Dani Ben-Zvi

Collaboration in learning and teaching statistics

This paper provides practical examples of how statistics educators may apply a cooperative framework to classroom teaching and teacher collaboration. Building on the premise that statistics instruction ought to resemble statistical practice, an inherently cooperative enterprise, our purpose is to highlight specific ways in which cooperative methods may translate to statistics education. So doing, we hope to address the concerns of those statistics educators who are reluctant to adopt more student-centered teaching strategies, as well as those educators who have tried these methods but ultimately returned to more traditional, teacher-centered instruction.

Research on Statistical Literacy, Reasoning, and Thinking: Issues, Challenges, and Implications

This book focuses on one aspect of the “infancy” of the field of statistics education research, by attempting to grapple with the definitions, distinctions, and development of statistical literacy, reasoning, and thinking. As this field grows, the research studies in this volume should help provide a strong foundation as well as a common research literature. This is an exciting time, given the newness of the research area and the energy and enthusiasm of the contributing researchers and educators who are helping to shape the discipline as well as the future teaching and learning of statistics. We point out that there is room for more participants to help define and construct the research agenda and contribute to results. We hope to see many new faces at future gatherings of the international research community, whether at SRTL-4, or 5, or other venues such as the International Conference on Teaching Statistics (ICOTS), International Congresson Mathematical Education (ICME), and the International Group for the Psychology of Mathematics Education (PME).

Technology for enhancing statistical reasoning at the school level

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.

REASONING ABOUT DATA ANALYSIS

OVERVIEW The purpose of this chapter is to describe and analyze the ways in which middle school students begin to reason about data and come to understand exploratory data analysis (EDA). The process of developing reasoning about data while learning skills, procedures, and concepts is described. In addition, the students are observed as they begin to adopt and exercise some of the habits and points of view that are associated with statistical thinking. The first case study focuses on the development of a global view of data and data representations. The second case study concentrates on design of a meaningful EDA learning environment that promotes statistical reasoning about data analysis. In light of the analysis, a description of what it may mean to learn to reason about data analysis is proposed and educational and curricular implications are drawn.

Developing Teachers’ Statistical Thinking

In this chapter learning experiences that teachers need in order to develop their ability to think and reason statistically are described. It is argued that teacher courses should be designed around five major themes: developing understanding of key statistical concepts; developing the ability to explore and learn from data; developing statistical argumentation; using formative assessment; and learning to understand students’ reasoning.

The Role of Context in Developing Reasoning about Informal Statistical Inference

Statistics education research is emerging as an important area of inquiry with multiple implications in school and tertiary curriculum design, instructional activities, technological tools that aid teaching and learning statistics, and teachers’ professional development. Over the past decade there has been an increasingly strong call for statistics education to focus more on statistical literacy, reasoning, and thinking. One of the main arguments presented is that traditional approaches to teaching statistics focus mainly on skills, procedures, and computations, which do not lead students to reason or think statistically. The papers in this Special Issue of Mathematical Thinking and Learning came out of discussions and presentations from the Sixth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL) in Brisbane, Australia in July 2009. SRTL is part of an international collaboration for research in statistics education that focuses on examining the nature and development of statistical literacy, reasoning, and thinking. SRTL organizes a series of biannual research forums since 1999 as an alternative to large conferences. The small size of these gatherings allows plenty of time for interaction and discussion of research data on a different clear thematic focus for each meeting with emphasis on qualitative analysis of classroom videos or interviews.

Students negotiating and designing their collaborative learning norms: a group developmental perspective in learning communities

This research shows how participants in classroom learning communities (LCs) come to take responsibility over designing their collaborative learning norms. Taking a micro-developmental perspective within a graduate-level course, we examined fine-grained changes in group discourse during a period of rapid change where this responsibility taking occurs, which we frame as the transition between the storming and norming stages of group development. Our findings indicate that this transition was based upon three sub-stages that included (a) recognition of a group crisis; (b) acceptance of responsibility; and (c) increased meaningfulness of norms. As an outcome of this transition, LC members took responsibility over negotiating and designing their collaborative norms as authority moved from moderators to students. We discuss the theoretical and practical contributions of this research on group development and LCs, as well as limitations and next steps for research.

Children’s Wonder How to Wander Between Data and Context

The knowledge and application of the problem context and its relation to data analysis is a key component in the development of students’ informal inferential reasoning. This case study analyzes children’s emergent understanding of the relationship between the context world and the data world while making informal statistical inferences in an inquiry-based learning environment using TinkerPlots. We focus on two fifth-grade students (aged 11) who participated in the 2010 Connections design experiment in Israel. We observe and analyze their first steps in the two worlds—data and context—in growing samples investigations. They developed gradually and inconsistently an understanding of making informal inferences considering both context and data. They moved from an initial conception of context and data as separate entities to two interconnected and relevant dimensions. We finally discuss this development and what might have supported it.

The teaching and learning of statistics: international perspectives

This book presents the breadth and diversity of empirical and practical work done on statistics education around the world. A wide range of methods are used to respond to the research questions that form its base. Case studies of single students or teachers aimed at understanding reasoning processes, large-scale experimental studies attempting to generalize trends in the teaching and learning of statistics are both employed. Various epistemological stances are described and utilized. The teaching and learning of statistics is presented in multiple contexts in the book. These include designed settings for young children, students in formal schooling, tertiary level students, vocational schools, and teacher professional development. A diversity is evident also in the choices of what to teach (curriculum), when to teach (learning trajectory), how to teach (pedagogy), how to demonstrate evidence of learning (assessment) and what challenges teachers and students face when they solve statistical problems (reasoning and thinking).

Design of Statistics Learning Environments

The goal of this chapter is to draw attention to the need to think about learning environments and their design as a way of considering how sustainable change in the learning and teaching of statistics can be supported. The goal is not to advocate one particular approach to the design of learning environments but rather to raise awareness of the need to consider this lens in statistics education. We first present the rationale for the importance of a focus on learning environments for statistics education. We provide several examples of learning environments that operationalize and integrate various design perspectives and are informed by two theoretical frameworks: social constructivist theory of learning and realistic mathematics education theory. We discuss these examples in a critical way by comparing and evaluating their designs, looking for common threads among them, and develop from them six design considerations for statistics learning environments. Finally, we discuss implications and emerging directions and goals for further implementation and research.