Research

  • This paper reports on the results of an empirical study of students' conceptions and understanding of statistics. Six qualitatively different conceptions are described, ranging from fragmented to inclusive views. Students expressing the more inclusive and holistic conceptions approach their study of statistics through a focus on 'higher-order' statistical thinking. Students expressing limited and fragmented views may not be able to understand the complexity or applications of the discipline. This paper describes the use of a qualitative methodology - phenomenography - that aims to explore the qualitatively different ways in which a group of people experience a specific phenomenon, in this case statistics. It also describes an overarching framework, the "Professional Entity," that relates students' understanding of statistics and their perceptions of working as a statistician. Investigating and describing the ways in which students learn statistics, how they understand statistics, and how they perceive their own work will enable teachers to develop curricula that focus on enhancing the student learning environment and guiding student conceptions of statistics.

  • This paper describes a case study based on data taken from the U.N.E.S.C.O. 1990 Demographic Year Book and The Annual Register 1992 giving birth rates, death rates, life expectancies, and Gross National Products for 97 countries. Suggested activities include exploratory graphical analyses to answer several central questions. These include an investigation into the wealth and life expectancies of different country groups and their population growth. Inequalities in the life experiences of different groups become readily apparent. Students are stimulated to generate their own questions and to find possible solutions.

  • The American Cancer Society and the National Cancer Institute both develop pamphlets and booklets to inform patients with cancer and their families about the nature and treatment of the illness. Written materials are often given to patients to reinforce verbal instructions, or in some cases, given in place of verbal instructions. Unfortunately, published materials may be written at a reading level that is difficult for many patients to understand.<br>The data presented here represent the readabilities of 30 booklets about cancer and the reading levels of 63 patients with cancer. A number of elementary but important statistical issues must be resolved before conclusions can be drawn. To analyze the data, students must be familiar with the notions of scales of measurement, data reduction, measuring center, constructing and interpreting displays, and reaching conclusions in real problems.

  • The paper reports on a two-year investigation into the feasibility of allocating three weeks of an undergraduate calculus-based probability course to statistics. This brief introduction to statistics would take the place of a course, thus constituting the students' only exposure to statistical science. At first glance, the request seemed quite reasonable. Statistical inference is based on probability, and statistical inference could be presented as an application of probability. Besides introducing some statistical concepts, it was hoped to enhance understanding of probability by highlighting this connection. However, it was not possible for the students to learn anything meaningful about statistical science in three weeks. In addition, any enhancements to the learning of probability were not significant enough to warrant the omission of material from that course.

  • Advances in technology coupled with increasing student enrollment numbers have led some universities to begin offering on-line classes. This paper discusses a study comparing a traditional offering of elementary statistics with a "hybrid" offering. In the hybrid offering the class met once a week, but students were required to learn the material on their own using web-based materials and a textbook. We examined differences in student performance, student satisfaction and investment of both student and instructor time. Performance of students in the hybrid offering equaled that of the traditional students, but students in the hybrid were slightly less positive in their subjective evaluation of the course.

  • In this report, the method of free recall is put forward as a tool to evaluate a prototypical statistical learning environment. A number of students from the faculty of Health Sciences, Maastricht University, the Netherlands, were required to write down whatever they could remember of a statistics course in which they had participated. By means of examining the free recall protocols of the participants, insight can be obtained into the mental representations they had formed with respect to three statistical concepts. Quantitative as well as qualitative analyses of the free recall protocols showed that the effect of the constructive learning environment was not in line with the expectations. Despite small-group discussions on the statistical concepts, students appeared to have disappointingly low levels of conceptual understanding.

  • A Research Project in Statistics is proposed as a major requirement of undergraduate statistics curricula to provide hands-on experience to students and equip them with the tools they will need after graduation. Such a requirement will train students to solve real-life problems by choosing a statistical model suitable to a problem, learning the details of that model, collecting and analyzing appropriate data, and interpreting the results obtained. After completing the project, students will have the ability to learn new techniques on their own, to do a literature review, and to carry out sample and survey design, and they will have enhanced their oral and written reporting skills. The case study reported in this paper suggests that students tend to learn more by doing such a project than in any regular coursework. The project is motivating and gives students a feeling of working in an almost real-life environment on a real problem. Such a project incorporates many aspects of the nonmathematical courses suggested by Higgins (1999a) and is expected to better prepare students to meet the needs of potential employers.

  • 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.

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