Literature Index

This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.

Recently there has been a trend towards admitting expert statistical evidence in UK court cases. There have been a number of cases, however, in which outcomes have been distorted by statistical or probabilistic misconceptions and by faulty inference. Typically, lawyers receive no training in these areas apart from their compulsory school mathematical education. In this study, data was taken from five groups of trainee lawyers. This demonstrated that they made errors in assessing likelihoods, irrespective of the level and type of mthematical education that they have received. The typical approaches and content of mathematical education at school or college need to be re-considered. Data from two other groups of subjects (one of statistical educators) with different types of mathematical backgrounds were available for comparison purposes.

In this paper we describe a model of pedagogical content knowledge with a formative cycle directed to simultaneously increase the teachers' statistical and pedagogical knowledge. In this cycle, teachers are first given a statistical project to work with and then carry out a didactical analysis of the project. An analysis guide, based on the notion of didactical suitability, helps increase the teachers' competence related to the different components of pedagogical content knowledge and their ability to carry out didactical analyses. At the same time it provides the teacher educator with information regarding the future teachers' previous knowledge and learning. Results of experimenting with this formative cycle for a particular project in a group of 55 prospective teachers indicated a need for better statistics preparation of these teachers and illustrated the usefulness of the formative cycle and analysis guide proposed.

In response to the critical role that information plays in our technological society, there have been international calls for reform in statistical education at all grade levels (e.g., National Council of Teachers of Mathematics, 1989; School Curriculum and Assessment Authority &amp; Curriculum and Assessment Authority for Wales, 1996). These calls for reform have advocated a more pervasive approach to the study of statistics, one that includes describing, organizing, representing, and interpreting data. This broadened perspective has created the need for further research on the learning and teaching of statistics, especially in the elementary grades, where instruction has tended to focus narrowly on graphing rather than on broader topics of data handing (Shaughnessy, Garfield, &amp; Greer, 1996).<br><br>Notwithstanding these calls for reform, there has been relatively little research on children's statistical thinking and even less research on the efficacy of instructional programs in data exploration. Although some elements of children's statistical thinking and learning have been investigated (Cobb, 1999; Curcio, 1987; Curcio &amp; Artz, 1997; De Lange et al., 1993; Gal &amp; Garfield, 1997; Mokros &amp; Russell, 1995), research on students' statistical thinking is emergent rather than well established. Existing research on children's statistical thinking has certainly not developed the kind of cognitive models of students' thinking that researchers like Fennema et al. (1996) deem necessary to guide the design and implementation of curriculum and instruction.<br><br>In this paper, we will discuss how our research has built and used a cognitive model to support instruction in data exploration. More specifically, the paper will: (a) examine the formulation and validation of a framework that describes students' statistical thinking on four processes; and (b) describe and analyze teaching experiments with grades 1 and 2 children that used the framework to inform instruction.