Reasoning with evidence–New opportunities in assessment

2007

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

International Electronic Journal of Mathematics Education, 2007

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

Reasoning from multivariate evidence is pervasive in political speeches and in the media, but is largely absent in UK schools. Currently, we do not prepare young people to understand important social debates, nor to make informed decisions about their personal well-being. We have evidence that students can work with multivariate data if supported appropriately with technology, and are working with teachers of mathematics, citizenship, and geography to develop curriculum materials designed to develop an understanding of complex issues in the curriculum, and reasoning from evidence in general. Examples of the use of survey data on sexually transmitted diseases, which students explore using powerful interfaces, are shown to illustrate our approach.

2009

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. THE ARTIST PROJECT

Much of the data presented by politicians and the media is multivariate in its nature. However, in the UK at least, the general public has little training to deal with such information. It is reasonable to explore the school curriculum to determine the nature and extent of students' preparation for dealing with multivariate data. In the UK, high-stakes examinations have a profound effect on the curriculum; it follows that one can best understand the curriculum by examining the content of high-stakes tests.

Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clement, A. J. Bishop, C. Keitel, J. Kilpatrick, J., & A. Y. L. Leung, (Eds.). Third International Handbook on Mathematics Education (pp. 643-689). New York: Springer. The purpose of this chapter is to provide an updated overview of digital technologies relevant to statistics education, and to summarize what is currently known about how these new technologies can support the development of students’ statistical reasoning at the school level. A brief literature review of trends in statistics education is followed by a section on the history of technologies in statistics and statistics education. Next, an overview of various types of technological tools highlights their benefits, purposes and limitations for developing students’ statistical reasoning. We further discuss different learning environments that capitalize on these tools with examples from research and practice. Dynamic data analysis software applications for secondary students such as Fathom and TinkerPlots are discussed in detail, . Examples are provided to illustrate innovative uses of technology. In the future, these uses may also be supported by a wider range of new tools still to be developed. To summarize some of the findings, the role of digital technologies in statistical reasoning is metaphorically compared with travelling between data and conclusions, where these tools represent fast modes of transport. Finally, we suggest future directions for technology in research and practice of developing students’ statistical reasoning in technology-enhanced learning environments.

The Turkish Online Journal of Educational Technology, 13(1), 2014

The focus of assessment in statistics has gradually shifted from traditional assessment towards alternative assessment where more attention has been paid to the core statistical concepts such as center, variability, and distribution. In spite of this, there are comparatively few assessments that combine the significant three types of statistical reasoning (reasoning about center, spread, and distribution) with information technology in the context of secondary school students. Hence, this paper intends to discuss the development and initial validation of a technology-based statistical reasoning assessment tool that has been created based on a previously developed statistical reasoning framework. This framework has been useful in evaluating students’ statistical reasoning levels in task-based interviews. The assessment tool formulated through this study will be used to refine and validate the initial statistical reasoning framework. There are five tasks in this instrument and each item is labeled according to four key constructs. The technological tool that has been used in solving tasks is dynamic mathematics software. This technology-based statistical reasoning assessment tool can be applied for further investigation.

Curriculum Development in …, 2004

The paper reviews the nature of statistics in the UK National Curriculum. While there is great opportunity for statistics to inform thinking in a range of disciplines, there is little coherence in the planning of activities for children. Formal assessment of statistical ability focuses on procedural knowledge, applied to univariate and bivariate problems. These provisions are inadequate for informed citizenship. We report work on World Class Tests, where students aged 9 and 13 years are presented with both paper-based and IT-based problem solving tasks in mathematics and science. Many of these tasks require students to work with 3 or more variables, often non-linearly related to each other. Students perform rather well on these tasks. Tasks are shown, together with performance data disaggregated by school and sex.

Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students' statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten students then participated in the second task-based interview, and the data obtained were used to validate the framework. The findings showed that the students' statistical reasoning levels were consistent across the four constructs, and this result confirmed the framework's cohesion. Developed to contribute to statistics education, this newly developed statistical reasoning framework provides a guide for planning learning goals and designing instruction and assessments.

2004

The paper reviews the nature of statistics in the UK National Curriculum. While there is great opportunity for statistics to inform thinking in a range of disciplines, there is little coherence in the planning of activities for children. Formal assessment of statistical ability focuses on procedural knowledge, applied to univariate and bivariate problems. These provisions are inadequate for informed citizenship. We report work on World Class Tests (WCT), where students aged 9 and 13 years are presented with both paper-based and IT-based problem solving tasks in mathematics and science. Many of these tasks require students to work with three or more variables, often non-linearly related to each other. Students perform rather well on these tasks. Tasks are shown, together with performance data disaggregated by school and sex. Features of the displays that make them well suited to the exploration of complex patterns are discussed, and our design principles are described. Our current activities set out to embed test items in curriculum materials suitable for use in mathematics and science classrooms. A good grounding in handling complex data is essential for informed citizenship. We are in the process of creating methods to help students develop appropriate skills.