• For this study, the probability problem-solving processes of 104 graduate students enrolled in different sections of an introductory probability and statistics course at an urban college of education were analyzed for the presence and type of errors occurring in their work.

  • The objective of this study is to compare the effects of two instructional approaches designed to overcome errors in the interpretation of psychological research.

  • Our investigation utilised Strauss and Bichler's conceptual organisation of the properties of the mean, and had three purposes: (1) to investigate what happens developmentally to those statistical properties that were not mastered by age 12-14; (2) to examine the qualities of the statistical properties, including their relative conceptual difficulty and their relative ability to evoke the concept of the mean; and (3) to determine the relative effectiveness of different testing formats in assessing subjects' knowledge about the component properties of the mean.

  • This study explored the guiding conceptions and misconceptions from which children and adults build their models of descriptive statistics. Unlike other empirical studies of children's conception of average, we focus on people's own constructions of the idea of average and explore the relationship between informal ideas about "typical", "representative", and "average" with formal definitions and algorithms learned in school.

  • This paper reports on one of the "Randomness" questions and on a set of ten "Comparison of Odds" questions, all of which were common to both studies, and for which results have not hitherto been published.

  • This paper presents a research study on probability teaching which belongs to research on interaction in the mathematics classroom. Whereas much research done in this field takes a constructivist perspective or is based on theories of communication, we shall focus primarily on epistemological constraints of mathematical knowledge in student-teacher interactions. Our specific interest will be to better understand how processes of concept development occur in everyday teaching and how meaning of mathematical concepts is embedded in social interaction.

  • The focus of this paper is on the first and third stages of the model, both of which depend on designing ways to identify misconceptions. In previous studies, researchers have used changes in performance on individual items to evaluate the effectiveness of instructional interventions. The instrument designed and used in this study differs from previous instruments, not in the content of the items, but in the way responses to items are analysed. Instead of considering responses to single items, pairs of items are designed so that meaningful error patterns can be identified. The identification of error patterns allow assessment that goes beyond the reporting of gain scores. Once error patterns are identified, an intervention can be evaluated according to the types of misconceptions (i.e. error patterns) that are affected.

  • Although there is a long tradition of research into concepts and intuitions regarding randomness and probability, few studies have been undertaken amongst United Kingdom university students. Thus the research done at Brunel University over the period 1984 to 1987 using a self-completion questionnaire to investigate the intuitive ideas concerning probability held by first year undergraduates was partly exploratory in nature. This paper presents the intuitive ideas about probability held by first year undergraduates studying mathematics or other scientific subjects.

  • This paper describes a study in which subjects were asked about various aspects of coin flipping. Many gave contradictory answers to closely-related questions. We offer two explanations for such responses: (a) switching among incompatible perspectives of uncertainty, including the outcome approach, judgment heuristics, and normative theory; and (b) reasoning via basic beliefs about coin flipping. As an example of the latter, people believe both that a coin is unpredictable and also that certain outcomes of coin flipping are more likely that others. Logically, these beliefs are not contradictory; they are, however, incomplete. Thus, contradictory statements (and statements at variance with probability theory) appear when these beliefs are applied beyond their appropriate domain.

  • A questionnaire was designed to study what first year university students already know about proportion and probability. Many questions were based on those previously used by others. The questionnaire was piloted at Brunel University, UK, in October 1989 with students newly enrolled on mathematics or statistics degree courses. An amended version was administered to some 60 students enrolled in a service course in statistics at the University of Waikato, NA, at the beginning of the 1990 academic year. The mathematical background of the NZ students varied from below the median in Form 5 (age 15-16) to slightly above the median in Form 7 (age 17-18). After answering each question the respondents were asked to give the reason for their reply. Analysis paid particular attention to the reasons given when questions were wrongly answered. The questionnaire used, together with tabulations of the students' answers and of the reasons given for those answers, are presented in a poster-paper.