# World whose central feature was the visibility of its

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world, whose central feature was the visibility of its mechanisms--how the random behavior of objects actually "worked". In this paper, we illustrate the theory by reference to a single case study chosen to illuminate the new knowledge. Our explanation will employ the notion of situated abstraction as an explanatory device that attempts to synthesize existing micro- and macro-level descriptions of knowledge construction. One implication will be that the apparent dichotomy between as affording different perspectives on a broadening of contextual neighbourhood over which a network of knowledge elements applies. Quinn, R. (2001). Using attribute blocks to develop a conceptual understanding of probability. Mathematics Teaching in the Middle School , 6(5), January, 290-294. Activities using attribute blocks can help middle school students construct knowledge about, and develop conceptual understanding of, probability. Schield, A. (2000). Statistical literacy: Difficulties in describing and comparing rates and percentages. ASA 2000 Proceedings of the Section on Statistical Education . A basic goal of statistical literacy is to construct readily understandable ratio-based comparisons that follow directly from data, take into account multiple factors and can support arguments about causation. College students have considerable difficulty constructing such comparisons using rates and percentages. This paper asserts that the main cause of student difficulties is the combination of complexity, subtlety and ambiguity. Complexity is the dominant source of difficulty. Indications of complexity include the unique grammars associated with the three kinds of arithmetic comparisons and four families of named ratios: ratio, percentage, rate and chance. To add to the complexity there are two ways of using percent, three ways of using percentage and seven ways of using rate in descriptions. For each of the 10 ways of using percentage or rate descriptions, there is a corresponding comparison. And there are four ways of using likely in comparisons. Examples of subtlety and ambiguity are presented. Subtle differences in syntax (grammar) are shown to cause significant difference in semantics (meaning). The defining and comparing of rates and percentages is also difficult because it includes most of the mathematical difficulty of using English to describe the concepts of variable, function, multivariate function and partial derivative. Web copy: Schield, M. (2001) Statistical literacy: Reading tables of rates and percentages. ASA 2001 Proceedings of the Section on Statistical Education . Statistical literacy depends on the ability to read and compare data presented in tables and graphs. Tables of rates and percentages are very useful in supporting arguments, but these tables are often difficult to decode. This paper presents rules for determining whether an index variable in such a table is part or whole depending on
56 whether the associated margin value is an average, a sum or a 100% sum. Tables with missing margin values ˆ date-indexed tables, half tables and control tables ˆ are analyzed. Recommendations are made to improve reader

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