Teaching is deciding and acting in a complex system. If a teacher attempts to fulfil demands to teach mathematics with a stronger problem solving orientation, it becomes even more complex. This complexity must not be reduced arbitrarily. Instead, a sufficient degree of sensitivity is necessary to competently and flexibly deal with emerging demands on the teacher. In this article I provide an introduction to the concept of sensitivity to complexity of mathematics teaching and report on specific realistic and interactive diagnostic instruments. A particular focus is placed on a diagnostic interview about decision-making situations which could occur in a mathematics lesson. A first pilot study with student teachers from different German universities - briefly outlined in the last part of this article - suggests its suitability for gaining important indications of the agent's degree of sensitivity to complexity of problem solving mathematics teaching.