Children’s development of sample space understanding and the effectiveness of sample space exercises on probability test performance

Abstract

Sample space refers to all possible elementary outcomes of an event (e.g. for a coin toss sample space refers to heads and tails). The understanding of sample space, which is crucial for understanding probability, has proven to be difficult for children. Children often only come up with the “sample set”, composed of the aggregated outcomes of an event. Using a counterbalanced repeated measure design in a sample of children aged 7 to 13, it was investigated whether sample space understanding develops through four stages: 1) no understanding of the concept of chance, 2) sample set thinking, 3) preliminary distinction between sample set and sample space and 4) distinction and comparison between sample set and sample space. Second, it was investigated whether sample space exercises enhance children’s probability test performance. Results indicated that the development of sample space understanding did not correspond to the four stage model. However, sample space understanding development did correspond to a three stage model in which the initial third and fourth stage were combined. Additionally, sample space exercises reduced performance on probability tests. These results suggest that there is an underlying latent ability of sample space understanding and that exercises used in the present study are not effective for enhancing probability test performance. Longitudinal research is needed that examines the development of sample space within children and whether other types of sample space exercises can enhance probability test performance.