Theory

In their article Ayton, Hunt and Wright address a number of issues that impinge on the concept of randomness. They appear to question not only the methodological soundness and general implications of research on "misconceptions" in statistics, but also the soundness of aspects of statistical inference. We concentrate here on a few key issues about which we are in disagreement (we think) with the authors.

In New Zealand, end-of-course examination based assessment is rooted in our past and while it may have served the past well, it is clear that it does not adequately serve our present needs. In 1991 the Education Subcommittee of the New Zealand Statistical Association suggested that these examinations may not be valid (unbiased) or reliable (have low variability) measures of ability. Further there is a growing concern that our examinations do not function equitably across all groups of students, and that they do not adequately measure either those skills needed by the general population for their everyday needs, or the skills needed to contribute to the country's economic growth. The debate on assessment procedures has, in part, arisen because of the differential performance of girls and boys in traditional mathematics examinations. In New Zealand a number of analyses of secondary school mathematics examination performance have been done (Stewart, 1987; Reilly et al, 1987; Forbes, 1988; Morton et al, 1988 and 1989; Forbes et al, 1990). These results all show a greater range of achievement within each gender than between the genders but typically the top grades are dominated my males. There are a number of forms of assessment in current use in statistics. Some types of assessment may unfairly advantage one group of students over another. A limited amount of research has been done comparing assessment methods to determine those which may best suit women, Maori (indigenous New Zealanders), or ethnic minorities. Women themselves cannot be classified as just one group. Forbes (1992) showed that a reduction in gender differences in performance in mathematics of one group of the New Zealand population (European) does not necessarily lead to a similar reduction in another group (Maori).

Traditional testing techniques (particularly those used in national or regional examinations) emphasize competitive perspectives of assessment where the main purpose is to differentiate between students for selection or relative ranking purposes (Suggett, 1985). For ranking purposes, information about knowledge possessed by individual students is largely irrelevant. The crucial dimension for both candidate and the examining authority is the position on the rank-order list. Such assessment approaches do not inform either the candidate (whether successful or not) or the teacher (whether past or future) about the level of conceptual development that has been reached or about the possible next steps in the learning process. This report describes some innovative assessment strategies used to explore conceptual development and to describe achievement in terms of the tasks that candidates can do (or not do) rather than in terms of rank order. Such mapping of a set of mathematics results provides more useful information for the parties to the assessment.

Knowledge of statistics is important in the curricula of students in psychology and education. Reasons are twofold. First, in other courses they deal with theories and research studies which rely on statistical analysis. Second, they have to undertake research in which they have to handle, analyse and interpret data. Statistics is for these students a tool, a means of communicating knowledge which is needed to read and evaluate surveys, experiments, and other studies dealing with substantive problems in the field of psychology and education; and is also used in doing research while planning a study, analysing the data, and interpreting the results. Both aspects rely on a knowledge base of statistics and of methodology; the second also requires competence in problem-solving skills.