Richer conceptual understanding of sampling

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richer conceptual understanding of sampling distributions and inference through discussion, problem-based investigations with their student data, and simulations using Fathom . Sampling distributions were used frequently in problems to provide evidence for differences in groups and to imbue a tolerance for variation. As the study progressed, increasing amounts of time were dedicated to the teachers’ own explorations. During the second week of the summer institute, teachers investigated a problem of their own choosing and presented their findings on the final day of the project to their peers and a group of researchers. At this time, clinical interviews were conducted to further probe teachers’ reasoning about group comparisons. Our particular interest was in inquiry surrounding the question: How do you decide if two groups are different? In the SRTL2 presentation, the videoed responses of four teachers in a clinical interview were examined. In the interview, which followed the project, teachers were asked to compare the relative performances of males and females on the state competency exam, given raw test scores for each group. Beyond the computational distinction made through descriptive statistics, teachers’ analysis of comparing two groups was examined using several other important concepts: tolerance for variability , understanding of the context , and an ability to draw conclusions , perhaps inferentially. A categorization for statistical thinking about comparing two groups was described with five levels of reasoning that teachers use when comparing two groups. Feedback during the presentation revealed commonalities with other areas of research in the focus group. Interestingly, the four members of the focus group (Jones, Moritz, Biehler, and Makar) represented research covering four different age levels: lower primary, upper primary and middle school, upper secondary, and professional; yet every age level struggled with similar concepts: understanding graphical representations and their connection to context, and conceptualizing variation. JERE CONFREY Department of Curriculum and Instruction Sanchez Building The University of Texas at Austin Austin, TX 78712 USA 10. CONFLICTING REPRESENTATIONS OF STATISTICAL ASSOCIATION JONATHAN MORITZ University of Tasmania, Australia [email protected] 10.1. BACKGROUND Social- and physical-sciences often aim to reach verbal conclusions of causation by collecting bivariate data that involve statistical association and by controlling for other variables. It is important to be aware of the translation processes among raw numerical data, graphical representations, and verbal summaries, and an understanding of what constitutes a statistical association when presented in these forms (Fig. 1).
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