Expectation versus variation: Students decision making in a chance environment

This study explores school students' understanding of variation within a probabilistic setting involving spinners. Sixty-six students in Grades 3 to 9 answered survey questions involving a single 50/50 spinner and then were interviewed using a protocol involving compound events with different types of spinners (50/50 and 25/75). Of interest in interviews were students' initial responses and changes in response and reasoning that occurred after experimentation with the spinners. Because there was the possibility of variation occurring in the experiments that could be considered contrary to expectation, responses following experimentation were analysed based on their appropriateness in terms of the observed experimental outcome. Data were used to determine a developmental progression among the students in the study and data from survey responses were considered in relation to the interview data. Differences were found between primary and secondary students. The outcomes of the study lead to suggestions for the classroom and for future research in relation to expectation and variation in probabilistic settings.