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In this chapter, we consider how problem posing forms an integral part of mathematical modelling and consider its placement during modelling processes. The problem and its formulation is an essential part of modelling, and a modelling process is usually associated with a continual adjustment and reformulation of the main problem. In addition, one may formulate conjectures, ask monitoring and control questions, and have a critical stance toward the model and its results. We consider how the educational intention of the modelling activity and the placement in the modelling cycle relates to the problems and questions being posed. We briefl y consider how problem posing may be implemented in mathematical modelling through the use of students' conjectures and by students acting as consultants and clients.

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In this study, we aim to explain choices that groups of preservice teachers made to implement modelling tasks in primary school. We found that the preservice teachers decided to facilitate everyday-inspired contexts for the tasks and that this could be explained by their reasoning that modelling is supposed to be an activity close to reality. Essentially, the groups preferred two different approaches to introducing students to the tasks: (1) by inviting students to physically participate in situations related to their local communities that were familiar to them (e.g. trash picking), and (2) through pre-structured problems that were recognisable to students (e.g. estimation of the number of beads in an irregular box). We found evidence that the preservice teachers tended towards avoiding focusing on possible mathematical answers to the tasks. This could be explained by lacking experience with how to find approximate solutions, or that the preservice teachers were engaged in observing students’ solution strategies and mathematical behaviour.