School-age children and being outdoors are intrinsically linked. Education and the outdoors offer unique opportunities to extend the learning potential of children at this age in a more engaging way. From the point of view of mathematics, this way of learning is very suitable and certainly motivating for the pupils since mathematics, especially geometry, is not very popular among pupils. Therefore, in this article, we describe how we used an out-of-school learning experience for second-level primary school pupils (sixth to ninth grade) to link mathematics to outdoor learning. Activities that we solved with pupils in the outdoor environment were solved in the teaching process using only modeling. Practical applications were illustrated through interesting topographic fieldwork, which we analyzed for their appropriate integration into the teaching process by means of a priori analysis. The inclusion of these practical problems was preceded by research on 781 pupils of primary schools who solved application problems related to the circle and the square. It was clear from the research that pupils have a significant problem with the geometric interpretation of simple geometric concepts, which can be improved with the use of mathematical modeling and the linking of similar problems that can be carried out in a non-school environment.

Interdisciplinary teaching enhances student learning but poses challenges in practical implementation. This study examines the co-design of an interdisciplinary MathCityMap trail by mathematics and physics educators, analyzing tensions and synergies through the ROGI framework (Resources, Orientations, Goals, Identity). Using qualitative methods, including reflective journals and co-design, we explore how disciplinary perspectives shape task design. A key constraint was the MathCityMap system’s requirement for verifiable outcomes, limiting open-ended inquiry, particularly in mathematics. While mathematics educators emphasized conceptual understanding, physics educators prioritized hands-on experimentation, leading to tensions in defining inquiry-based learning. Despite these challenges, the collaboration yielded innovative solutions, such as adapting tasks to balance system feasibility with inquiry-driven exploration. The study highlights the need for digital tools that accommodate both procedural and exploratory learning and emphasizes interdisciplinary collaboration as a valuable professional development approach. Future research should focus on enhancing digital platforms to support inquiry-based methodologies in STEM education.