Productive reasoning of any kind is achieved through heuristics, and motivated by an anticipatory approach structured as intuition. This recognition has had important consequences in thinking about probability, since the intuitive substrate available in this domain is relatively inconsistent and ambiguous. A proper curriculum of probability learning should, then, take into account this primary intuitive substrate, and concern itself with improving it and with finding methods of building new intuitions which are readily compatible with it. Two main directions of research have been taken in relation to the formation of the concept of probability. The first originated by Tolman and Brunswick, concerns what has been termed probability learning. The second main line of research concerns the organisation of conceptual schemas in the domain of probability: the development of concepts such as chance, proportion, and the estimation of odds, and the development on children of the concepts and procedures of combinatorial analysis. These two directions of research are focussed on rather different problems, and the techniques they use are, consequently, different. Yet, as will be seen in the following chapters, their findings can be successfully combined in an effort to reach a unified view of this area.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education