Making connections between the sample space and the probability of an event

Abstract

In this paper, I explore students' emerging thinking about "sample space" and "probability of an event" through an observation of 9- to 10-year-olds, challenged to reason about conditional probability in both "with" and "without" replacement situations. This study used a cognitive framework that captures the nature of students' probabilistic reasoning across four levels (subjective, transitional, informal quantitative, numerical) in relation to conditional probability tasks. The results show shifts in the structural complexity of students' thinking across the first three levels. However, none of the students reached level 4.