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

  • Irene FerrandoEmail author
  • Lluís Albarracín
Original Article


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.


Fermi problems Mathematical modelling Modelling sequences 


Funding information

This research is supported by the projects EDU2017-84377-R and EDU2017-82427-R (Ministerio de Economía, Industria y Competitividad, Spain) and also 2017 SGR 497 (AGAUR, Generalitat de Catalunya).


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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2019

Authors and Affiliations

  1. 1.Dpt. de Didáctica de la Matemática de la Universitat de València (UVEG)Universitat de ValènciaValenciaSpain
  2. 2.Dpt. de Didàctica de la Matemàtica i les Ciències Experimentals de la Universitat Autònoma de Barcelona (UAB)BellaterraSpain

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