Research

  • In the focus over the past decade on data-driven, realistic approaches to building statistical literacy and data analysis curriculum, the explicit development of probability reasoning beyond coins and dice has received less attention. There are two aspects of probability at the introductory tertiary level: for use in introductory data analysis; and as foundation for further study in statistical modelling and applications, and increasingly in areas in information technology, engineering, finance, health and others. This paper advocates a minimalist objective-oriented approach in the former, and a constructivist, collaborative and data-linked approach in the latter. The latter is the main focus here, with strategies to help students unpack, analyse and extend what they have brought with them to tertiary study, enabling them to consciously develop coherent probabilistic understanding and linking with real investigations and processes.

  • Focusing on the word "literacy" in the phrase "statistical literacy," the present study explored what happened to the non-numerically based aspects of statistical literacy when students in Grades 7 and 9 were exposed to a unit of work in chance and data that emphasized variation. To test the suggestion of transfer of thinking skills to the literacy side of statistical literacy, 20 items from a larger survey were selected, upon which changes in literacy skills could be measured. Ninety students in each of Grade 7 and Grade 9 were asked the questions in a longer survey before and six weeks after taking part in a unit on chance and data devised by their usual classroom mathematics teacher as part of their schools' mathematics programs.

  • The ability to extract qualitative information from quantitative information, and/or to create new information from qualitative and quantitative information is the key task of statistical literacy in the 21st century. This paper presents a hierarchy of the graph interpretation aspect of statistical literacy that includes such ability. Participants from junior high to graduate students took part and some of them were interviewed. The SOLO Taxonomy is used for decoding the students' responses and the Rasch model is used for clarifying the construction of the hierarchy. Five different levels of graph interpretation are distinguished: Idiosyncratic, Basic graph reading, Rational/Literal, Critical, Hypothesising and Modelling. These results will supply guidelines for teaching statistical literacy.

  • In 2002, an international survey on reading graphs and tables of rates and percentages was conducted by the W. M. Keck Statistical Literacy Project. Respondents included US college students, college teachers worldwide and professional data analysts in the US and in South Africa. The survey focused on reading informal statistics - rates and percentages in tables and graphs. Some high error rates were encountered, but helping students learn these skills takes considerable time. A new on-line tool has been developed to help students practice using ordinary English to describe and compare rates and percentages. This tool decreased the class time necessary to teach this skill and helped make it possible to teach statistical literacy online. Statistical educators now have both the rules and the tools to teach students how to read and interpret summary data, and for teaching students to read and write comparisons of rates and percentages correctly.

  • Current school curriculum documents stress the need for assessment to support learning. Teachers use assessment information to infer students' development and plan appropriate intervention. In order to do this, a framework is needed within which the assessment can be developed and interpreted, and a suitable task is required to obtain the necessary information about students' performances. The responses of 586 students to performance assessment tasks developed for the purpose of assessing a numeracy construct, rather than statistical understanding, were analysed against a previously identified hierarchy of Statistical Literacy. The findings suggest that the tasks provided reliable and interpretable evidence of performance in Statistical Literacy, using a classroom-based process rather than a traditional test.

  • Computers facilitate reasoning with complex data. We report a study where 195 students aged 12 to 15 years were presented with computer based tasks that require reasoning with multivariate data, together with paper based tasks from a well established scale of statistical literacy. All the tasks fitted well onto a single Rasch scale; computer tasks were cognitively more complex, but ranked only slightly more difficult than paper tasks on the Rasch scale. Implications for assessment, the curriculum, and public presentations of data are discussed.

  • This paper describes the ARTIST project which was designed to address the assessment challenge in statistics education. The goals of the ARTIST project are to assist faculty who teach statistics across many disciplines in assessing student learning of statistics, enabling them to better evaluate individual student achievement, to evaluate and improve their courses, and to allow them to assess the impact of reform-based instructional methods on the attainment of statistical literacy, reasoning, and thinking. ARTIST consists of a website that provides resources designed to meet these goals. Among the resources are a large, searchable assessment item database, several online topic tests, and a comprehensive test of statistical literacy and reasoning (CAOS). Details of the development of the ARTIST resources, results from an extensive evaluation of the project, and the development of future ARTIST resources are presented.

  • In this paper we analyse an intuitive approach to the study of the empirical law of large numbers by a pair of student teachers. The learning is based on the use of a random experiment simulation applet with feedback by a lecturer. The analysis is based on some theoretical tools taken from the onto-semiotic approach to mathematical cognition and instruction (Godino, 2002). In particular we assess the epistemic, cognitive and instructional suitability of the study process. We deduce some requirements of the simulation device characteristics and the lecturer's role to increase the suitability of the teaching and learning process.

  • Prior investigation of student experiences with a computer interaction indicated that the simulation was only partly successful in facilitating developmental learning of statistical inference. The simulation was re examined in the light of subsequent multimedia design research and cognitive theory. A new simulation was developed with less extraneous information and reduced on screen text. In addition the new simulation incorporated audio narration and a higher degree of student control in progressing through signalled stages of development.

  • Educational software for statistics and data analysis provides a variety of tools for seeing and expressing ideas about data distributions. However, the ideas that learners find important to express often depend on an interaction between software and the shape of the distributions themselves. In this interview study of teachers participating in the VISOR professional development program, we investigate how distributional shape (symmetric or skewed) and choice of software tool (TinkerPlots or Fathom) affect the variety of ways that teachers discuss data distributions when comparing groups. We find teachers' confidence is increased when different measures or ways of viewing data "say the same thing," which more often holds true with symmetric distributions. When these seem to conflict, typically with skew distributions, teachers work to understand the measures themselves, and introduce new ways of characterizing data, so that they can make coherent sense of the distributions. The paper introduces a distinction between rule-driven and value-driven measures which we find important in understanding teachers' analytic methods.

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