Literature Index

The following paper will present some tentative ideas for the discussion on how the further evolution of curricula may react to changes in statistics which have become visible by the emergence of EDA. The emergence of Exploratory Data Analysis (EDA) presents a challenge to more traditional views, attitudes and value systems of statistics, which are often also the implicit basis of curricula and teaching approaches to statistics and probability. Simple examples, ideas and techniques of EDA are sometimes considered to be a new curriculum content, because it is hoped that they may replace the rather boring teaching of techniques of descriptive statistics by more interesting examples of real data analysis, where the students may become more actively involved in processes of discovering relevant features of the systems the data refer to.

For a quick and overall assessment of data sets, graphical methods are used extensively. Graphic statistics are devices for representing or summarizing numerical data or information. In this paper, some relatively new techniques, frequently referred to as methods of exploratory data analysis, are dicussed and illstrated with numerical examples.

Explored 5th graders' reasoning about data modeling by conducting 2 design experiments. In Exp 1, 10 Ss assumed the role of data analysts and developed a survey, collected and coded data, and used the dynamic notations of hypermedia to compare the lifestyles of American colonists to their own. In Exp 2, 2 5th graders and their teacher developed and used a randomized distribution to reason about the likelihood of ESP. Analysis of student conversations, including their dialogue with the teacher-researcher, indicated that the construction of data was an important preamble to description and inference. Students' ideas about many elements of data modeling were related to forms of notation. Experimentation afforded a framework for teaching about inference, grounded by the creation of a randomization distribution of the students' data.

Construing a collection of values of a sample statistic as a distribution is central to<br>developing a coherent understanding of statistical inference. This paper discusses key developments that<br>unfolded over three consecutive lessons in a classroom teaching experiment designed to support a group of<br>high school students in developing such a construal. Instruction began by engaging students in activities<br>that focused their attention on the variability among values of a common sample statistic. There occurred a<br>critical shift in students' attention and discourse away from individual values of the statistic and toward a<br>collection of such values as a basis for inferring the value of a population parameter. This was followed by<br>their comparisons of such collections and by the emergence and application of a rule for deciding whether<br>two such collections were similar. In the repeated application of their decision rule students structured these<br>collections as distributions. We characterize aspects of these developments in relation to students'<br>classroom engagement, and we explore evidence in students' written work that points to how instruction<br>shaped their conceptions.