Theory

  • No discussion of the context of teaching statistics would be complete without acknowledgement of the anxiety that students bring to clss. According to Onwuegbuzie (in press) two-thirds to four-fifths of graduate students experience high levels of stress while enrolled in statistics courses. Some delay taking these courses until late in their academic programs (Onwuegbuzie, 1997a, 1997b); some drop ot completely (Richardson &amp; Suinn, 1972). Some just "labor through the course, making it a high anxiety arena for their classmates and instructors: (Wilson, 1999, P. 2).<br>As statistics instructors, there are at least four questions we need to examine:<br>(1) Should we acknowledge the existence of statistics anxiety or just ignore it?<br>(2) If we acknowledge it, should we attempt to reduce it?<br>(3) If we attempt to reduce it, what strategies might we employ?<br>(4) Should we differentiate instruction--content, proess, and product--in order to address teh comfort levels as well as the learning styles and peferences of our students?

  • According to Vygotsky (1934), the meaning of words are the main units to analyse psychological activity, since words relfect the union of thought and language, and include the properties of the concept to which they refer. As such, one main goal in statistics education research is finding out what meanings students assign to statistical concepts, symbols and representations and explaining how these meanings are constructed during problem solving activities and how they evolve as a consquence of instruction to progressively adapt to the meanings we are trying to help students construct.<br><br>In trying to develop a systematic research program for mathematics and statistics education at the University of Granada, Spain we have developed a theoretical model to carry out these analysie (Godino &amp; Batanero, 1994; 1998), which has been successfully applied in defferent research work in statistics education., in particular in some PhD these carried out at different Universities in Spain. The aim of this paper is to describe this model and suggest a research agenda for statistics education based on the same.

  • In this article, we highlight a series of tensions inhrent to understanding randomness. In doing so, we locate discussions of randomness at the intersections of a broad range of literatures concerned with the ontology of stochastic events and epistemology of probabilistics ideas held by people. Locating the discussion thus has the advantage of emphasizing the growth of probabilisitic reasoning and deep connections among its aspects.

  • This article discusses five papers focused on "Research on Reasoning about Variation and Variability", by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould, which appeared in a special issue of the Statistics Education Research Journal (No. 3(2) November 2004). Three issues emerged from these papers. First, there is a link between the types of tools that students use and the type of reasoning about variation that is observed. Second, students' reasoning about variation is interconnected to all parts of the statistical investigation cycle. Third, learning to reason about variation with tools and to understand phenomena are two elements that should be reflected in teaching. The discussion points to the need to expand instruction to include both exploratory data analysis and classical inference approaches and points to directions for future research.

  • This article is a discussion of and reaction to two collections of papers on research on Reasoning about Variation: Five papers appeared in November 2004 in a Special Issue 3(2) of the Statistics Education Research Journal (by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould), and three papers appear in a Special Section on the same topic in the present issue (by Makar and Confrey, delMas and Liu, and Pfannkuch). These papers show that understanding of variability is much more complex and difficult to achieve than prior literature has led us to believe. Based on these papers and other pertinent literature, the present paper, written by the Guest Editors, outlines seven components that are part of a comprehensive epistemological model of the ideas that comprise a deep understanding of variability: Developing intuitive ideas of variability, describing and representing variability, using variability to make comparisons,<br>recognizing variability in special types of distributions, identifying patterns of variability in fitting models, using variability to predict random samples or outcomes, and considering variability as part of statistical thinking. With regard to each component, possible instructional goals as well as types of assessment tasks that can be used in research and teaching contexts are illustrated. The conceptual model presented can inform the design and alignment of teaching and assessment, as well as help in planning research and in organizing results from prior and future research on reasoning about variability.

  • In the paper, we argue that the persistence of students' difficulties in reasoning about the stochastic despite significant reform efforts in statistics education might be the result of the continuing impact of the formalist mathematical tradition. We first provide an overview of the literature on the formalist view of mathematics and its impact on statistics instruction and learning. We then re-consider some well-known empirical findings on students' understandingof statistics, and form some hypotheses regarding the link between student difficulties and mathematical formalism. Finally, we briefly discuss possible research directions for a moreformal study of the effects of the formalist tradition on statistics education.

  • The need for higher standards of quantitative literacy, or numeracy, in America schools is discussed. Topics include the value of numeracy in political, economic and business life, differences between standard math and quantitative literacy, and suggestions for implementing numeracy in schools.

  • All sectors of society must have a basic knowledge of statistically sound concepts in order to make optimal use of research data and statistically significant information. The encouragement of statistical thinking can be facilitated through the federal statistical system, schools and universities and the media. Lastly, professional statisticians must strive to elucidate the whole statistical process whenever an appropriate oppourtunity arises.

  • It is essential to base instruction on a foundation of understanding of children's thinking, but it is equally important to adopt the longer-term view that is needed to stretch these early competencies into forms of thinking that are complex, multifaceted, and subject to development over years, rather than weeks, or month. We pursue this topic through our studies of model-based reasoning. We have identified four forms of models and related modeling practices that show promise for developing model-based reasoning. Models have the fortuitous feature of making forms of student reasoning public and inspectable - not only among the community of modelers, but also to teachers. Modeling provides feedback about student thinking that can guide teaching decisions, an important dividend for improving professional practice.

  • The reasoning behind the theory of testing of hypothesis is that if a sample does not resemble the characteristics of the population specified by the null hypothesis, then the null hypothesis is rejected. In this paper I draw a parallel between this reasoning and the 'representativeness heuristic.' I claim that the widely accepted view that this heuristic is a misconception in probability is a result of mixing-up the concepts of likelihood and probability on the part of statistics education researchers. While the concept of likelihood is very intuitive and comes naturally to people, the concept of probability is abstract and normally requires formal training.

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