Journal Article

  • According to Jacob Bernoulli, even the 'stupidest man' knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people's intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the 'empirical law of large numbers' distinguish between two kinds of tasks--one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results.

  • Quantitative literacy addresses citizen's needs to function knowledgably in a society that is data-intensive. Such literacy is as necessary as reading and writing. Colleges and universities fulfill this educational imperative with a variety of goals and requirements. To equip students for life in the Computer Era, a sharper focus is called for , in undergraduate education for numeracy.

  • This article discusses a lesson that explores important mathematical topics in the context of this popular board game [Scrabble]. Specifcally, this lesson meets the recommendations of the National Council of Teachers of Mathematics to give middle school students opportunities to make conjectures and to gather, represent, and interpret statistical data while engaging in an enjoyable, cooperative, interdisciplinary activitiy (NCTM 1989).

  • This paper examines the effects of quantitative literacy on the likelihood of employment among young adults in the United States. The data set used in the 1985 Young Adult Literacy Assessment Survey. This survey of persons 21 to 25 years old makes available scores achieved by individuals sampled on a test measuring proficiency in the application of arithmetic skills to practical problems encountered every day. We use these scores as one of a set of variables in a probit model explaining the probability of a person being fully employed. It is found that quantitative literacy skills are a major factor raising the likelihood of full-time employment. Furthermore, low quantitative literacy appears to be critical in explaining the lower probability of employment of young Black Americans relative to Whites.

  • Literacy and informed decision making in an uncertain world require the ability to reason statistically. However, research indicates that, although conceptions of statistics and probability have steadily advanced within scientific and mathematical communities, adults in mainstram American society cannot think probabilistically or statistically about important societal issues. This problem is addressed through implementation and evaluation of a novel statistics course for students who are teachers or are considering a career in teaching. The course is designed to help students use statistical concepts as tools for social reasoning within simulations of real-world problem situations. The course is unique because of its connections with the community and its commitment to achieving a high degree of authenticity through simulations of realistic social problem solving.

  • Data are hot! Everyone -- students, teachers, parents, employers -- is interested in data, but few know how to collect and interpret data intelligently. Data is the basis of science, and statistical thinking is key to the scientific method, yet few graduates of high school and college understand how science works. For these and other reasons, statistics must become a major component of the modern K-12 mathematics curriculum and achieve a stronger presence in the undergraduate curriculum, as recommended by a wide variety of educational groups.

  • This design study tracks the development of student thinking about natural variation as late elementary grade students learned about distribution in the context of modeling plant growth at the population level. The data-modeling approach assisted children in coordinating their understanding of particular cases with an evolving notion of data as an aggregate of cases. Students learned to "read" shapes of distributions as signatures of prospective mechanisms of plant growth and conducted sampling investigations to represent repeated growth. These investigations, in turn, supported students' interpretations of the effects of added light and fertilizer. The authors argue for both the feasibility and importance of tools such as distribution and inference for supporting education that builds on children's own investigations of the world. (Fall 2004)

  • The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

  • Mathematics anxiety has always maintained a central focus in the education literature. However, there has been a recent focus on "statistics anxiety" as experienced by undergraduates. This paper presents the development of an instrument that assesses "statistical anxiety" in psychology graduate students. This measure was administered to 10 students enrolled in a graduate statistics course in an effort to refine the measure via student feedback. The refined instrument could be used as a screening tool for psychology students prior to taking graduate--level statistics course work; Such evaluation can assist instructors in identifying remedial need or counseling intervention.

  • Compared kindergartners', third graders', and undergraduates' understanding and attribution of randomness. Found that kindergartners' interpretations were deterministic or outside the determinancy-indeterminancy frame. Most third graders had some grasp of randomness; their interpretations were less dominated by false attribution of determinism than kindergartners'. Undergraduates also showed performance deficiencies, suggesting that interpreting random phenomena constitutes a nontrivial challenge even for adults.

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