Teachers' understanding of the arithmetic mean

A review of the current literature about statistical and probabilistic ideas was undertaken. The concept of the arithmetic mean was chosen as the focus of an experimental study. A questionnaire was administered which required increasingly sophisticated understanding of this concept in the concrete-symbolic mode, and also allowed for ikonic mode processing. Responses gained from 136 pre- and in-service teachers were analysed from three perspectives. Qualitative analysis allowed some comparison of the responses from this sample to similar studies by other researchers. Differences between sub-groups of respondants were analysed quantitatively for significance. Consideration of these results from the viewpoint of cognitive development provided some possible explanations. Developmental cycles in both ikonic and concretesymbolic mode were identified and described. A theoretical model is proposed to explain the interaction between these cycles. From this recommendations are made for teacher development, and further research.