Proceedings

  • Given the importance of instruction in promoting students' statistical literacy, a cohesive picture of the development of students' statistical thinking is needed to better inform classroom teachers and curriculum developers. With this in mind, one of the authors developed a framework to characterize middle school students' statistical thinking within four statistical processes, across four levels of thinking. A subsequent study (Langrall, Mooney, Hofbauer, & Johnson, 2001) addressed gaps in Mooney's framework. This paper describes how the findings of the Langrall et al. study were merged with the framework and reports on resulting modifications to the entire framework.

  • We desired to improve student learning in our introductory, algebra-based statistical methods course. Marketing claims as well as anecdotal evidence suggested that electronic forms of educational material improve student learning. Some recent empirical evidence presented in the statistical literature uses both qualitative and quantitative data to evaluate computer-based learning aids. In order to contribute to evaluation of educational technology we designed an experiment to evaluate the use of ActivStats Multimedia Educational Software (on CD) and CyberStats Introduction to Statistics (on the web). Specifically, we assessed how the use of these two forms of educational material in the statistics laboratory portion of our course impacted student learning and attitudes. Implications of these results are discussed as well as lessons learned for designing future experiments.

  • In this work, we describe the elements of meaning related to normal distribution, which appear in a data analysis course based on the use of computers. The course was directed to students in their first year of university studies. We study the elements implemented in a teaching unit for the normal distribution in which computers were introduced as a didactic tool. We pay special attention to the specific meaning conveyed by the use of computers as well as to the meaning attributed by the students throughout the teaching sequence.

  • Traditionally, the concept of sampling distribution has been seen as fundamental to an understanding of introductory statistical inference. As a result many computer packages have been developed which offer activities intended to support the development of this concept. However, we need to recognise that the concept of sampling distribution is complex and multi-faceted, with many different mathematical and symbolic representations possible. Computer simulations of the sampling distribution tend to address only the empirical representation of this concept, and leave the linking of representations to the user. And it is the development of these links which is critical to the development of understanding in statistical inference. This paper reports some results of a study analysing the role of the computer-based technology in the development of understanding of sampling distribution.

  • Psychology remains addicted to null hypothesis significance testing despite decades of effort by reformers. Extensive changes in statistical understanding and practices are needed. The authors propose a model of reform-the statistical re-education of psychology-by making an analogy with the conceptual change model of learning. Four diverse components of reform are identified, and illustrated by brief examples of research. Reform is especially challenging because many statistics teachers in psychology first need to achieve conceptual change themselves. In relation to a highly desirable increase in use of confidence intervals (CIs), it seems that many psychologists do not understand CIs well, and guidelines for CI use are lacking. The conceptual change model is offered to guide research needed on many aspects of reform, and the important and exciting task of the statistical re-education of psychology.

  • The cognitive-theoretic instructional and assessment approaches described here represent our efforts to develop and measure students' abilities to reason spontaneously and flexibly with statistics in the context of complex real-world activity. We report results from two instructional projects based on situated cognition, in which students were taught statistical reasoning through guided participation in simulations of authentic professional activities requiring presentation and critique of statistical arguments. Although students' statistical reasoning improved in selected ways, the approach was costly and difficult to implement and sustain. In search of more practical and powerful approaches, current experiments are investigating whether instruction based on video technologies and Cognitive Flexibility Theory can speed development of ability to think flexibly with statistics while seeing interacting themes in real-world situations.

  • Statistics has become an integral part of individuals' formal and everyday lives. Experiences that help learners make sense of statistical information are needed so that they can make informed decisions. The view of statistics as a decision-making tool can be emphasized in project-based environments, where students investigate problems that require formulating questions and collecting, analyzing, and representing data to address these questions. Producing investigations in collaboration with peers and presenting results to classmates require that students articulate the understanding that formed the basis of particular design decisions. We found that decisions in this context can be mitigated by factors (e.g., efficiency and social influences) that circumvent the appropriate application of principles (e.g., sampling) in the discipline or practices established in the classroom (e.g., use of criteria to assess peer projects) even though students understand them.

  • WWW-based mathematics and statistics courses frequently incorporate machine-scorable items (i.e., True-False, Multiple Choice, and Matching) in both formative and summative assessments. For instance, WebCT and BlackBoard provide interfaces for the development and delivery of closed-form quizzes and examinations. Using these technologies, it is relatively easy to determine whether students possess detailed factual knowledge. It is much more difficult, using these technologies, to assess higher order thinking skills. This paper presents a Java-based extension to closed-form testing that may be better suited to assessing higher-order thinking skills.

  • As statistical education evolves as a discipline more research involving the examination of statistical reasoning across disciplines is anticipated. For example, statistical investigations can cross into areas of scientific reasoning quite easily. In both situations, research questions are posed; data are collected, analyzed, graphed and interpreted. Instead of integrating statistics in the curriculum there is still a division of labour, whereby math educators are responsible for the teaching of statistics, and science teachers the teaching of scientific inquiry. Cross-disciplinary relationships need to be further examined in terms of our definitions of statistical reasoning and how we assess learning and problem-solving across disciplines. Two case studies will be contrasted to reveal the differences between statistical reasoning in a middle school science classroom and a mathematics classroom.

  • Teacher educators have a concern about the level of mathematical (including statistical) content knowledge of students who enter teacher education programs. Many students have knowledge of certain statistical procedures but lack a real understanding of those procedures such as why and when some should be used in preference to others. This paper reports on a study into the statistical knowledge of primary (elementary) teacher education students. An open-ended task (using a small multi-variate data set) was given to the students and required them to examine and report any interesting features in the data. Aspects of the students' level of 'data sense' was evaluated through an investigation of the statistical procedures that they used in relation to the report which they produced on what the data showed.

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