Watson j m moritz j b 2000 development of

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for teaching statistics at both the secondary and preservice teacher education levels are discussed briefly. Watson, J. M. & Moritz, J. B. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior , 19, 109-136. The development of understanding sampling is explored through responses to four items in a longitudinal survey administered to over 3000 students from grades 3 to 11. Responses are described with reference to a three-tiered framework for statistical literacy, including defining terminology, applying concepts in context, and questioning claims made without proper justification. Within each tier increasing complexity is observed as students respond with single, multiple, and integrated ideas to the four different tasks. Implications for mathematics educators of the development of sampling concepts across the years of schooling are discussed. Watson, J. M. & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education , 31, 44-70. In developing ideas associated with statistical inference, a key element involves developing concepts of sampling. The objective of this research is to understand the characteristics of students’ constructions of the concept of sample. Sixty-two students in grades 3, 6, and 9 were interviewed using open-ended questions
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57 related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure and objectives of statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions. Wood, M. (2001). The case for crunchy methods in practical mathematics, Philosophy of Mathematics Education Journal 14 , available at . This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives of user-friendliness, reliability (in the sense that misuse is less likely), educational efficiency and realism. This means that they offer very considerable potential for simplifying the mathematical underlying many areas of applied mathematics such as management science and statistics: crunchier methods can provide the same, or greater, technical power, flexibility and insight, while requiring only a fraction of the mathematical conceptual background needed by their cleverer brethren.
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58 RECENT DISSERTATIONS Mark Earley (2001). Investigating the development of knowledge structures in
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