A Model for the Promotion of Statistical Thinking

This paper presents a model for statistical thinking in empirical enquiry, based on practitioner behaviour. The conjectured types of thinking that are fundamental to the statistics discipline are then used to analyse an assessment item and teaching situation. It is concluded that such an analysis is possible and that mOre discussion and research is needed on defining, clarifying, and articulating the statistical thinking that is embedded and inherent in statistic,al practice. Over the last thirty years introductory statistics teaching has been moving from mathematical statistics towards empirical statistics. At the same time significant shifts have been occurring in statistical practice with the increasing availability and power of computer technology and with many applied statisticians broadening their domain of practice to all parts of the problem solving empirical enquiry cycle. These shifts in practice are refocu.sing the emphasis in teaching from how to do, for example, a graph, mean or confidence interval, to how to think aboutthem. However, the development of students' statistical thinking can only be promoted if we know the type of thinking that is characteristic of the statistics discipline. Many articles discussing and characterising the core elements of statisti~al thinking have been written (e.g., Moore, 1990; Biehler, 1994). The Wild and Pfannkuch (1999) four-dimension~l model (Fig. 1 )~as an attempt to characterise practitioner thinking in the statistics dIscipline. The ,model' was developed as a result of: interviewing statisticians and tertiary students about statistical projects' they had been involved in; interviewing tertiary students as they performed statistical tasks; and analysing the literature. The focus of the statistical thinking was at the broad level of the statistical enquiry cycle, ranging from problem formulation to the communication of conclusions. The multidimensional natLJre of statistical thinking is captured in the model. Thus a thinker operates in all ,four dimensions at once. For example the thinker could be categorised as being currently in the analysis stage of the Investigative Cycle (Dimension 1), dealing with some aspect of variation in Dimension 2 (Types of Thinking) by criticising a proposed analysis against contextual knowledge of the situation in Dimension 3 (Interrogative Cycle) driven by scepticism in Dimension 4 (Dispositions). This paper focuses on the thinking that we believe is fundctmental' to statistics and how we might use these defined characteristics to analyse assessment items and teaching situations for the promotion of statistical thinking.