Literature Index

Stochastic thinking denotes a person's cognitive activity when coping with stochastic problems, and/or the process of conceptualization, of understanding, and of information processing in situations of problem coping, when the chance or probability concept is referred to, or stochastic models are applied. In accordance with our view on stochastic thinking in decision making under uncertainty, three different aspects may be emphasized in psychological research: (1) the behavioral analysis, which may focus on analyzing or improving the product of the decision process. (2) The procedural analysis, which may, for instance, attempt to identify cognitive strategies of heuristics when tracing the process of thinking; and (3) the semantic or conceptual side, for instance, when analyzing the individuals's knowledge about probability or his/her use of probability to conceptualize uncertainty. Chapters: 1. Toward an understanding of individual decision making under uncertainty 2. The "Base-Rate Fallacy" - heuristics and/or the modeling of judgmental biases by information weights 3. A conceptualization of the multitude of strategies on base-rate problems 4. Modes of thought and problem framing in the stochastic thinking of students and experts (sophisticated decision makers) 5. Stochastic thinking, models of thought, and a framework for the process and structure of human information processing

For introductory statistics education, several types of software are relevant and in use: custom designed educational programs for a specific educational goal, statistical systems for data analysis (in full professional version, in student version or as a specifically designed tool for students), statistical programming environments, spreadsheets and general purpose programming languages. We can perceive a double dilemma on a practical and on a theoretical level, which is the worse the lower the educational level we have in mind. On the one hand, we have professional statistical systems that are very complex and call for high cognitive entry costs, although they flexibly assist experts. On the other hand, custom designed educational software is of necessity constrained to enable students to concentrate on essential aspects of a learning situation and to make likely certain intended cognitive processes. Nevertheless, as these microworlds, as we will call them here, for short, are often not adaptable to teachers' needs they are often criticized as being too constrained. Their support for flexible data analysis is limited, and to satisfy the variety of demands one would need a collection of them. However, coping with uncoordinated interfaces, notations and ideas in one course would overtax the average teacher and student. This practical dilemma is reflected on a theoretical level. It is not yet clear enough what kind of software is required and helpful for statistics education. We need a critical evaluation and analysis of the design and use of existing educational and professional programs. The identification of key elements of software that are likely to survive the next quantum leap of technological development and that are fundamental for introductory statistics is an important research topic. Results should guide new "home grown" developments of educational programs or, facing the difficulty of such developments, should influence the adaptation and elaboration of existing statistical systems toward systems that are also more adequate for purposes or, facing the difficulty of such developments, should influence the adaptation and elaboration of existing statistical systems toward systems that are also more adequate for purposes of introducing and learning statistics. We will give some ideas and directions that are partly based on results of two projects.

This paper provides practical examples of how statistics educators may apply a cooperative framework to classroom teaching and teacher collaboration. Building on the premise that statistics instruction ought to resemble statistical practice, an inherently cooperative enterprise, our purpose is to highlight specific ways in which cooperative methods may translate to statistics education. So doing, we hope to address the concerns of those statistics educators who are reluctant to adopt more student-centered teaching strategies, as well as those educators who have tried these methods but ultimately returned to more traditional, teacher-centered instruction.

In this paper I summarize my 25 years of research on teaching and learning statistics, as I participated in the emergence of statistics education as a research discipline. This summary and reflection are presented through stories of research projects I have been involved in, all of which involved collaborations with colleagues who have made important contributions to the research and from whom I have learned many important lessons. I summarize and reflect on three interconnected areas of research: synthesizing and building on research studies across diverse disciplines, developing and using good assessment instruments to evaluate and improve student learning, and studying the role of technological tools in developing students' reasoning about specific concepts.