Literature Index

Statistical literacy encompasses competencies regarding the use of mathematical representations and the manipulation of data through reduction. Dealing with data referring to authentic situations, basic activities of modeling are linked to this domain of statistical literacy. Based on the recently introduced German standards emphasizing the importance of representations and modeling, our study aims at assessing competencies of middle graders in German classrooms. Therefore, a pilot study with more than 180 fifth- and eight-graders in upper secondary schools was conducted with the additional aim of testing the properties of a set of assessment tasks. The results support on the one hand typical misconceptions of students and specify on the other hand the status quo of the domain of statistical literacy in question. Using Rasch-analysis we can support the hierarchical concept.

To support NCTM's newest process standard, the potential of multiple representations for teaching repertoire is explored through a real-world phenomenon for which full understanding is elusive using only the most common representation (a table of numbers). The phenomenon of "reversal of a comparison when data are grouped" is explored in surprisingly many ways, each with their own insights: table, circle graph, slope & correlation coefficients, platform scale, trapezoidal representation, unit square model, probability (balls in urns), matrix determinants, linear transformations, vector addition, and verbal form. For such a mathematically-rich phenomenon, the number of distinct representations may be too large to expect a teacher to have time to use all of them. Therefore, it is necessary to learn which representations might be more effective than others, and then form a sequence from those selected. Pilot studies were done with pre-service secondary teachers (n1 = 7 at a public research university and n2 = 3 at a public comprehensive university) on exploring a sequence of 7 different representations of Simpson's Paradox. Students tended to want to stay with the most concrete and visual representations (note: a concrete-visual-analytic progression may not be expected to apply in the usual manner in the particular case of Simpson's Paradox).

The first section introduces a distinction between two families of cognitive operations, called System 1 and System 2. The second section presents an attribute-substitution model of heuristic judgement, which elaborates and extends earlier treatments of the topic. The third section introduces a research design for studying attribute substituion. The fourth section discusses the controversy over the representativeness heuristic. The last section situates representativeness within a broad family of prototype heuristics, in which properties of a prototypical exemplar dominate global judgements concerning an entire set.

Features of software tools that can support learning and doing statistics in introductory courses are the focus of this paper. We will start with describing assumptions concerning the direction in which introductory statistics education should move and improve, which are discussed in more detail elsewhere (e.g. Biehler (1992); Biehler (1993); Gordon & Gordon (1992); Thisted & Vellemann (1992)). Our notion of introductory statistics education comprises the teaching of "stochastics" within mathematics education in schools and data analysis in other school subjects. After that, we will discuss requirements of software in more detail, and how we integrated requirements in the paper-and-pencil prototype of the MEDASS-project in Biehler & Rach (1992).