Research-based guidance and classroom activities for teachers of mathematics

Distribution

Distribution is a theme within reasoning about uncertainty. Links to relevant activities and resources are on the right hand side of this page. 

Piaget and Inhelder reported how the intellectual demands of constructing probabilistic knowledge included not only an understanding of randomness and proportion, but also combinatorics.

Knowledge of combinatorics enables the delineation of the sample space associated with a random variable. For example, whereas constructing the sample space for the throw of a single die might be trivial for older students, there might be rather more difficulties in identifying the 36 items in the sample space for the throw of two dice.

Often students have difficulty in managing the order of the elements, for example not including both (1,2) and (2,1). Students also need to recognise the relationship between the sample space and the distribution of results. What actually happens might be seen as simply a matter of luck, or it might not be appreciated that a direct association depends on the number of trials.