Proceedings

This study examine 56 elementary school teachers' knowledge of statistics before and after a three-week statistics workshop. Content knowledge was assessed through a paper-and-pencil instrument of twelve, open-ended statistics questions; responses were scored holistically.

Much has been written about methods of teaching statistics and about how to assess students' knowledge of statistics, but almost nothing on the extent to which assessment procedures measure whether students understand statistical concepts, or whether they understand what is involved in the application of statistical techniques. There has in fact been very little research on the development of instruments designed specifically to measure statistical understanding. There is, however, work in related areas which has some bearing on the assessment of understanding of statistical concepts. In reviewing this work this paper discusses the extent to which understanding is covered by some classification schemes which have been developed for use in mathematics and looks at ways in which attitude scales investigate understanding. Some alternatives to traditional methods of examining brought about by changes in the method of teaching are also considered.

Statistical power is defined as the likelihood that a particular test will correctly determine a false null hypothesis. This paper describes an ongoing research program focused on the teaching, learning, and understanding of ideas related to statistical power. The research described includes investigations of the effectiveness of instruction using a specially designed interactive software program (the Power Simulator), and the development and use of assessment instruments to measure students' informal understandings of power prior to instruction.

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.