Students estimating large quantities: From simple strategies to the population density model

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© 2018 by the authors; licensee Modestum Ltd., UK. We study how a group of 16-year-old students solve a sequence of problems that require estimating large quantities. The problem sequence was designed to foster students creating mathematical models. We characterise the models constructed by the students while working both individually and in small teams and analyse how they evolve throughout the sequence because of having to deal with the restrictions imposed by the real-life context of the different problems. We observe that: a) the students progressively abandon the poorest strategies of the initial individual schemes to embrace strategies adaptable to a greater number of scenarios; b) students change the conceptual strategies that support their models, not as a result of a conceptual discussion, but as a consequence of a procedural obstacle or limitation; c) they adjust their models by introducing nuances, because of a better mathematization of the given situation. As a group, they finally reach a model - a generalization of the idea of population density - that is not only useful for solving a particular problem, but can apply to other situations.
Original languageEnglish
Article numberem1579
Pages (from-to)1-15
JournalEURASIA Journal of Mathematics, Science and Technology Education
Issue number10
Publication statusPublished - 1 Jan 2018


  • Compulsory secondary education
  • Estimation
  • Modelling-eliciting activities
  • Models
  • Population density


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