Students Reasoning About Variation in Risk Context

  • José Antonio Orta AmaroEmail author
  • Ernesto A. Sánchez
Part of the ICME-13 Monographs book series (ICME13Mo)


This chapter explores students’ reasoning about variation when they compare groups and have to interpret spread in terms of risk. In particular, we analyze the responses to two problems administered to 87 ninth-grade students. The first problem consists of losses and winnings in a hypothetical game; the second is about life expectancy of patients after medical treatments. The problems consist of comparing groups of data, and choosing one in which it is more advantageous to bet or to receive medical treatment. In this research we propose three levels of students’ reasoning when they interpret variation. Decision making in the third level of reasoning is influenced by risk. As a conclusion, some characteristics of the problems and the solutions provided by the students are highlighted.


Middle school students Reasoning Risk Statistics education Variation 



Grant EDU2016-74848-P (FEDER, AEI). Grant CONACYT No. 254301.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José Antonio Orta Amaro
    • 1
    Email author
  • Ernesto A. Sánchez
    • 2
  1. 1.Escuela Nacional para Maestras de Jardines de NiñosMexico CityMexico
  2. 2.Departamento de Matemática EducativaCentro de Investigación y de Estudios Avanzados del Instituto Politécnico NacionalMexico CityMexico

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