Chapter

  • Book description<br>How can anyone be rational in a world where knowledge is limited, time is pressing, and deep thought is often an unattainable luxury? In our book, "Simple Heuristics That Make Us Smart," we invite readers to embark on a new journey into a land of rationality that differs from the familiar territory of cognitive science and economics. Traditional models of rationality in these fields have tended to view decision-makers as possessing supernatural powers of reason, limitless knowledge, and an eternity in which to make choices. But to understand decisions in the real world, we need a different, more psychologically plausible notion of rationality. This book provides such a view. It is about fast and frugal heuristics-simple rules for making decisions with realistic mental resources. These heuristics can enable both living organisms and artificial systems to make smart choices, judgments, and predictions by employing bounded rationality.<br><br>But when and how can such fast and frugal heuristics work? What heuristics are in the mind's "adaptive toolbox," and what building blocks compose them? Can judgments based simply on a single reason be as accurate as those based on many reasons? Could having less knowledge even lead to systematically better predictions than having more knowledge? We explore these questions by developing computational models of heuristics and testing them through theoretical analysis and practical experiments with people. We show how fast and frugal heuristics can yield adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high-school drop-out rates, and profiting from the stock market.<br><br>We have worked to create an interdisciplinary book that is both useful and engaging and will appeal to a wide audience. It is intended for readers interested in cognitive psychology, evolutionary psychology, and cognitive science, as well as in economics and artificial intelligence. We hope that it will also inspire anyone who simply wants to make good decisions.

  • Statistical reasoning is an art and so demands both mathematical knowledge and informed judgment. When it is mechanized, as with the institutionalized hybrid logic, it becomes ritual, not reasoning. Many colleagues have argued that it is not going to be easy to get researchers in psychology and other sociobiomedical sciences to drop this comforting crutch unless one offers an easy-to-use substitute. But this is exactly what I want to avoid - the substitution of one mechanistic dogma for another. It is our duty to inform our students of the many good roads to statistical inference that exist and to teach them how to use informed judgment to decide which one to follow for a particular problem. At the very least, this chapter can serve as a tool in arguments with people who think they have to defend a ritualistic dogma instead of good statistical reasoning. Making and winning such arguments is indispensable to good science.

  • This chapter looks at symbolizing and mathematical learning from a social constuctivist perspective that is motivated by an interest in instructional design. The central theme is that of a concern for the way students actually use tools and symbols. Point of departure are analyses treat people's activity with symbols as an inegral aspect fo their mathematical reasoning rather than as external aids to it. As a consequence, the process of learning to use symbols in general, and conventional mathematical symbols in particular, is cast in terms of participation. Symbol use then seen not so much as somthing to be mastered, but qas a consituent part of the mathematical practices in which students come to participate. This view corresponds with the author's perspective, according to which it is essential to account for the mathematical learning not merely of individual students but of the classroom community taken as a unit of analysis in its own right. To account for this collective learning, the thoeretical construct of a classroom mathematical practice is introduced, which involves taken-as-shared ways of symbolizing.<br>Against this background an analysis is presented of the mathematical practices established duing a seventh-grade classroom teaching experiment that focused on statistical data analysis, that is based on RME theory. This analysis is supplemented with a description of the taden-as-shared ways in thish two computer-based analysis tools were used in the classroom, which is cast in terms of the emergence of a chain of signification. The chapter finishes with a reflection on the general notion of modeling. In connection with the notion of participation, a distinction is made between the use fo the term model in mathematical discourse, and an alternative formulation that relates to both semiotics and design theory.

  • A most basic and long standing conern of philosophers, psychologists, and educators is the probblem of knowledge elicitiation and represntation. How do we assess and represent an individual's knoledge? Philosophers, when asking these questions, have usually expressed an interest in general or world knowledge. Pschologists and educators, on the other hand, have often been more internerestedin the problem of assessing and representing a person's knowledge of some particular topic or area. It is this problem , as it arises in the assessment of classroom types of knoledge, that is the concern of the present chapter. Knowledge assessmetn and representation, as carried out in the classroom, appears as a relatively straghtforward matter. Knowledge is assessed by simply asking factual questions and is represented by presenting the indicidual's relatice standing in terms of a percentile. We begin with a critique of this conventional approach to assessing and representing classroom knowledge.

  • The papers in this book are intended to evaluate the achievements of Chinese statisticians, in both the theoretical and applied fields, during the ten-year period beginning from the late seventies. These papers provide selected information about this question, rather than a complete picture of statistics in China. Yet we strongly believe that the articles presented here will enable the reader to grasp some unique features of the development and nature of statistics in China.

