Visual support in Fermi problems: Exploring the role of representational pictures in pre-service teachers’ self-efficacy, flexibility and modelling performance

Fermi problems can be used to introduce mathematical modelling in primary education, yet they remain challenging even for pre-service primary teachers because they require estimating quantities without given numerical data, combining assumptions, spatial reasoning and simple calculations. This quasi-experimental study examines the role of representational pictures in pre-service teachers’ Fermi problem solving. A total of 151 pre-service teachers solved the same sequence of Fermi problems in one of two conditions: with or without pictures of the problem context. We analysed task-specific self-efficacy, modelling performance and intra-task flexibility, understood as the generation of different solution types within the same problem. Participants in the Picture condition achieved higher modelling performance and displayed greater intra-task flexibility than those in the No-picture condition, whereas task-specific self-efficacy did not differ between conditions. Intra-task flexibility was positively related to modelling performance in the Picture condition, but not in the No-picture condition. Within the Picture condition, participants who left visible material traces on the pictures achieved higher modelling performance, although not greater flexibility. Overall, the findings suggest that representational pictures may support Fermi problem solving by helping solvers organise the problem situation and consider alternative modelling approaches, while their role in supporting self-efficacy appears limited.