Journal Article

  • In this article, we describe a classroom demonstration that uses the Gambler's Fallacy to illustrate misconceptions about random processes and how they affect statistical interpretation. The demonstration used a database collected from simulated gambling by students picking professional football games with the point spread (i.e., a real-life random process). The results of student picks illustrated that random processes are not self-correcting and reinforced the relation between sample size and variability. Formal and informal feedback from students indicated that the demonstration was well received and recommended for future classes.

  • Plotting girls' and boys' weights on a medical growth chart in the introductory statistics course illustrates variability, the normal distribution, percentiles, z scores, outliers, bivariate graphing, and simple regression. The chart presents the spread of weights for newborns through 36 months, includes percentile scores, and represents a bivariate distribution with age on the abscissa and weight on the ordinate. Students plot their own weights to understand how the chart works and then plot the weights of a selected boy and girl to understand how the chart identifies outliers for follow-up tests on hormone levels, nutrition, and intellectual development. Instructors in other psychology courses (e.g., developmental, child, abnormal, introductory, and educational psychology) may also find the chart useful when covering infant development.

  • Many studies have shown that the strategies used in making judgments of chance are subject to systematic bias. Concerning chance and randomness, little is known about the relationship between the external structuring resources, made available for example in a pedagogic environment, and the construction of new internal resources. In this study I used a novel approach in which young children articulated their meanings for chance through their attempts to "mend" possibly broken computer-based stochastic gadgets. I describe the interplay between informal intuitions and computer-based resources as the children constructed new internal resources for making sense of the total of 2 spinners and 2 dice.

  • This study focuses on the feasibility of implementing independent learning in a traditional university and the feasibility of providing this independent learning by means of an electronic interactive learning environment. Three experimental variables were designed: learning environment, delivery, and support. This created five different learning conditions to which subjects were assigned at random.

  • This article presents an active learning demonstration available on the Internet using Java applets to show a poorly designed experiment and then subsequently a well-designed experiment. The activity involves student participation and data collection.

  • Statistical literacy is the ability to read and interpret data: the ability to use statistics as evidence in arguments. Statistical literacy is a competency: the ability to think critically about statistics. This introduction defines statistical literacy as a science of method, compares statistical literacy with traditional statistics and reviews some of the elements in reading and interpreting statistics. It gives more emphasis to observational studies than to experiments and thus to using associations to support claims about causation.

  • This article has four main sections. Section 2 summarizes the state of academic mathematics and statistics and argues that, in most institutions, the two disciplines need each other. It would repeat false starts from the past to think primarily of statistics departments, or even of large research universities more generally. I believe that growth of undergraduate statistics programs in other institutions will generally require the cooperation of the mathematics department, and that mathematics may be ready for more cooperation. Section 3 presents some market research--data on trends that ought to influence our thinking about statistics for undergraduates. Section 4 offers some cautionary findings from research in mathematics education. The unifying theme of these three sections is the need for realism in discussing programs for undergraduates.

  • 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 four different tasks. Implications for mathematics educators of the development of sampling concepts across the years of schooling are discussed.

  • Our purpose is to bring together perspectives concerning the processing and use of statistical graphs to identify critical factors that appear to influence graph comprehension and to suggest instructional implications. After providing a synthesis of information about the nature and structure of graphs, we define graph comprehension. We consider 4 critical factors that appear to affect graph comprehension: the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics. A construct called graph sense is defined. A sequence for ordering the introduction of graphs is proposed. We conclude with a discussion of issues involved in making sense of quantitative information using graphs and ways instruction may be modified to promote such sense making.

  • This article is the culmination of the work on curriculum for Bachelor of Science degrees in statistical science from both the workshop on undergraduate curriculum held on April 28-29, 2000, and the symposium on improving the workforce of the future.

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