Topic of the diploma thesis: Problem solving in the teaching of mathematics Objective: Problem solving is a universal cognitive process and is thus essential not only in our daily lives but also in research and at school. The aim of this diploma thesis is to give an answer to the question of how different problem-solving strategies can be implemented in class. Consequently, the findings may help develop a realistic concept of teaching and practising problem-solving skills. Implementation: This diploma thesis is divided into two parts. The first one serves to provide some theoretical information on problem solving. The theory also comprises definitions from a psychological, a mathematical and a didactical point of view. Besides, there is an introduction to the problem-solving methods. The second part is the more practical part. In this section, the author analyses the results of the problem-solving tasks applied in class.