Task-based interviews were used to investigate some aspects of probabilistic thinking in 74 children (aged 5 to 12 years) from three different Australian schools, who had received little or no instruction in this topic. As expected, there was evidence of the development of probabilistic reasoning with age, but analysis of the children's responses and explanations revealed a variety of decision making strategies. Further comparisons between the mathematical structure of each task and the

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... ics inherent in the strategies used by the children, suggest that the design of the task, including the actual materials chosen, may be a crucial factor in teaching basic probability concepts to children. A recent direction in the research on the development of probability concepts in children is the attempt to develop a comprehensive framework that can be used to describe and assess children's understanding, which in turn can provide guidance for teaching (Watson and Collis, 1994; Fischbein and Schnarch, 1997; Jones, Langrall, Thornton, and Mogill, 1997). Hopefully this will also make it easier to link together the information gathered from the numerous specific studies, and facilitate the mapping of the relationship between basic probability concepts and other mathematical concepts. The study described in this paper is one that has attempted to take advantage of the fairly unique opportunity to examine intuitive understandings of probability concepts in school age children. This situation has arisen due to the absence of the topic of Probability from the New South Wales (Australian State) primary mathematics syllabus. The children for the study were drawn from three different schools and were nominated by teachers as being fairly representative of the school's mathematical performance. A set of games in which the children were asked to make certain choices and explain their reasoning were designed and used in one-to-one tape recorded interviews. The set of games evolved during the study so that none of the three schools completed exactly the same interview protocol. The sample size for each of the five research tasks ranged from 25 to 74 children. One task, Bears in a Box, was complete by every child in the study. RESEARCH QUESTIONS The key research questions for this exploratory study were: ICOTS 5, 1998: Jenni Way