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This cumulative thesis presents a PhD research on mathematical modelling with real-world information, objects, places and situations in the classroom, remote teaching, and outdoor learning in Luxembourg. We investigated different technology-enhanced tasks, learning, and teaching settings that could likely engage students in understanding and transferring mathematical modelling to their living environments through design-based explanatory studies. The selected design-based research methodology and its characteristics allowed us to adapt task designs, settings and methods throughout the research process. Hence, firstly, we investigated process skills learning (e.g., mathematical modelling) with an automated tutoring system (i.e., the educational technology software MathemaTIC) based on real-world information from arithmetic word problems within an international project. Although findings were promising, we redesigned interventions to connect mathematical modelling with real-world objects. Thus, secondly, we performed mathematical modelling tasks with augmented reality applications, CAD software and 3D printing on real-world objects in remote teaching and special needs education with elementary school students. Thirdly, we undertook our final study utilising findings of these studies and redesigned an intervention that was based on outdoor mathematical trails. We explored outdoor mathematical modelling with an integrated STEAM (Science, Technology, Engineering, Arts, and Mathematics) approach. Through such a holistic approach, we collected data on education-related perceptions of different elementary school education stakeholders (i.e., students, parents, in-service, and pre-service teachers) and developed conceptual frameworks on task creation, mathematical modelling, and stakeholders roles. In this cumulative thesis, we aspired to contribute and to explain how in-class learning and teaching could be connected and tra eingereicht von Ben Haas Universität Linz, Dissertation, 2021