• While many teachers of statistics are likely to focus on transmitting knowledge, many students are likely to have trouble with statistics due to non-cognitive factors, such as negative attitudes or beliefs towards statistics. Such factors can impede learning of statistics, or hinder the extent to which students will develop useful statistical intuitions and apply what they have learned outside the classroom. This paper reviews the role of affect and attitudes in the learning of statistics, critiques current instruments for assessing attitudes and beliefs of students, and explores assessment methods teachers can use to gauge students' dispositions regarding statistics.

  • At many small colleges the only statistics course offered to a mathematics major is the standard sequence in probability and mathematical statistics. This paper offers concrete suggestions on infusing this course with more data and applications so that students coming out of the course better appreciate the nature of statistics as a discipline separate from mathematics.

  • 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.

  • The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deducted from former more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on introducing the chance concept illustrates this conflict. The interaction between teacher and his students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the chance concept is conceived of as a concrete generalization, which takes "chance" as a fixed and universalized pattern of explanation instead of unfolding potential and variable conceptual relations of "chance" or "randomness" and developing the theoretical mature of this concept in an appropriate way for students' comprehension.

  • 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).

  • This paper is motivated by a concern about the increasingly important role being given to computer-based simulations of random behavior in the teaching and learning of probability and statistics. Many curriculum developments in this area make the implicit assumption that students accept the computer algorithm for generating random outcomes as an appropriate representation of random behavior. This paper will outline some reasons for questioning this assumption, and will indicate a need to investigate how students' mental models of random behavior differ from their understanding of the computer representation of randomness.

  • 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.

  • This paper considers the display of statistical models involving either one or two variables by means of their probability or probability density function.

  • 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.

  • This document explores some reasons why statistics and probability are appropriate topics for primary and secondary schools.