Pictures in Fermi Problems: How Do Prospective Teachers Use Them in the Modelling Process?

The process of solving a modelling problem is complex and requires decision-making, estimation, proposing a model, mathematical work, and, often, revising the model and modifying to adapt it to the conditions of the real context in which the problem is formulated. This chapter develops an exploratory study focusing on the use of pictures in the model development process. For this purpose, a qualitative analysis of the written productions of 64 prospective mathematics teachers from Turkiye and Spain has been carried out. Several examples of solutions in which some prospective teachers make their estimations directly on the picture and some use the picture as a mediator to modify the model are discussed. It is also observed that reasoning based on visual information provided by the picture allows the incorporation of realistic assumptions in the solutions.