Connecting the real world to mathematical models in elementary schools in Luxemburg

In the Luxemburgish national curriculum for elementary schools (MENFP, 2011) experimentations and discoveries of mathematics concepts in courses are strongly recommended. Elementary school teachers should engage students in active mathematical modelling approaches, where they can develop processes and content skills through discoveries. Moreover, learned skills should be connected to real-world problems and situations to foster a better understanding of students’ living environments. Nevertheless, this teaching culture in mathematics is unusual in elementary schools and teachers tend to teach based on textbooks. Students mostly learn mathematics by imitation and repetition rather than through modelling mathematics with real-world problems and situations. Thus, to develop new methodologies in teaching mathematics and to meet the requirements of the national curriculum, we designed different technology-enhanced teaching and learning methods to engage students in experimental approaches within and outside classrooms. Moreover, we conducted three studies with digital and physical modelling, augmented reality, and a tutoring system in elementary school mathematics courses. Based on our collected data, we identified settings and tasks likely to support active mathematical modelling approaches.