningful way.

Methods
The study began with a review of research on the introduction of advanced mathematical topics at non-university levels, with special attention to topology. A second review examined the educational value of digital games in mathematics teaching. Based on these findings, a set of learning situations was designed around interactive geometry and topology games available on the platform Geometry Games. The proposal integrates principles of game-based learning and inquiry-based learning: students explore virtual environments, formulate conjectures, test ideas, and discuss their conclusions. Activities were structured to connect topological concepts with everyday contexts and real-world applications.

Results
The implementation suggests that interactive digital games can make abstract concepts more accessible and engaging. Students showed increased motivation and were able to identify topological properties such as continuity and transformation through guided exploration. The activities also supported the development of logical reasoning, spatial awareness, and problem-solving skills.

Conclusions
Introducing topology through structured game-based experiences is both feasible and pedagogically valuable in Secondary Education. While careful guidance is needed to ensure conceptual clarity, this approach opens new possibilities for bringing advanced mathematics closer to younger learners in a meaningful and motivating way.