Real Objects as a Reason for Mathematical Reasoning -- A Comparison of Different Task Settings

In this article, the goal is to describe students' mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to problem-solving and modelling, theoretical potentials for mathematical reasoning emerge. In a qualitative study with 19 secondary school students these are empirically tested. The evaluation of the video recordings of the students' solution processes are coded with the help of qualitative content analysis, among others with references to problem-solving and linguistic categories of conclusive speech acts. The results show that mathematical reasoning can be observed especially in the work with photos and that the work with real objects generally evokes reasoning activities in the area of planning and exploration of strategies.