Journal Article

  • The Mathematics Learning Study committee offers a promising mechanism for helping those concerned with school mathematics begin to use the available research more productively. The committee of practitioners, research mathematicians, cognitive psychologists, researchers in mathematics education, and a representative from the business community was convened by the National Research Council to synthesize the research on preK-8 mathematics learning to provide recommendations for best practice in the early years of schooling. Committee members applied the criteria of relevance, soundness, and generalizability in examining the evidence on mathematics learning and looked for a body of evidence that converged on a single point and that made good common and theoretical sense among the research studies that met those criteria for a given topic. A consensus had to be reached on the studies that would be cited in the draft report and the language that would be used to describe them. The entire draft was then reviewed by 15 independent reviewers.

  • Human perception and memory are often explained as optimal statistical inferences that are informed by accurate priorprobabilities. In contrast, cognitive judgments are usually viewed as following error-prone heuristics that are insensitive to priors. We examined the optimality of human cognition in a more realistic context than typicallaboratory studies, asking people to make predictions about the duration or extent of everyday phenomena suchas human life spans and the box-office take of movies. Our results suggest that everyday cognitive judgments follow the same optimal statistical principles as perception and memory, and reveal a close correspondence between people's implicit probabilistic models and the statistics of the world.

  • Identifies and describes students' variation-type thinking observed in a small sample of middle-school students as they conducted a statistical investigation.

  • Presents and discusses examples that illustrate the nature and scope of elementary and middle school students' reasoning when they are faced with tasks that involve making inferences and predictions from data. Shows that the range in thinking is not so much dependent on age as on the experiences students have in data exploration.

  • Statistics are more pervasive than ever. We encounter statistical information in newspapers, magazines, advertisements, and on the radio and television. Political, social, economic, scientific, and personal decisions are made on the basis of data. To operate effectively in our world, we must be able to make senes of statistical information. There are new ways to think about the discipline of statistics and about the ways students develop their understanding of statistics.<br>Statistics learning involves a process of doing meaningful statistics (Ben-Zvi, 2000). This process includes four key components: posing questions, collecting data, analyzing distributions, and interpreting results. This process is dynamic, with interactions among the four components being the norm.

  • This article contains two cautionary tales based on my experience working with students, adults, and teachers on research and professional development projects involving data and chance. The first arose from observing two grade 9 boys who ignored instructions and then tried to supplements samples of size two with other samples of size two in order to make samples of size four. The second was related to several observations of students and adults expressing beliefs about dice tossing that were contrary to my expectations: either expecting peaks in distributions that should be uniform or expecting uniformity in distributions that should be peaked. The solution to the dilemmas presented in these two tales would appear to be the creation of cognitive conflict to illustrate forcefully the importance of sample size and the difference between equally likely and non-equally likely outcomes. To handle the situations however, teachers need to be aware that these beliefs may be abroad, to experience the activities that can lead to conflict resolutions, and then plan their own strategies.

  • A modeling approach to the teaching and learning of mathematics shifts the focus of the learning activity from finding a solution to a particular problem to creating a system of relationsips that is generalizable and reusable. In this article, we discuss the nature of a sequence of tasks that can be used to elicit the development of such systems by middle school students. We report the results of our reserach with these tasks at two levels. First, we present a detailed analysis of the mathematical reasoning development of one small group of students across the sequence of tasks. Second, we provide a macrolevel analysis of the diversity of thinking patterns identified on two of the problem tasks where we incorporate data from multiple groups of students. Student reasoning about the relationships between and among quantites and their application in related situations is discussed. The results suggest that students were able to create generalizable and reusable systems or models for selecting, ranking, and weighting data. Furthermore, the extent of variations in the approaches that students took suggests that there are multiple paths for the development of ideas about ranking data for decision making.

  • The purpose of the present study is to investigate evidence of the validity of Survey of Attitudes Toward Statistics Scale (SATS) scores and their relationship with scores from two other measures of attitudes toward statistics, the Attitude Toward Statistics Scale (ATS) and the Statistics Attitude Survey. The pre- and postcourse responses of 342 graduate and undergraduate students enrolled in inferential statistics courses at a large midwestern university were analyzed. Internal consistency reliability estimates were greater than .90 for total scores and greater than .70 for subscale scores for all instruments. Regression analyses confirmed the importance of SATS subscale scores over and above demographic variables in a theoretical model predicting statistics course achievement. Factor analyses suggested that both the ATS and the SATS have two domains, which is contrary to the four-factor solution proposed by the developers of the SATS.

  • The effectiveness of simulations for teaching statistical concepts was compared to the effectiveness of a textbook. The variable Medium (simulation versus textbook) and Question specificity (specific versus Non-specific), were manipulated factorially. The subjects consisted of 115 college students. The dependent variable was performance on problems requiring subjects to apply what they learned to ill defined everyday problems. Subjects trained by simulation performed significantly better than those trained with a textbook. subjects in the "specific" condition performed better than those in the "Non-specific" condition, although the difference did not reach conventional levels of significance. these results support the increasing use of simulation in education and training.

  • Most college students are required to enroll in statistics and quantitative research methodology courses as a necessary part of their degree programmes. Unfortunately, many students report high levels of statistics anxiety while enrolled in these classes. Recent years have seen an increase in the number of articles on statistics anxiety appearing in the literature, as researchers have recognised that statistics anxiety is a multidimensionality construct that has debilitative effects on academic performance. Thus, the purpose of this article is to provide a comprehensive summary of the literature on statistics anxiety. In particular, the nature, etiology, and prevalence of statistics anxiety are described. Additionally, antecedents (i.e. dispositional, situational and environmental) of statistics anxiety are identified, as well as their effects on statistics achievement. Furthermore, existing measures of statistics anxiety are documented. Finally, based on the literature, successful interventions for reducing statistics anxiety are described. Implications for future research are provided.

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