Task enrichment is an important teacher competency that can be considered as a special case of problem posing. For that reason, the theoretical framework of this article includes an overview of this topic, complemented with the analysis of inverse problems. The field work of this research was carried out in master courses in the University of Granada, Spain, where a couple of modelling problems were proposed to prospective teachers, who were asked to reformulate them in an inverse way to produce a richer version. The results are described, and the prospective teachers' strategies for problem posing and task enrichment are analysed, and also conclusions about this experience in teacher training courses are presented.