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The integration of query generation and user feedback continues to challenge information retrieval technologies. Relevance feedback, while useful to professionals, is frequently inappropriate for lay users, because the initial query generation is manual and the subsequent feedback solicitation is intrusive or inconsistent with many lay users' information needs. To provide lay users with automated query generation and nonintrusive feedback solicitation, the concept of a personal information retrieval assistant is developed. A personal information retrieval assistant is a software agent embedded in an application. The assistant allows the application in which it is embedded to become part of an infrastructure of distributed information sources. Background samples of the application's usage are collected and used in retrievals from the sources. Feedback is never solicited explicitly, and is utilized only when volunteered. Retrieval is adjusted through background sampling, anydata indexing, and dual space feedback. 1

of Mathematics (NCTM) added a pre-K-12 Standard on representation, urging that students be able to develop a repertoire of mathematical representations that can be used purposefully and flexibly to model and interpret physical, social, and mathematical phenomena (NCTM 2000). This article aims to explore the potential of including multiple representations in one's teaching repertoire through an accessible phenomenon for which full insight is not obvious from using only the single most common representation. The phenomenon chosen, Simpson's paradox, can be concisely defined as the reversal of a comparison when data are grouped. In this particular example, we will see that it is possible for women to be hired at a higher rate than men within each of two departments but at a lower rate than men when the data from both departments are pooled together. THE RELEVANCE OF SIMPSON'S PARADOX Simpson's paradox was first noted in 1951 by the British statistician E. H. Simpson but was discussed as early as 1903 by the Scottish statistician George Yule (Wagner 1983). Simpson's paradox can involve a comparison of overall rates, ratios, percentages, proportions, probabilities, averages, or measurements that are weighted averages of subgroup counterparts. Students are likely vulnerable to this paradox if they have the related "averaging the averages " misconception, in which they compute the ordinary average in problems requiring the weighted average. In a weighted average, an overall average is computed by weighting the individual averages by the sizes of their corresponding individual groups. For example, if the average final exam

When examining how the history of probability and statistics can be useful in the classroom, it is first useful to examine the styles in which the history of the subjects is written. These styles may be divided into internalist (those working within the area) and externalist (those outside the area) approaches. It is natural for teachers of probability and statistics to follow an internalist approach for classroom discussion. In order to discover what principles apply in transferring the lessons of history to the classroom, the work of William Sealy Gosset (Student) is discussed as a case study. What follows from this case study is that the most important historical lesson to convey is the motivation for an individual’s work. This lesson is illustrated further in discussions of the solution to the problem of points or division of stakes and of the Fisher-Neyman dispute over their approaches to statistical inference. 1.

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Almost any introductory statistics textbook is a compendium of the history of elementary probability since the Middle Ages and statistical methods since the seventeenth century. Of course, more modern developments obtained throughout the twentieth century are also included in these texts. Dicing probabilities, sometimes given as problems to solve in these texts, first