Transnumerative thinking: finding and telling stories within data

A critical component in the development of students' statistical thinking and reasoning is transnumerative thinking; that is, changing representations of data to engender an understanding of observed phenomena. Examples from Years 6 to 9 New Zealand students' and Australian students' representations of data from a given multivariate dataset are described. Their representations are discussed in terms of their developing abilities to explore data and unlock the stories contained therein. The implications of changing the focus of statistics instruction and the curriculum from merely teaching students how to construct graphs to exploring and representing patterns and relationships in data are presented.