Levels of Reasoning of Middle School Students about Data Dispersion in Risk Contexts

Abstract: The aim of this research study is to explore students ’ reasoning concerning variation when they compare groups and have to interpret dispersion in terms of risk. In particular, we analyze in this paper the responses to two problems from a questionnaire administered to 82 ninth-grade students. The problems consist of choosing between two and three groups of data by comparing them. The first one composed of losses and winnings coming from a hypothetical game; the second is about medical treatments. The results show the difficulty students had in interpreting variation in a risk context. Although they identify the data group with more variation, this is not enough for interpreting the variation in terms of risk and making a rational decision. The psychological categories of risk-seeking and risk-aversion are used to explain the behavior of students who choose one group or another when they identify correctly the risk in each situation. As a conclusion, it i