Literature Index

"Variation is the reason why people have had to develop sophisticated statistical methods to filter out any messages in data from the surrounding noise" (Wild &amp; Pfannkuch, 1999, p. 236). Both variation, as a concept, and reasoning, as a process, are central to the study of statistics and as such warrant attention from both researchers and educators. This discussion of some recent research attempts to highlight the importance of reasoning about variation. Evolving models of cognitive development in statistical reasoning have been discussed earlier in this book (Chapter 5). The focus in this chapter is on some specific aspects of reasoning about variation.<br>After discussing the nature of variation and its role in the study of statistics, we will introduce some relevant aspects of statistics education. The purpose of the chapter is twofold: first, a review of recent literature concerned, directly or indirectly, with variation; and second, the details of one recent study that investigates reasoning about variation in a sampling situation for students aged 9 to 18. In conclusion, implications from this research for both curriculum development and teaching practice are outlined.

This paper reports one recent study that was part of a project investigating tertiary students' understanding of variation. These students completed a questionnaire prior to, and at the end of, an introductory statistics course and this paper focuses on interviews of selected students designed to determine whether more information could have been gathered about the students' reasoning. Clarification during interviews reinforced researcher interpretation of responses. Prompting assisted students to develop better quality responses but probing was mostly useful for assisting students to re-express reasoning already presented. Cognitive conflict situations proved challenging. The diversity of activities identified by students as assisting the development of their understanding provides a challenge for educators in planning teaching sequences. Both educators and researchers need to listen to students to better understand the development of reasoning.

Teachers often come to our professional development programs thinking that statistics<br>is about mean, median, and mode. They know how to calculate these statistics, though<br>they don't often have robust images about what they mean or how they're used. When<br>they begin working with computer data analysis tools to explore real data sets, they are<br>able to see and manipulate the data in a way that hasn't really been possible for them<br>before. They identify particular points on graphs and can interpret what their positions<br>mean. They notice clumps and gaps in the data and generally find that there's a lot<br>more to see in the data than they ever imagined before. In addition, those exploring<br>data in this way often ground their interpretations in the range of things they know<br>from the contexts surrounding the data. They discover the richness and complexity of<br>data.<br>Yet all this detail and complexity can be overwhelming. Without some method of<br>focusing or organizing or otherwise reducing the complexity, it can be impossible to say<br>anything at all about a data set. How do people decide what aspects of a data set are<br>important to attend to? What methods do they use to reduce the cognitive load of trying<br>to attend to all the points? This paper will begin to describe some of the ways that<br>people do this while using new, software-driven representational tools. In the process,<br>we will begin to sketch out a framework for the techniques that people develop as they<br>reason in the presence of variability.

Reasoning with data is already pervasive in society, and its importance as a life skill is increasing. We argue that the current statistics curriculum in the United Kingdom at the secondary level does not prepare our young people adequately, and suggest ways in which it could be improved.