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Theory

  • 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 idea of data as a mixture of signal and noise is perhaps the most fundamental concept in statistics. Research suggests, however, that current instruction is not helping students to develop this idea, and that though many students know, for example, how to compute means or medians, they do not know how to apply or interpret them. Part of the problem may be that the interpretations we often use to introduce data summaries, including viewing averages as typical scores or fair shares, provide a poor conceptual basis for using them to represent the entire group for purposes such as comparing one group to another. To explore the challenges of learning to think about data as signal and noise, we examine the "signal/noise" metaphor in the context of three different statistical processes: repeated measures, measuring individuals, and dichotomous events. On the basis of this analysis, we make several recommendations about research and instruction.

  • This chapter proposes design principles for developing statistical reasoning in elementary school. In doing so, we will draw on a classroom design experiment that we conducted several years ago in the United States with 12-year-old students that focused on the analysis of univariate data. Experiments of this type involve tightly integrated cycles of instructional design and the analysis of students' learning that feeds back to inform the revision of the design. To ground the proposed design principles, we first give a short overview of the classroom design experiment and then frame it as a paradigm case in which to tease out design principles that address five aspects of the classroom environment that proved critical in supporting the students' statistical learning:<br>o The focus on central statistical ideas<br>o The instructional activities<br>o The classroom activity structure<br>o The computer-based tools the students used<br>o The classroom discourse

  • The collection of studies in this book represents cutting-edge research on statistical literacy, reasoning, and thinking in the emerging area of statistics education. This chapter describes some of the main issues and challenges, as well as implications for teaching and assessing students, raised by these studies. Because statistics education is a new field, taking on its own place in educational research, this chapter begins with some comments on statistics education as an emerging research area, and then concentrates on various issues related to research on statistical literacy, reasoning, and thinking. Some of the topics discussed are the need to focus research, instruction, and assessment on the big ideas of statistics; the role of technology in developing statistical reasoning; addressing the diversity of learners (e.g., students at different educational levels as well as their teachers); and research methodologies for studying statistical reasoning. Finally, we consider implications for teaching and assessing students and suggest future research directions.

  • This article explores misconceptions that students hold about sampling techniques on surveys and discusses implications for instruction.

  • Pfannkuch (1997) contends that variation is a critical issue throughout the statistical inquiry process, from posing a question to drawing conclusions. This is particularly true for K-6 teachers when they attempt to use the process of statistical investigation as a means of teaching and learning across the spectrum of the K-6 curricula. In this context statistical concepts and ideas are taught and learned in conjunction with the important content area ideas and concepts. For a K-6 teacher, this means that the investigation must not only be planned in advance, but also aimed at being responsive to students. The potential for surprise questions, unanticipated responses and unintended outcomes is high, and teachers need to "think on their feet" statistically and react immediately in ways that accomplish content objectives, as well as convey correct statistical principles and reasoning. The intellectual demands in this context are no different than in other instances where teachers are trying to teach for understanding (i.e., Cohen, McLaughlin, &amp; Talbert, 1993; Ma, 1999).

  • Describes the PMOSE/IKIRSCH document readability formula for documents. Main document components in which the formula was based; Graphic documents; Entry documents; Density of documents; Usefulness in measuring document complexity.

  • This book aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. Four different perspectives, each related to a corresponding conception of algebra, provide avenues for its introduction: generalization, problem solving, modeling, and functions. The analysis of research on these perspectives is illuminated by a dual focus on epistemological (via the history of the development of algebra) and didactic concerns. Series: Mathematics Education Library, Vol. 18

  • The capacity for abstraction and concentration has changed. Methods of teaching Probability and Statistics must also evolve. Following is a presentation of an organized set of images, analysed using Graphs Theory, specifically adapted by syntax to each type of information. We use these, not as an illustration but as an exhaustive proof. We make this claim after having established the isomorphism between possibilities and elementary surfaces. Probability and statistics are thus unified and simplified. Combinatory Algebra and Mathematical Analysis remain tools. No more theorem will need to be learnt by heart. Fear and mathematical inferiority will be changed into an intellectual comfort. We have been using this teaching method for more than 25 years, in a basic course for non-specialized students, having written the corresponding books. Clinical and statistical tests already show its efficacy.

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