# Was built up through examining the statistics

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was built up through examining the statistics discipline itself and can be thought of as a way of describing the type of thinking that should be fostered in students. Some interviews with 11 and 12 year-olds (Rubick, 2000), while conducting their own statistical investigation with a small multivariate data-set created by Watson, Collis, Callingham and Moritz (1995), were presented as well as the students’ written tables, graphs and conclusions. The data were analysed through the four lens of transnumeration, consideration of variation, reasoning with statistical models and integrating the statistical with the contextual (Yoon, 2001). These four aspects were identified in the Wild and Pfannkuch framework as being fundamental types of statistical thinking. The analysis of the data attempted to describe the students’ reasoning through these four lens. For example, data were provided to demonstrate students’ noticing local and global variation, explaining local and global variation, controlling variation and quantifying variation. All these data showed students’ emergent understandings of variation. The following four aspects were highlighted as a result of group discussion about the data presented. First that students’ views of data throughout a statistical investigation involve not only an intertwinement of local and global statistical thinking but also an intertwinement of local and global contextual thinking. Second that students created their own representations for displaying multivariate data which seemed to be fostering statistical thinking and seemed to be part of learning how to represent data. Third that developing an awareness of the need to converse with the data as well as to have different conversations with data in their various representations is part of the reasoning process throughout an investigation. These conversations build up an understanding of relationships in a data-set and enable students to learn more in the context sphere. Four that students need to play the dual role of corroborator and discoverer. The corroborator uses data to justify a claim whereas the discoverer is the explorer or data-detective or hypothesis generator who looks at data for possible interesting patterns, features, anomalies and so forth. REFERENCES Rubick, A. (2000). The statistical thinking of twelve year 7 and year 8 students. Unpublished Master’s thesis. The University of Auckland, New Zealand. Watson, J., Collis, K., Callingham, R. & Moritz, J. (1995). A model for assessing higher order thinking in statistics. Educational Research and Evaluation , 1, 247-275. Wild, C. & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion ). International Statistical Review , 67(3), 223-265. Yoon, C. (2001). An analysis of students’ statistical thinking. Unpublished Master’s dissertation, The University of Auckland, New Zealand.

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