Students from grade 2 to grade 10 solving a Fermi problem: analysis of emerging models

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of elements distribution and the strategy used. The results show how the students adapt their solutions in order to tackle the problem from their available knowledge. Indeed, younger students have important difficulties to deal with two-dimensional mathematical contents, but they overcome them by simplifying the problem. Finally, we also discuss the possibilities of using the proposed problem as part of a sequence to promote mathematical modelling in each educational stage, in basis of the potentialities identified in our analysis.