Journal Article

  • For the past 15 years, pre-university students in many countries including the United States have encountered data analysis and probability as separate, mostly independent strands. Classroom-based research suggests, however, that some of the difficulties students have in learning basic skills in Exploratory Data Analysis stem from a lack of rudimentary ideas in probability. We describe a recent project that is developing materials to support middle-school students in coming to see the "data in chance" and the "chance in data." Instruction focuses on four main ideas: model fit, distribution, signal-noise, and the Law of Large Numbers. Central to our approach is a new modeling and simulation capability that we are building into a future version of the data-analysis software TinkerPlots. We describe three classroom-tested probability investigations that employ an iterative model-fit process in which students evaluate successive theories by collecting and analyzing data. As distribution features become a focal point of students' explorations, signal and noise components of data become visible as variation around an "expected" distribution in repeated samples. An important part of students' learning experience, and one enhanced through visual aspects of TinkerPlots, is becoming able to see things in data they were previously unable to see.

  • The Iterative Evaluation Model for Improving Online Educational Resources (IEM) was developed to provide a valid evaluation model to be used to improve online resources, to make them more effective and have a greater positive impact on student learning. The model focuses on the iterative evaluation of four components: (a) evaluation planning, (b) web design and content, (c) use of the educational resource, and (d) educational impact. This paper describes the IEM which was developed as part of the NSF-funded ARTIST (Assessment Resource Tools for Improving Statistical Thinking) project and used to evaluate the online resources developed by this project. The ARTIST evaluation is described in order to illustrate how the IEM may be used.

  • This article describes a subset of results from a larger study (Rubel, 2002) that explored middle school and high school students' probabilistic reasoning abilities across a variety of probabilistic contexts and constructs. Students in grades 5, 7, 9, and 11 at an urban, private school for boys (n = 173) completed a Probability Inventory, comprising adapted tasks from the research literature, which required students to provide answers as well as justifications of their responses. Supplemental clinical interviews were conducted with 33 students to provide further detail about their reasoning. This article focuses specifically on the probabilistic constructs of compound events and independence in the context of coin tossing.

  • Many educators and researchers are trying to define statistical literacy for the 21st<br>century. Kimura, a Japanese science educator, has suggested that a key task of<br>statistical literacy is the ability to extract qualitative information from quantitative<br>information, and/or to create new information from qualitative and quantitative<br>information. This article presents research that offers a theoretical basis using the<br>SOLO Taxonomy to capture students' ability to create new information from<br>qualitative and quantitative information. This research shows that the "creation of<br>dimensionally new information" is a complex construct requiring further research<br>and a deeper analysis than Kimura appears to have used.

  • Coordinate graphs of time-series data have been significant in the history of statistical graphing and in recent school mathematics curricula. A survey task to construct a graph to represent data about temperature change over time was administered to 133 students in Grades 3, 5, 7, and 9. Four response levels described the degree to which students transformed a table of data into a coordinate graph. "Nonstatistical" responses did not display the data, showing either the context or a graph form only. "Single Aspect" responses showed data along a single dimension, either in a table of corresponding values, or a graph of a single variable. "Inadequate Coordinate" responses showed bivariate data in two-dimensional space but inadequately showed either spatial variation or correspondence of values. "Appropriate Coordinate" graphs displayed both correspondence and variation of values along ordered axes, either as a bar graph of discrete values or as a line graph of continuous variation. These levels of coordinate graph production were then related to levels of response obtained by the same students on two other survey tasks: one involving speculative data generation from a verbal statement of covariation, and the other involving verbal and numerical graph interpretation from a coordinate scattergraph. Features of graphical representations that may prompt student development at different levels are discussed. (Contains 8 figures and 2 tables.)

  • The study describes levels of thinking in regard to the design of statistical studies.<br>Clinical interviews were conducted with 15 students who were enrolled in high<br>school or were recent high school graduates, and who represented a range of<br>mathematical backgrounds. During the clinical interview sessions students were<br>asked how they would go about designing studies to answer several different<br>quantifiable questions. Several levels of sophistication were identified in their<br>responses, and are discussed in terms of the Biggs and Collis (1982, 1991) cognitive<br>model.

  • nderstanding essential for them to apply correctly the statistical techniques at their<br>disposal and to interpret their outcomes appropriately. It is also commonly believed<br>that the sampling distribution plays an important role in developing this<br>understanding. This study clarifies the role of the sampling distribution in student<br>understanding of statistical inference, and makes recommendations concerning the<br>content and conduct of teaching and learning strategies in this area.

  • Research in student learning can be based on a theoretical framework, observations<br>of students' learning, the products of this learning, and students' own conceptions<br>of the subject and of learning. In the final analysis, such investigations have a clear<br>purpose - to improve student learning. We report on using the results of research<br>into student learning in statistics to improve the learning environment in a<br>university class on regression analysis. We believe this is an effective method of<br>becoming "researchers of practice" in statistics education.

  • Assessment has become the "buzzword" in academia; a demonstration of criteria used for the assessment of retention of what was learned is now mandated by various accrediting agencies. Whether we want our students to be good users of statistics who make better decisions, or good consumers of statistics who are better informed citizens, we must reflect on how key statistical concepts can be ingrained in the students' knowledge base. This article seeks to address the overall issue of assessing the retention of essential statistical ideas that transcend various disciplines.

  • Concerns about the importance of variation in statistics education and a<br>lack of research in this topic led to a preliminary study which explored<br>pre-service teachers' ideas in this area. The teachers completed a written<br>questionnaire about variation in sampling and distribution contexts.<br>Responses were categorised in relation to a framework that identified levels<br>of statistical thinking. The results suggest that while many of the students<br>appeared to acknowledge variation, they were not able to provide adequate<br>explanations. Although the pre-service teachers have had more real-life experiences<br>involving statistics and have been involved in the study of statistical<br>concepts at secondary school level, they still demonstrated the same misconceptions<br>as those of younger students reported in research literature. While<br>more students showed competence on the sampling question, they were less<br>competent on the distribution task. This could be due to task format or<br>contextual issues. The paper concludes by suggesting some implications for<br>further research and teaching.

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