Drawing Connections from Modelling Distribution to Data-centric Distribution

Drawing connections between theoretical frequencies and observed relative frequencies is advocated by various researchers. Little is known, however, about the process by which these connections are developed. The focus of this paper is on students' (aged 14 to 15 years) constructions of meanings about the intentionality interpretation when co-ordinating the two perspectives on distribution. Extracts from two research studies illustrates students' construction of the intentionality route from the model (modelling distribution) to the data (data-centric distribution) through their attempts to transform, the specific modelling distribution, and observing how that changes a graph/histogram of the actual outcomes, by using on screen control mechanisms to change the way that the computer generates the data within a carefully design computer simulation. In many respects their interpretations were based on similar characteristics to those of experts.