Literature Index

This paper focuses on the theme of statistical education and includes the following topics: 1. Theories of learning: how we think students learn 2. What we would like students to learn: in terms of statistical ideas, concepts, skills and beliefs 3. Research on teaching and learning statistics 4. Research on teaching and learning mathematics that relates to teaching and learning statistics 5. Implications of research for teaching statistics 6. One example: an alternative statistics course 7. What we still need to find out: a research agenda 8. Current projects

This paper provides an overview of current research on teaching and learning statistics, summarizing studies that have been conducted by researchers from different disciplines and focused on students at all levels. The review is organized by general research questions addressed, and suggests what can be learned from the results of each of these questions. The implications of the research are described in terms of eight principles for learning statistics from Garfield (1995) which are revisited in the light of results from current studies.

Once upon a time there was only one t distribution, the familiar central t, and it was monopolised by the Null Hypotheses (the Nulls), the high priests in Significance Land. The Alternative Hypotheses (the Alts) felt unjustly neglected, so they developed the noncentral t distribution to break the monopoly, and provide useful functions for researchers-calculation of statistical power, and confidence intervals on the standardised effect size Cohen's d. I present pictures from interactive software to explain how the noncentral t distribution arises in simple sampling, and how and why it differs from familiar, central t. Noncentral t deserves to be more widely appreciated, and such pictures and software should help make it more accessible to teachers and students.

Attempts to teach statistical thinking using corrective feedback or a ``rule-training'' approach have been only moderately successful. A new training approach is proposed which relies on the assumption that the human mind is naturally equipped to solve many statistical tasks in which the relevant information is presented in terms of absolute f requencies instead of probabilities. In an investigation of this approach, people were rained to solve tasks involving conjunctive and conditional probabilities using a requency grid to represent probability information. It is suggested that learning by doing, whose mportance was largely neglected in prior training studies, has played a major role in the current training. Study 1 showed that training that combines external pictorial epresentations and learning by doing has a large and lasting effect on how well people an solve conjunctive probability tasks. A ceiling effect prevented comparison of the requency grid and a conventional pictorial representation (Venn diagrams) with respect o effectiveness. However, the grid representation was found to be more effective in Study 2, which dealt with the more difficult topic of conditional probabilities. These results uggest methods to optimize the teaching of statistical thinking and the presentation of statistical information in the media.