Likelihood and sample size: The understandings of students and their teachers

• Students’ understanding of probability and sample size.
• Teachers’ pedagogical knowledge of probability and sample size.
• No student difference in performance for problem context.
• Teachers aware of some, not all, student strategies.

The aim of this study was to consider the match of student statistical understanding and teacher pedagogical content knowledge in relation to sample size and likelihood. Students were given two contexts within which to compare the likelihood of events for different sample sizes. Teachers were presented with one of the contexts and asked what their students would do and how they would remediate incorrect responses. The data also provided the opportunity for a detailed hierarchical analysis of students’ and teachers’ understandings. Analysis of student solutions revealed a wide range of reasoning, some of which was apparently unfamiliar to teachers.