  • The appendeces from a report on teaching statistics which presents the Statistics Focus Group's recommendations:<br>Appendix A: Helping Students Learn (Garfield)<br>Appendix B: Examples<br>--Classroom experiments (Taylor)<br>--Project NABs (Gunst)<br>Appendix C: Making it Happen<br>--Interesting and Available Data (Lock)<br>--EDSTAT-L Discussion List (Arnold)<br>Appendix D: Report of workshop of Statistical education (Hogg)

  • The Handbook of Research Design in Mathematics and Science Education is based on results from an NSF-supported project (REC 9450510) aimed at clarifying the nature of principles that govern the effective use of emerging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research designs that:<br>* have been pioneered recently by mathematics and science educators;<br>* have distinctive characteristics when they are used in projects that focus on mathematics and science education; and<br>* have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the development of mathematics or science students and teachers, or for the development, dissemination, and implementation of innovative programs of mathematics or science instruction.<br>The volume emphasizes research designs that are intended to radically increase the relevance of research to practice, often by involving practitioners in the identification and formulation of the problems to be addressed or in other key roles in the research process. Examples of such research designs include teaching experiments, clinical interviews, analyses of videotapes, action research studies, ethnographic observations, software development studies (or curricula development studies, more generally), and computer modeling studies. This book's second goal is to begin discussions about the nature of appropriate and productive criteria for assessing (and increasing) the quality of research proposals, projects, or publications that are based on the preceding kind of research designs. A final objective is to describe such guidelines in forms that will be useful to graduate students and others who are novices to the fields of mathematics or science education research. The NSF-supported project from which this book developed involved a series of mini conferences in which leading researchers in mathematics and science education developed detailed specifications for the book, and planned and revised chapters to be included. Chapters were also field tested and revised during a series of doctoral research seminars that were sponsored by the University of Wisconsin's OERI-supported National Center for Improving Student Learning and Achievement in Mathematics and Science. A Web site with additional resource materials related to this book can be found at http://www.soe.purdue.edu/smsc/lesh/

  • The Handbook of Research Design in Mathematics and Science Education is based on results from an NSF-supported project (REC 9450510) aimed at clarifying the nature of principles that govern the effective use of emerging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research designs that:<br>* have been pioneered recently by mathematics and science educators;<br>* have distinctive characteristics when they are used in projects that focus on mathematics and science education; and<br>* have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the development of mathematics or science students and teachers, or for the development, dissemination, and implementation of innovative programs of mathematics or science instruction.<br>The volume emphasizes research designs that are intended to radically increase the relevance of research to practice, often by involving practitioners in the identification and formulation of the problems to be addressed or in other key roles in the research process. Examples of such research designs include teaching experiments, clinical interviews, analyses of videotapes, action research studies, ethnographic observations, software development studies (or curricula development studies, more generally), and computer modeling studies. This book's second goal is to begin discussions about the nature of appropriate and productive criteria for assessing (and increasing) the quality of research proposals, projects, or publications that are based on the preceding kind of research designs. A final objective is to describe such guidelines in forms that will be useful to graduate students and others who are novices to the fields of mathematics or science education research. The NSF-supported project from which this book developed involved a series of mini conferences in which leading researchers in mathematics and science education developed detailed specifications for the book, and planned and revised chapters to be included. Chapters were also field tested and revised during a series of doctoral research seminars that were sponsored by the University of Wisconsin's OERI-supported National Center for Improving Student Learning and Achievement in Mathematics and Science. A Web site with additional resource materials related to this book can be found at http://www.soe.purdue.edu/smsc/lesh/

  • In this paper, we examine the role of technology in statistics education from the viewpoint of a developing country. We begin with a brief overview of the developing region in question. We next provide a definition of statistics education which, in our view, may be used to identify in general who needs statistics education, who should provide it, and at what level statistics education should begin.<br>The role of statistics education is explored in relation to three broad areas where it plays an important role, namely, in business and industry, some aspects of government, and overall socioeconomic and scientific progress. Following this, technologies for effective teaching and learning statistics at different levels are explored. This paper ends with a discussion of the questions to be addressed regarding the role of technology in statistics education. Recommendations for research are suggested, especially in relation to developing regions.

  • We need to look beyond the view of computer-based technology as a means of enhancing the teaching and learning of current curricula; the end result of such activities is often no more than a translation of what are essentially pencil-and-paper-based activities onto a computer screen, albeit often done in an exciting and enlightening manner. As we move into an era in which computer-based technology becomes the new pencil and paper, such developments will become of historical interest at most (Kaput, 1992). Although there is undoubted benefit in using computer-based technology to reduce the time students spend on statistical computation, or in using it to illustrate the Central Limit Theorem, for example, the ultimate power in the technology lies in its ability to reshape the nature of intellectual activity in the statistics classroom. To see why this might be, we need to look generally at the ways in which interacting with technology of this sort has the potential to affect human intellectual performance. We will do this by using a theoretical framework proposed by Salamon, Perkins, and Globerson (1991) which has implications for both future classroom practice and research.

Pages

register