Students Reasoning About Variation in Risk Context

Abstract

This chapter explores students’ reasoning about variation when they com- pare 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 com- paring 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 rea- soning is influenced by risk. As a conclusion, some characteristics of the problems and the solutions provided by the students are highlighted.