One hundred eight students in Grades 3, 5, 6, 7, and 9 were asked about their beliefs concerning fairness of dice before being presented with a few dice (at least one of which was "loaded") and asked to determine whether each die was fair. Four levels of beliefs about fairness and four levels of strategies for determining fairness were identified. Although there were structural similarities in the levels of response, the association between beliefs and strategies was not strong. Three or four years later, we interviewed 44 of these students again using the same protocol. Changes and consistencies in levels of response were noted for beliefs and strategies. The association of beliefs and strategies was similar after three or four years. We discuss future research and educational implications in terms of assumptions that are often made about students' understanding of fairness of dice, both prior to and after experimentation.

A key element in developing ideas associated with statistical inference involves developing concepts of sampling. The objective of this research was to understand the characteristics of students' constructions of the concept of sample. Sixty-two students in Grades 3, 6, and 9 were interviewed using open-ended questions related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure, and objectives elf statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions.

This paper presents an analysis of three questionnaire items which explore students’ understanding of chance measurement in relation to the development of ideas of formal probability. The items were administered to 1014 students in Grades 3,6 and 9 in Tasmanian schools. The analysis, using the NUD•IST text analysis software, was based on the multimodal functioning SOLO model. An analysis of the results and a developmental model for understanding chance measurement are presented, along with implications for curriculum and teaching practice.

A survey item based on a newspaper article about coin tosses was administered to 1256 students from grades 6 to 11. Few students determined the probability of four successive tails. Most students considered that heads and tails were equally likelyfor a subsequent fifth toss, often describing the probability as "50-50". Students in higher grades were more likely to respond appropriately. Results are discussed with reference to equiprobability, independence, the gambler'S fallacy, and the outcome approach to probability.