Conference Paper

  • During a research project investigating understanding of variation students in a tertiary level introductory statistics course completed a questionnaire prior to, and at the end of, the course. This paper reports on interviews of selected students designed to determine whether more information could be gathered, and to identify those teaching and learning activities that assisted students to develop understanding. Prompting assisted students to develop better quality responses but cognitive conflict situations proved challenging. The diversity of activities identified by students as assisting development of understanding provides a challenge for educators in planning teaching sequences. Both educators and researchers need to listen to students to better understand the development of reasoning.

  • Year 11 (15-year-old) students are not exposed to formal statistical inferential methods. Therefore, when drawing conclusions from data, their reasoning must be based mainly on looking at graph representations. This study investigates the type of reasoning that might develop students' informal inferential statistical reasoning towards a more formal level. A perspectives model is developed for a teacher's informal inferential reasoning from the comparison of boxplots. The model is then used to analyse her students' responses to an assessment task. The resultant analysis produced a conjectured hierarchical model for students' reasoning. The implications of the findings for instruction are discussed.

  • Reasoning proportionally about collections of a sample statistic's values is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded in a classroom teaching experiment designed to support students constructing such understanding. Instruction engaged students in activities that focused their attention on the variability among outcomes of randomly drawn samples. There occurred a critical shift in students' attention and discourse away from individual sample outcomes and toward the distribution of a collection of sample outcomes. This shift supported further developments concerning how to compare entire distributions of sample outcomes as a basis for conceptualizing a notion of statistical unusualness. We characterize aspects of these developments in relation to students' classroom engagement.

  • Data and chance are the two related topics that deal with uncertainty. On the discussions of probability and statistics in both research and instruction, the existing literature depicts an artificial separation, to which other researchers (Shaughnessy, 2003; Steinbring, 1991) have already called attention in recognition of the inseparable nature of data and chance. Hence, this paper addresses how to integrate the discussions of distributions and probability, starting from the elementary grades. We report on a study that examines fourth-grade students' informal and intuitive conceptions of probability and distribution through a sequence of tasks for developing their understandings about probability distributions. These tasks include various random situations that students explore with a set of physical chance mechanisms and that can be modeled by a binomial probability distribution.

  • In this research we approach a fundamental stochastic idea. The random variable is based on other mathematics and probabilistic concepts and, in turn, is the support of many probability and statistics subjects. In this paper, we present some results from an exploratory study carried out with two university students. The aim was observing the difficulties the students face when they try to solve a problem that involves the concept of random variable.

  • In this paper we discuss the teacher's role in the introduction of probability to students aged from 11 to 18 years old. Coutinho (2001) has showed that model-building approaches enable students to attend to the duality of the probability concept. However, Gonçalves (2004) argues that teachers do not easily appropriate such teaching situations, because their conception are associated with their own practices, built from classic approaches to probability. In this paper, we discuss a teacher education project on teaching and learning probability problems, in which teachers and researchers collaborate during face-to-face and virtual sessions, to reflect upon and about teaching practices and especially about the possibilities associated with a model-building approach to probability.

  • 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.

  • Carnegie Mellon University was funded to develop a "stand-alone" web-based introductory statistics course, openly and freely available to individual learners online. The goal of this project is to develop statistical literacy among people who do not have access to academic institutions because of remote locations, financial difficulties or social barriers. In order to achieve this goal, the design of the course has been a collaboration among statistics faculty, cognitive scientists and experts in human computer interaction. This paper discusses the challenges in developing such a learning environment and ways in which the course tries to address them. We also describe the design and results of a pilot study where the degree to which the course is successful in developing statistical literacy has been examined.

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