Bücher der Reihe Kolner Beitrage zur Didaktik der Mathematik

Mathematical problem posing as the substantive formulation of mathematical problems is an activity that lies at the heart of mathematics. In recent years, research in mathematics education has endeavored to gain insights into problem posing-conceptually as well as empirically. In problem-posing research, there has been a focus on analyzing products, that is, the posed problems. Insights into the processes that lead to these products, however, have so far been lacking. Within four journal articles, summarized in this cumulative dissertation, the author attempts to contribute to the understanding of problem-posing processes through conceptual considerations and empirical investigations. The conceptual part consists of a conducted systematic literature review to investigate problem-posing situations and problem-posing activities. The studies in the empirical part deal with the analyses of problem-posing processes of pre-service mathematics teachers from a macroscopic and microscopic perspective. The aim is to develop coherent and meaningful conceptual perspectives for analyzing empirical observations of problem-posing processes.

The use of Likert scale instruments for measuring teachers' beliefs is criticized because of amplifying social desirability, reducing the willingness to make differentiations, and often providing less or no contexts.