An Exploration of Students' Statistical Thinking with Given Data

This paper examines how two twelve-year-old students built up their recognition and understanding of relationships in a set of data. Using a small multivariate dataset created by Watson, Collis, Callingham and Moritz (1995), the students conducted an investigation of their choice in a pencil-and-paper environment. The students' thinking across the three representations of cards, tables and graphs is analysed from the perspectives of transnumeration, consideration of variation, reasoning with statistical models, and integrating the statistical with the contextual, which were identified as fundamental statistical thinking elements in empirical enquiry in the framework of Wild and Pfannkuch (1999). The ways of thinking within each element across the representations are identified. In the analysis, references are also made to the types of statistical thinking present in the other ten students in the study. From the analysis we identified five issues that should be considered for determining how students construct meanings from data. They are: prior contextual and statistical knowledge; thinking at a higher level than constructed representations; actively representing and construing; the intertwinement of local and global thinking; and the changing statistical thinking dialogue across the representations.