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  • This paper describes how one group of students came to reason about data while developing statistical understandings related to exploratory data analysis. Episodes taken from a 7th grade classroom in which a 12-week teaching experiment was conducted are presented. One of the goals of the teaching experiment was to investigate ways to support middle school students' development of statistical reasoning proactively. The use of computer tools was viewed as an integral aspect of statistical reasoning rather than an add-on. Two computer tools were designed with the intention of supporting students' emerging mathematical notions while simultaneously providing them with tools for data analysis. The intent of the instructional sequences developed in the course of the teaching experiment is outlined first. The rest of the paper consists of descriptions of episodes from the classroom that highlight students' development of sophisticated ways to reason about data.

  • This paper considers the possibilities of using computers not only to amplify, but to reorganize children's thinking and mental functioning. These two different conceptualizations of the transformational role of noncomputer cognitive technologies (such as written language) in human intelligence and cognitive change are sketched, and the different implications to be drawn from these conceptualizations are considered in relation to human thinking and the educational processes. Several examples of software as cognitive technologies are analyzed, and the advantages of the reorganizer approach are detailed. It is argued that since the cognitive technologies we invent can serve as instruments of cultural redefinition (shaping who we are by what we do), the selecting of values for educational goals becomes important. Finally, it is suggested that the urgency of updating educational aims and methods recommends an activist research paradigm for simultaneously creating and studying changes in the processes and outcomes of human learning with new cognitive and educational technologies.

  • Computers are playing a fundamental role in enhancing exploratory learning techniques in education. This volume in the NATO Special Programme on Advanced Educational Technology covers the state of the art in the design and use of computer systems for exploratory learning. Contributed chapters treat principles, theory, practice, and examples of some of the best contemporary computer-based learning environments: Logo, Boxer, Microworlds, Cabri-Géomètre, Star Logo, Table Top, Geomland, spreadsheets, Function Machines, and others. Emphasis is on mathematics and science education. Synthetic chapters provide an overview of the current scene in computers and exploratory learning, and analyses from the perspectives of epistemology, learning, and socio-cultural studies.

  • Technology has been used as an active learning tool in Workshop Statistics, a project that involved the development and implementation of curricular materials which guide students to learn fundamental statistical ideas through self-discovery. Using the workshop approach, the lecture-format was completely abandoned. Classes are held in microcomputer-equipped classrooms in which students spend class-time working<br>collaboratively on activities carefully designed to enable them to discover statistical concepts, explore statistical principles, and apply statistical techniques.<br><br>The workshop approach uses technology in three ways. First, technology is used to perform the calculations and present the visual displays necessary to analyze real datasets, which are often large and cumbersome. Freeing students from these computational chores also empowers the instructor to focus attention on the understanding of concepts and interpretation of results. Second, technology is used to conduct simulations, which allow students to visualize and explore the long-term behavior of sample statistics under repeated random sampling. Whereas these two uses of technology are fairly standard, the most distinctive use of technology within the workshop approach is to enable students to explore statistical phenomena. Students make predictions about a statistical property and then use the computer to investigate their predictions, revising their predictions and iterating the process as necessary.

  • The success of any probability curriculum for developing students' probabilistic reasoning depends greatly on teachers' understanding of probability as well as a much deeper understanding of issues such as students' misconceptions (Stohl, p. 351, this chapter).<br><br>The purpose of this chapter is to investigate issues concerning the nature and development of teachers' probability understanding. The chapter begins with a discussion of central issues that affect teachers' efforts to facilitate students' probabilistic understanding. I then examine teachers' knowledge and beliefs about probability, their ability to teach probabilistic ideas, and lessons learned from programs in teacher education that have aimed at developing teachers' knowledge about probability.

  • The purpose of this chapter is to share the insights we gained from implementing a task with sixth-grade students as they learned to draw inferences from empirical data. To accomplish this goal we begin by describing the key features of the task that elicit and extend students' reasoning. Next we provide several contrasting examples that exemplify the notion of "compelling evidence" among middle grades students, and then offer provisions for individual differences. Finally we argue that carefullydesigned instructional tasks can engage students of all different ages in statistical inference and promote the development of powerful connections between data and chance.

  • 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 on skills, procedures, and computations, which do not lead students to reason or think statistically. This book explores the challenge posed to educators at all levels-how to develop the desired learning goals for students by focusing on current research studies that examine the nature and development of statistical literacy, reasoning, and thinking. We begin this introductory chapter with an overview of the reform movement in statistics education that has led to the focus on these learning outcomes. Next, we offer some preliminary definitions and distinctions for these often poorly defined and overlapping terms. We then describe some of the unique issues addressed by each chapter and conclude with some summary comments and implications.

  • There has been an increasingly strong call from practicing statisticians for statistical education to focus more on statistical thinking (e.g., Bailar, 1988; Snee, 1993; Moore, 1998). They maintain that the traditional approach of teaching, which has focused on the development of skills, has failed to produce an ability to think statistically: "Typically people learn methods, but not how to apply them or how to interpret the results" (Mallows, 1998, p. 2).<br>Solutions offered for changing this situation include employing a greater variety of learning methods at undergraduate level and compelling students to experience statistical thinking by dealing with real-world problems and issues. A major obstacle, as Bailar (1988) points out, is teacher inexperience. We believe this is greatly compounded by the lack of an articulated, coherent body of knowledge on statistical thinking that limits the pedagogical effectiveness even of teachers who are experienced statisticians. Mallows (1998) based his 1997 Fisher Memorial lecture on the need for effort to be put into developing a theory for understanding how to think about applied statistics, since the enunciation of these principles would be useful for teaching.<br>This chapter focuses on thinking in statistics rather than probability. Although statistics as a discipline uses mathematics and probability, as Moore (1992b) states, probability is a field of mathematics, whereas statistics is not. Statistics did not originate within mathematics. It is a unified logic of empirical science that has largely developed as a new discipline since the beginning of the 20th century. We will follow the origins of statistical thinking through to an explication of what we currently understand to be statistical thinking from the writings of statisticians and statistics educationists.

  • The focus of this chapter is on the nature of mathematical and statistical reasoning. The chapter begins with a description of the general nature of human reasoning. This is followed by a description of mathematical reasoning as described by mathematicians along with recommendations by mathematics educators regarding educational experiences to improve mathematical reasoning. The literature on statistical reasoning is reviewed and findings from the general literature on reasoning are used to identify areas of statistical reasoning that students find most challenging. Statistical reasoning and mathematical reasoning are compared and contrasted, and implications for instruction and research are suggested.

  • This chapter examines cognitive models of development in statistical reasoning and the role they can play in statistical education. The meaning of statistical reasoning is explored and cognitive models of development are examined. Cognitive models of development include both maturational and interactionist effects. This chapter uses a developmental model to analyze different aspects of statistical reasoning, such as, reasoning about center, spread, and association. Implications for curriculum design, instruction, and assessment are also discussed.

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