Mathematics does not only happen in the classroom—it is all around us. Buildings, streets, parks, and public spaces offer countless opportunities to explore mathematical ideas in real-world contexts. This is exactly where Mathtrails come in.
A Mathtrail is a structured learning path in a real environment: learners move through their surroundings and solve mathematical problems directly on site. In doing so, they connect mathematical concepts with authentic situations—from geometry in architecture to estimation, measurement, and modelling tasks.
Mathtrails are a part of outdoor education. They can be used in school context to offer a reallife experience beside of textbooks. Nevertheless, a mathtrail requires good preparation and a solid postprocessing in the classroom.
Many examples for tasks coming from geometrical background. It is obvious to ask for the height of building or a statue, as well as asking for the volume of a pond. But there is more to discover, combinatorical problems can be solved, functions can be discovered or even statistics are possible.
Benefits
Mathtrails support a modern, student-centered approach to mathematics education and are strongly aligned with current research and development goals.
- Authentic and contextualized learning
Students experience mathematics as something meaningful and applicable to real life, rather than abstract theory. - Increased motivation and engagement
Outdoor learning, movement, and discovery-based activities foster curiosity and active participation. - Development of key mathematical competencies
Math Trails promote problem-solving, mathematical modelling, and reasoning—core goals of contemporary mathematics education. - Support for inclusive and differentiated learning
Tasks can be adapted to different ability levels, allowing all learners to participate meaningfully. - Sustainable understanding through experience
By connecting concepts to physical experiences, students develop deeper and longer-lasting understanding.
Overall, Mathtrails combine cognitive, physical, and social learning, making mathematics more accessible, engaging, and relevant.
MathCityMap
One way to implement these ideas is the MathCityMap-System (www.mathcitymap.eu). MathCityMap is a Mathtrail management system, where users can create tasks and trails and share them amongst themselves or with the public.
With MathCityMap, implementing Mathtrails becomes both practical and powerful in everyday teaching. The platform provides a comprehensive digital environment that supports the entire learning process—from task design to classroom implementation and evaluation.
Teachers can easily create their own tasks and trails or draw on a large, shared collection of existing materials. Using the mobile app, students are guided through their surroundings and solve tasks directly at specific locations, turning the environment into an interactive learning space. Immediate feedback on their solutions helps them to reflect on their thinking and supports self-regulated learning. At the same time, teachers can organize activities within digital classrooms, monitor progress in real time, and gain valuable insights into students’ learning processes through integrated analytics. In this way, MathCityMap seamlessly connects outdoor exploration with structured, data-informed teaching.
Within the European project METEOR (Modern Math Trail Experiences for Europe), MathCityMap will be further developed to meet the evolving needs of education and to ensure that outdoor mathematics remains a sustainable and future-oriented approach. A central focus lies on the integration of artificial intelligence, which enables more adaptive and individualized learning experiences.