Journal Article

  • Although P(A&B|X) can never exceed P(A|X) (the conjunction rule), it is possible for P(X|A&B) to exceed P(X|A). Hence, people who rank A&B as more probably than A are not necessarily violating any normative rule if the ranking is done in terms of the probability of these events to yield an event X. Wolford, Taylor, and Beck (1990) have argue that this indeed is what happens in some problems (e.g. Tversky & Kahneman's (1983) Linda Problem). The claim made here is that the Linda problem is hard to reconcile with this interpretation; that there is little if any evidence that subjects utilize this interpretation; and that in any case, representativeness can account for all Linda problem results.

  • The foundations of adult reasoning about probabilities are found in children's reasoning about frequencies.

  • In recent years many national bodies concerned with American education have recommended integrating topics from probability, statistics, and data analysis into the K-12 mathematics curriculum. A variety of efforts are under way to carry out these recommendations, including the ASA's Quantitative Literacy Project. This report describes another such effort. A statistician and a mathematics educator offered current high school teacher a one-semester course that would give them a background knowledge of statistics to help them implement the recommendations. In designing the course, we unearthed some resources that might be of use to others. In offering the course, we experienced a variety of successes and failures that may be of interest to anyone else considering a similar course. These experiences led us to rethink how we would teach such a course in the future and to consider alternative approaches to teacher (re)training. We describe our experience and provide a of suggestions we hope might aid in implementing the new curriculum recommendations.

  • As part of the project Design, Development and Assessment in Mathematics Education, I spent four weeks at Whitnall High School in Milwaukee, Wisconsin, testing a booklet on descriptive statistics called Data Visualization.

  • There is a growing feeling in the statistical community that significant changes must be made in statistical education. Statistical education has traditionally focused on developing knowledge and skills and assumed that students would create value for the subject in the process. This approach hasn't worked. It is argued that we can help students better learn statistical thinking and methods and create value for its use by focusing both the content and delivery of statistical education on how people use statistical thinking and methods to learn, solve problems, and improve processes. Learning from your experiences, by using statistical thinking in real-life situations, is an effective way to create value for a subject and build knowledge and skills at both the graduate and undergraduate levels. The learnings from psychology and behavioral science are also shown to be helpful in improving the delivery of statistics education.

  • Authors will strive to present information to help teachers (1) understand students' conceptions or misconceptions of important ideas, (2) consider various approaches to teaching, and (3) offer activities that probe students' understanding. Although research offers no one correct answer to the many perplexing problems surrounding teaching and learning mathematics, the suggestions and perspectives may help teachers pursue their work with new insights. It is hoped that the department will also stimulate researchers to reflect on connecting research to the classroom. Communication and collaboration between teachers and researchers will benefit both groups and help each grow in appreciation of the other's tasks.

  • Six hundred and eighteen pupils, enrolled in elementary and junior-high-school classes (Pisa, Italy) were asked to solve a number of probability problems. The main aim of the investigation has been to obtain a better understanding of the origins and nature of some probabilistic intuitive obstacles. A linguistic factor has been identified: It appears that for many children, the concept of "certain events" is more difficult to comprehend than that of "possible events". It has been found that even adolescents have difficulties in detaching the mathematical structure from the practical embodiment of the stochastic situation. In problems where numbers intervene, the magnitude of the numbers considered has an effect on their probability; bigger numbers are more likely to be obtained than smaller ones. Many children seem to be unable to solve probability questions, because of their inability to consider the rational structure of a hazard situation: "chance" is, by itself, an equalizing factor of probabilities. Positive intuitive capacities have also been identified; some problems referring to compound events are better solved when addressed in a general form than when addressed in a particular way.

  • This article illustrates some common applications of probability and statistics in the field of epidemiology as they may presented to an undergraduate class in probability and statistics.

  • Over the past several years, we have been working on the Reasoning Under Uncertainty (RUU) project, whose goal has been to develop and test a computer-supported environment in which high school students could learn how to think in probabilistic and statistical terms. The central ideas of the project are to use the computer as a tool for data gathering, manipulation, and display, and to have students investigate questions that are meaningful to them. In contrast to the usual emphasis in statistics courses on formulas and computational procedures, RUU emphasizes reasoning about statistical problems. We believe that students should be able to engage in statistical reasoning about uncertainties that either they or society face. Such a course conforms well to the National Research Council's suggestion that "elementary statistics and probability should now be considered fundamental for all high school students" and to the new NCTM guidelines for including probability and statistics in the elementary and secondary curriculum.

  • Searle (1989) cited the need for caution when using statistical computing packages. He suggested that classroom time is best spent on learning the why and when of statistics and that the how is unworthy of academic credit. We must not let misplaced caution cause us to lose this additional opportunity to educate students in the proper use of statistical methods. Teaching portions of statistical computer packages can give students an appreciation of the knowledge and care that must go into using techniques that are not covered in the classroom. Equally important, we must not leave the teaching of statistical computer packages to nonstatisticians.