Journal Article

  • This article explains and synthesizes two theoretical perspectives on the use of counterintuitive examples in statistics courses, using Simpson's Paradox as an example. While more research is encouraged, there is some reason to believe that selective use of such examples supports the constructivist pedagogy being called for in educational reform. A survey of college students beginning an introductory (non-calculus based) statistics course showed a highly significant positive correlation (r = .666, n = 97, p < .001) between interest in and surprise from a 5-point Likert scale survey of twenty true statistical statements in lay language, a result which suggests that such scenarios may motivate more than they demoralize, and an empirical extension of the model from the author's developmental dissertation research. [this paper was subsequently selected by the editors for inclusion in Getting the Best from Teaching Statistics, a collection of the best articles from volumes 15-21].

  • A university's introductory statistics course was redesigned to incorporate technology (including a website) and to implement a standards-based approach that would parallel the recent standards-based education mandate for the state's K-12 schools. The author collected some attitude (pre and post) and performance (post only) data from the "treatment" section and two "comparison (i.e., more traditional)" sections. There was a pattern of positive attitude towards the redesigned aspects of the course, including group work, lab and project emphasis, criterion-referenced assessment and examples from real-life. On the three problems given to the three sections at the end of the course, the only significant ANOVA (F(2,101) = 4.2, p = .0168) involved the treatment section scoring higher than the other sections. This occurred on a problem involving critical thinking (with a graphic from USA Today), an emphasis supported by the particular standards of the redesigned course.

  • ) Describes classroom explorations of the interpretation and calculation of probabilities involved in a representative state lottery. TI-83 calculator commands are given for simulating drawings as well as for calculating relevant probabilities using the binomial, geometric, Poisson, and other distributions.

  • Examples of highly original lyrics (e.g., educating "The Gambler" about playing the lottery) are given that are rich in statistical content and/or related to current events.

  • Students' ready understanding of and interest in the context of songs and music can be utilized to motivate all grade levels to learn probability and statistics. Content areas include generating descriptive statistics, conducting hypothesis tests, analyzing song lyrics for specific terms as well as "big picture" themes, exploring music as a data analysis tool, and exploring probability as a compositional tool. Musical examples span several genres, time periods, countries and cultures. [note: this appears to have been the first refereed comprehensive article on using song in the statistics classroom].

  • This article presents a sequence of explorations and responses to student questions ( Why not use perpendicular deviations? Why not minimize the sum of the vertical deviations? Why not minimize the sum of the absolute deviations? Why minimize the sum of the squared deviations?) about the rationale for the commonly used tool of line of best fit. A noncalculus-based motivation is more feasible than is often assumed for each aspect of the least-squares criterion "minimize the sum of the squares of the vertical deviations between the fitted line and the observed data points."

  • Spreadsheets are used to explore the lottery, addressing common misconceptions about various lottery "strategies" and probabilities and providing real-world applications of topics such as discrete probability distributions, combinatorics, sampling, simulation and expected value. Additional pedagogical issues are also discussed. Examples discussed include the probability that an integer appearing in consecutive drawings, the probability that a single 6-ball drawing includes at least two consecutive integers, the probability that exactly one person wins the jackpot, and the probability that a frequent player eventually wins the jackpot.

  • The representativeness heuristic has been invoked to explain two opposing expectations - that random sequences will exhibit positive recency (the hot hand fallacy) and that they will exhibit negative recency (the gambler's fallacy). We propose alternative accounts for these two expectations: (1) The hot hand fallacy arises from the experience of characteristic positive recency in serial fluctuations in human performance. (2) The gambler's fallacy results from the experience of characteristic negative recency in sequences of natural events, akin to sampling without replacement. Experiment 1 demonstrates negative recency in subjects' expectations for random binary outcomes from a roulette game, simultaneously with positive recency in expectations for another statistically identical sequence - the successes and failures of their predictions for the random outcomes. These findings fit our proposal but are problematic for the representativeness account. Experiment 2 demonstrates that sequence recency influences attributions that human performance or chance generated the sequence.

  • In this article, we highlight a series of tensions inhrent to understanding randomness. In doing so, we locate discussions of randomness at the intersections of a broad range of literatures concerned with the ontology of stochastic events and epistemology of probabilistics ideas held by people. Locating the discussion thus has the advantage of emphasizing the growth of probabilisitic reasoning and deep connections among its aspects.

  • This paper reports the findings of a qualitative study undertaken by the authors to investigate what students see when participating in a computer simulation session designed to support the development of conceptual understanding of the role of the sampling distribution in hypothesis testing. We have observed and documented the students' assisted interaction with a dynamic and interactive computer simulation, and looked for patterns and themes arising from the data. On the basis of the data collected, we have identified four developmental stages through which the students progressed during the activity, and we have termed these stages as recognition, integration, contradiction and explanation. The identification of the stages has given us some direction for the development of further computer interactions.

Pages

register