# Optimization in mathematical modeling

In the context of this material didactic research project, we would like to explore ways towards a problem-oriented, interdisciplinary and authentic mathematics / modeling teaching that moves away from working in rigid lessons towards a more open project teaching. The research focus is optimization in mathematical modeling with students.

Optimization problems, described as a fundamental idea of mathematics, are highly diverse and multifaceted (cf. Vogel, 2010, p. 6; Humenberger, 2015). On the one hand, they permeate the most diverse areas of mathematics (both discrete and continuous mathematics) and draw on numerous elementary mathematical foundations and concepts. On the other hand, such problems hide behind diverse applications and technologies. Be it when the optimal irradiation of tumors is simulated and determined before the actual radiation therapy, when the wings of an airplane are optimally designed with respect to aerodynamics, or when faces of people are to be recognized in the best possible way in automatic face recognition. Optimization problems have an enormous relevance for problems in everyday life and research and thus represent a promising candidate for mathematical modeling with students.

By selecting suitable problems and designing and implementing innovative modeling projects for students, the following questions in particular are to be answered:

- What mathematical understanding is required to work on optimization problems and to formulate them in such a way that good solutions are found?
- To what extent can the discussion of central aspects in the modeling of optimization problems be realized in a problem-oriented way by an appropriate design of learning material?
- To what extent can teachers be "enabled" and motivated to teach such modeling projects by appropriate teaching-learning material?

**Literature:**

Humenberger, H. (2015). Zur Einführung. In: Der Mathematikunterricht. Schwerpunkt: Optimieren. (61) 1/2015, Velber: Friedrich Verlag.

Vogel, D. (2010). Maximal, minimal, optimal,… In: mathematik lehren Nr. 159, Velber: Friedrich Verlag.