Reflecting on mathematics

In our society, which is based on the division of labor, the ability to communicate with experts is a core competence. Reflection plays a central role for non-experts/laypersons in classifying and evaluating expert statements, and in the closely related decision-making process. Reflection is seen as a cognitive ability as well as an attitude. Mathematical concepts and models are applied in many socially relevant areas. For a (better) understanding of these, their fit, effects, limitations as well as their role and meaning, they should be dealt with and reflected on different levels. In the paper, the following levels of reflection are considered in more detail from this social perspective: mathematics-oriented, model-oriented, context-oriented, and subject-oriented reflection. The fact that such reflections can also be integrated into mathematics lessons is demonstrated by means of concrete tasks.