Journal Article

  • This paper examines how two twelve-year-old students built up their recognition and understanding of relationships in a set of data. Using a small multivariate dataset created by Watson, Collis, Callingham and Moritz (1995), the students conducted an investigation of their choice in a pencil-and-paper environment. The students' thinking across the three representations of cards, tables and graphs is analysed from the perspectives of transnumeration, consideration of variation, reasoning with statistical models, and integrating the statistical with the contextual, which were identified as fundamental statistical thinking elements in empirical enquiry in the framework of Wild and Pfannkuch (1999). The ways of thinking within each element across the representations are identified. In the analysis, references are also made to the types of statistical thinking present in the other ten students in the study. From the analysis we identified five issues that should be considered for determining how students construct meanings from data. They are: prior contextual and statistical knowledge; thinking at a higher level than constructed representations; actively representing and construing; the intertwinement of local and global thinking; and the changing statistical thinking dialogue across the representations.

  • The article argues that the persistence of student difficulties in reasoning about the stochastic, despite significant reform efforts, might be the result of the continuing impact of the formalist mathematical tradition, affecting instructional approaches and curricula and acting as a barrier to instruction that provides students with the skills necessary to recognize uncertainty and variability in the real world. It describes a study driven by the conjecture that the reform movement would have been more successful in achieving its objectives if it were to put more emphasis on helping students build sound intuitions about variation. It provides an overview of how the conjecture guiding the study was developed and linked to classroom practice, and briefly discusses the experiences and insights gained from a teaching experiment in a college level, introductory statistics classroom, which adopted a nontraditional approach to statistics instruction with variation at its core. By contrasting students' intuitions about the stochastic prior to instruction to their stochastical reasoning at the completion of the course, it illustrates the potential of the instructional approach as an alternative to more conventional instruction.

  • Over the last fifteen years there has been a strong emphasis on active learning, use of real data in the classroom, and innovative uses of technology for helping students learn statistics. A recent survey in the United States (Garfield, 2001) documents that many tertiary teachers of statistics courses have made changes toward these recommendations. Now more than ever, more research is needed on the effects of these instructional methods and materials on student learning, retention, and motivation. This research need first requires the determination of effective research methodology in statistics education. In assessing students' conceptual understanding, reasoning abilities, and attitudes, and their development, alternative methods of gathering student data are needed that supplement comparative experiments and improve on traditional assessment items that focus on calculations, definition, and rote manipulations. This article will present and critique additional methods for obtaining research data on how students develop an understanding of statistics, including classroom-based research and videotaped student interviews/observations.

  • Despite the recommendation of the General Dental Council that statistical methods and data analysis should form part of the curriculum of undergraduate dental degrees, little is known about the teaching of statistics in dental schools. This informal study was carried out to obtain information on the methods of teaching and assessment used in dental schools in Britain and Ireland.

  • Over the past 25 years or so there has been a growing interest and amount of research work into the teaching of probability and statistics. This interest and research has been reflected in the five International Conferences on Teaching Statistics, the establishment of journals such as Teaching Statistics and the Journal for Statistics Education as well as an increasing number of articles in other journals and papers at other conferences. Initially the emphasis was on school pupils but, increasingly, there has been an emphasis on teaching undergraduates.<br>In their bibliography, Sahai, et al (1996) list 2367 references up until the year 1994. With so much published work it is difficult for newcomers to the field to know where to start. The following list of basic references attempts to pull together the various strands of research about undergraduate teaching so that new lecturers will be able to get a quick overview of current thinking and where it has come from. The many older references are to give an historical context and reflect the influences on today's practice.<br>As in all such summary bibliographies there is a lot of subjectivity in the choice of what to include. It was difficult to decide whether or not to include textbooks. In the end I decided to include a few that had been particularly influential on the way statistics is taught at undergraduate level. I have not included any of the very interesting references that are specific to the school level because this would have made what was intended to be a short list even longer than it has become. The list has been circulated amongst a lot of people working in the field of statistical education and I have benefited from their advice. In the final analysis, though, the final decision was mine and any errors and omissions are mine. I would welcome correspondence about any important contributions that are missing and any references that I have included that you think should not be.

  • This paper reports the results of an exploratory study of the characteristics of key information products released by statistics agencies. Such products are central to debates and decisions in the public arena, but have received little attention in the literature on statistical literacy, statistics education, or adult numeracy. Based on a qualitative analysis of Internet-based products of six national and international statistics agencies, the paper sketches the characteristics of five product types (Indicators, Press releases, Executive summaries, Reports, and Aggregate data) and of the environment in which they are found. The paper discusses implications for the specification of the skills needed for accessing, filtering, comprehending, and critically evaluating information in these products. Directions for future research and educational practice are outlined.

  • This paper begins with a discussion of the nature of statistical reasoning, and then describes the development and validation of the Statistical Reasoning Assessment (SRA), an instrument consisting of 20 multiple-choice items involving probability and statistics concepts. Each item offers several choices of responses, both correct and incorrect, which include statements of reasoning explaining the rationale for a particular choice. Students are instructed to select the response that best matches their own thinking about each problem. The SRA provides 16 scores which indicate the level of students' correct reasoning in eight different areas and the extent of their incorrect reasoning in eight related areas. Results are presented of a cross-cultural study using the SRA to compare the reasoning of males and females in two countries.

  • Students in the same statistics course learn different things, and view the role of the lecturer in different ways. We report on empirical research on students' conceptions of learning statistics, their expectations of teaching, and the relationship between them. The research is based on interviews, analysed using a qualitative methodology, with statistics students studying for a mathematics degree. Students expressed a range of conceptions of learning in statistics and a range of conceptions of their lecturers' teaching. These conceptions of learning and teaching were related, but not as closely or as exclusively as previous researchers have indicated. Looking at what students expect of teachers and their views of their own learning provides an opportunity for teachers to develop teaching practices that challenge students to move towards more integrated conceptions of statistics learning.

  • In this paper we present an exploratory study intended to characterise University students' understanding of correlation and regression. We analyse the solutions to two problems from an intentional sample of 193 students who had previously received a course of descriptive statistics at the University. We study the student's procedures and discuss their difficulties and errors concerning the centre of gravity in the scatter plot, regression lines, correlation coefficient, type of relation between the variables and prediction.

  • The aim of this study was, first, to provide evidence to support the notion of statistical literacy as a hierarchical construct and, second, to identify levels of this hierarchy across the construct. The study used archived data collected from two large-scale research projects that studied aspects of statistical understanding of over 3000 school students in grades 3 to 9, based on 80 questionnaire items. Rasch analysis was used to explore an hypothesised underlying construct associated with statistical literacy. The analysis supported the hypothesis of a unidimensional construct and suggested six levels of understanding: Idiosyncratic, Informal, Inconsistent, Consistent non-critical, Critical, and Critical mathematical. These levels could be used by teachers and curriculum developers to incorporate appropriate aspects of statistical literacy into the existing curriculum.

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