Report

  • Assessed understanding of decision making about repeated uncertain events, using hypothetical and in-vivo prediction tasks modeled after those used in probabilitiy-learning research. Previous studies have been unclear on whether suboptimal choices reflected reasoning errors and lack of strategic thinking, or confounding factors. Quantitative and qualitative analyses of subjects' choices and strategy explanation showed that up to 50% of college students did not fully understand the relative value of different strategies. Only 5 % of subjects preferred a "true" probability matching strategy, included on an in-vivo task. High-school students showed greater misunderstandings. Large gender differences in prediction strategies and in related computational skills were observed. Understanding was discussed in terms of subjects' inferences from knowledge of independence of events, (lack of) computational skills, and correlates of the quantitative nature of prediction tasks. Implications for research on decision making, including need to address individual differences, are discussed.

  • This communication describes the first results obtained from an exploratory study carried out with primary-school teachers about their conceptions with respect to a fundamental aspect of probabilistic knowledge: The notion of the concept of randomness. The results obtained indicate the partial and poorly formed character of their conceptions and indicate the necessity of developing specific training on probabilistic knowledge, its learning and teaching, based on the aforementioned conceptions.

  • Data handling has recently been introduced in the United Kingdom as a major component of the mainstream school mathematics curriculum. A survey of teachers in Northern Ireland showed that they are generally not well prepared to teach new material, particularly probability.

  • Three software modules were created to help students learn to visualize hypothesis tests, based either on scenarios or on a Do-It-Yourself control panel to set up the experiment. The one-sample and two-sample modules illustrate tests of means or variances. For each sample, there is a dot plot with optional overlays of the populations or sampling distributions, table of statistics and parameters, confidence intervals, and theoretical distribution of the test statistic with the rejection region shaded. The ANOVA module offers stacked dot plots, ANOVA table, and sample statistics. Each module allows replication experiments to estimate empirical Type I or II error. There is an extensive help system. Software has been tested on students. The modules are part of an NSF-supported project to enhance quantitative reasoning and motivate students.

  • This paper discusses the following features of the author's ideal introductory statistics course: (1) a clear statement of the goals of the course, (2) a careful discussion of the fundamental concept of 'variable', (3) a unification of statistical methods under the concept of a relationship between variables, (4) a characterization of hypothesis testing that is consistent with standard empirical research, (5) the use of practical examples, (6) the right mix of pedagogical techniques: lectures, readings, discussions, exercises, activities, group work, multimedia, (7) a proper choice of computational technology, and (8) a de-emphasis of less important topics such as univariate distributions, probability theory, and the mathematical theory of statistics. The appendices contain (a) recommendations for research to test different approaches to the introductory course and (b) discussion of thought-provoking criticisms of the recommended approach.

  • This report deals with the use of portfolios in assessing student performance in statistics. It gives a background on the use of portfolios, information on portfolio development, and issues surrounding portfolio assessment. It also provides a sketch of what a portfolio in statistics might look like.

  • The present study used both quantitative and qualitative methods to investigate the learning and motivational strategies used by students in a beginning-level statistics course. The research questions that guided the investigation are: (1) Do motivational variables account for unique variance in the academic performance of statistics students?, (2) Do deeper-level processing strategies account for unique variance in the academic performance of statistics students?, and (3) Do successful students report using different motivation and learning strategies than unsuccessful students in a beginning-level statistics course? Ninety-four students enrolled in six sections of the same course over a two-year period completed measures designed to assess attitudes about statistics, motivation and learning strategies use as well as previous math and statistics knowledge. In addition, randomly selected participants were interviewed about how they prepared for their midterm exam. The results of the study show that both motivation and learning strategies variables influenced performance in the introduction to statistics class. These results help to expand our understanding of what is involved in the process of learning statistics. Also, suggestions for teaching statistics are explored.

  • The theoretical basis of this paper is the modeling of students' knowledge about a specific subject as a qualitative and systemic construct. Following therefrom, a discussion about the role of multivariate analysis for studying the structure of this knowledge and for building explanatory models relating its structure to task, cognitive and instructional variables. Correspondence analysis in an empirical study referring to statistical association is used as an example.

  • This report covers the topic of assessment. It provides a broad overview of the definition of assessment and the different types of assessments (portfolio, authentic, performance), and it then discusses issues such as what the purposes of assessment are, what should be assessed, how assessment should proceed, and what the implications of assessment are for instructors.

  • In this paper the responses of 247 secondary students to 8 test items used in classical studies of probabilistic reasoning (representativeness, equiprobability bias and outcome approach) are analyzed. The study was designed to assess the quality of probabilistic reasoning of two levels of secondary students (14 and 18 year-old students). These groups are compared revealing few differences in their responses.

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