Journal Article

  • The purpose of this research was to investigate the evolution, with age, of probabilistic, intuitively based misconceptions. We hypothesized, on the basis of previous research with infinity concepts, that these misconceptions would stabilize during the emergence of the formal operation period. The responses to probability problems of students in Grades 5, 7, 9, and 11 and of prospective teachers indicated, contrary to our hypothesis, that some misconceptions grew stronger with age, wheras others grew weaker. Only one misconception investigaged was stable across ages. An attempt was made to find a theoretical explanation for this rather strange and complex situation.

  • People attempting to generate random number sequences usually produce more alternations than expected by chance. They also judge overalternating sequences as maximally random. In this article, the authors review findings, implications, and explanatory mechanisms concerning subjective randomness. The authors next present the general approach of the mathematical theory of complexity, which identifies the length of the shortest program for reproducing a sequence with its degree of randomness. They describe three experiments, based on mean group responses, indicating that the perceived randomness of a sequence is better predicted by various measures of its encoding difficulty than by its objective randomness. These results seem to imply that in accordance with the complexity view, judging the extent of a sequence's randomness is based on an attempt to mentally encode it. The experience of randomness may result when this attempt fails.

  • The effects of a visible author (one who reveals aspects of him- or herself) on women's experience reading statistical texts were examined among 47 female college students who read texts that differed in the extent to which the author revealed attitudes and personality. Data included "think-and-feel aloud" protocols, measures of concentration, mood, level of perceived challenge, and readers' images of the author. Women reading the visible author text interacted with the author while reading: this relationship appeared to influence the relations among comprehension, motivation, and affective response. For these women, author image and initial self-efficacy for statistics were related to cognitive engagement, feelings of accomplishment, and intrinsic motivation. Implications for text construction and methodology in research on the interaction of cognition and affect during learning tasks are discussed.

  • The purpose of this study was to explore the basis of test anxiety expressed when taking a statistics course using a structural modeling approach. The study involved 219 university students. The data indicated that statistical test anxiety was different from general test anxiety. The females expressed more general and statistical test anxiety than males, and students who had taken more prior math courses had higher math self-concept scores. Math self-concept and achievement in statistics were negatively related to statistical test anxiety, and the students who reported high levels of general anxiety also reported high levels of statistical anxiety. The structural model revealed variables not studied previously to be important in understanding statistical test anxiety.

  • We highlight one interpretation of Pearson's r (largely unknown to behavioral scientists), inspired by the genetic measurement of inbreeding. The coefficient of inbreeding, defined as the probability that two paired alleles originate from common descent, equals the correlation between the uniting gametes. We specify the statistical conditions under which r can be interpreted as probability of identity by descent and explore the possibility of generalizing that meaning of correlation beyond the inbreeding context. Extensions to the framework of agreement between judges and to that of sequential dependencies are considered. Viewing correlation as probability is heuristically promising. We examine the implications of this approach in the case of three types of bivariate distributions and discuss potential insights and risks.

  • We demonstrate that one can teach conditional probability in a manner consistent with many features of the statistics education reform movement. Presenting a variety of applications of conditional probability to realistic problems, we propose that interactive activities and the use of technology make conditional probability understandable, interactive, and interesting for students at a wide range of levels of mathematical ability. Along with specific examples, we provide guidelines for implementation of the activities in the classroom and instructional cues for promoting curiosity and discussion among students.

  • The interconnected themes of quality and the marketing of the discipline of statistics are explored. An understanding of statistics as the study of the process of scientific inquiry is advocated as a consciously targeted market position. Because it reaches such a high proportion of the managers and decision makers of the future, the introductory university or college statistics course is highlighted as a potent marketing opportunity for enhancing the long-term health of statistics. Attention is given to teaching students to think statistically, to become educated consumers of statistical expertise, and to communicate well with nonstatisticians.

  • Exclusionary gendered language discourages women from pursuing graduate and professional training programs that lead to careers in statistics by excluding them from (1) the readership of statistical literature, (2) the characters portrayed in examples and problems, and (3) those people qualified to use statistical methods; and by (4) stereotyping women characters into nonscientific careers or careers that are not as prestigious and high paying as men's, (5) reinforcing the existing imbalance in the proportion of men and women engaged in scientific research and development, and (6) portraying professional women as incompetent. Thus this article challenges the continuing use of exclusionary gendered language in statistical literature, bringing this bias to the attention of the statistical community. Numerous examples are used to illustrate how the use of gendered language has symbolically excluded women from access to statistical advancements and careers both historically and now.

  • Statistics pervade our society, yet the understanding of statistics has remained the domain of a select few. Although the majority of the literature has focused on the adult learner, there is a movement toward teaching statistics to children. This article addresses the ways in which the study of statistics has been examined in the elementary and secondary schools in terms of content, readiness of children to learn, pedagogy, and assessment. A proposal is presented of how a cognitive apprenticeship model can be developed from the empirical research findings in order to build more effective instructional and assessment methods for statistics education.

  • The formal use of cooperative learning techniques developed originally in primary and secondary education proved effective in improving student performance and retention in a college freshman level statistics course. Lectures interspersed with group activities proved effective in increasing conceptual understanding and overall class performance.

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