The Intuitive Sources Of Probabilistic Thinking In Children

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The Intuitive Sources of Probabilistic Thinking in Children

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The Intuitive Sources of Probabilistic Thinking in Children by H. Fischbein Book Resume:

About a year ago I promised my friend Fischbein a preface to his book of which I knew the French manuscript. Now with the printer's proofs under my eyes I like the book even better than I did then, because of, and influenced by, new experiences in the meantime, and fresh thoughts that crossed my mind. Have I been influenced by what I remembered from the manuscript? If so, it must have happened unconsciously. But of course, what struck me in this work a year ago, struck a responsive chord in my own mind. In the past, mathematics teaching theory has strongly been influenced by a view on mathematics as a heap of concepts, and on learning mathematics as concepts attainment. Mathematics teaching practice has been jeopardised by this theoretical approach, which in its most dangerous form expresses itself as a radical atomism. To concepts attainment Fischbein opposes acquisition of intuitions. In my own publications I avoided the word "intuition" because of the variety of its meanings across languages. For some time I have used the term "constitution of mathematical objects", which I think means the same as Fischbein's "acquisition of intuitions" - indeed as I view it, constituting a mental object precedes its conceptualising, and under this viewpoint I tried to observe mathematical activities of young children.

Intuition in Science and Mathematics

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Intuition in Science and Mathematics by H. Fischbein Book Resume:

In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Decision Making under Uncertainty

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Decision Making under Uncertainty by R.W. Scholz Book Resume:

This volume contains the revised papers of an international symposium on research on fallacies, biases, and the development of decision behavior under uncertainty. The papers are organized in five main sections. The Introduction outlines the conceptual framework and how three of the sections - Cognitive Decision Research, Social Interaction, and Development and Epistemology - are interrelated and also how new fields, such as research into developmental questions, can be productively integrated. In the fifth section Comments are collected, which evaluate the impact of the contributions on decision research itself, and also on cognitive psychology, social psychology, economic theory, ant the discipline of mathematics education.

Exploring Probability in School

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Exploring Probability in School by Graham A. Jones Book Resume:

Exploring Probability in School provides a new perspective into research on the teaching and learning of probability. It creates this perspective by recognizing and analysing the special challenges faced by teachers and learners in contemporary classrooms where probability has recently become a mainstream part of the curriculum from early childhood through high school. The authors of the book discuss the nature of probability, look at the meaning of probabilistic literacy, and examine student access to powerful ideas in probability during the elementary, middle, and high school years. Moreover, they assemble and analyse research-based pedagogical knowledge for teachers that can enhance the learning of probability throughout these school years. With the book’s rich application of probability research to classroom practice, it will not only be essential reading for researchers and graduate students involved in probability education; it will also capture the interest of educational policy makers, curriculum personnel, teacher educators, and teachers.

Children’s Logical and Mathematical Cognition

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Children’s Logical and Mathematical Cognition by C.J. Brainerd Book Resume:

For some time now, the study of cognitive development has been far and away the most active discipline within developmental psychology. Although there would be much disagreement as to the exact proportion of papers published in developmen tal journals that could be considered cognitive, 50% seems like a conservative estimate. Hence, a series of scholarly books to be devoted to work in cognitive development is especially appropriate at this time. The Springer Series in Cognitive Development contains two basic types of books, namely, edited collections of original chapters by several authors, and original volumes written by one author or a small group of authors. The flagship for the Springer Series will be a serial publication of the "advances" type, carrying the subtitle Progress in Cognitive Development Research. Each volume in the Progress sequence will be strongly thematic, in that it will be limited to some well-defined domain of cognitive-developmental research (e. g. , logical and mathematical de velopment, semantic development). All Progress volumes will be edited collec tions. Editors of such collections, upon consultation with the Series Editor, may elect to have their books published either as contributions to the Progress sequence or as separate volumes. All books written by one author or a small group of authors will be published as separate volumes within the series. A fairly broad definition of cognitive development is being used in the selection of books for this series.

Key Ideas in Teaching Mathematics

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Key Ideas in Teaching Mathematics by Anne Watson,Keith Jones,Dave Pratt Book Resume:

Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers, researchers and mathematics educators, and many teachers and researchers have been involved in the thinking behind this book, funded by the Nuffield Foundation. An associated website, hosted by the Nuffield Foundation, summarises the key messages in the book and connects them to examples of classroom tasks that address important learning issues about particular mathematical ideas.

New Studies in Deontic Logic

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New Studies in Deontic Logic by R. Hilpinen Book Resume:

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings (D. Reidel Publishing Company, Dordrecht 1971): its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts of obligation, permission and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic' (1951). Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities.

Concept Formation in the Humanities and the Social Sciences

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Concept Formation in the Humanities and the Social Sciences by T. Pawlowski Book Resume:

Uniqueness of style versus plurality of styles: in terms of these aesthetic categories one of the most important differences between the recent past and the present can be described. This difference manifests itself in all spheres of life - in fashion, in everyday life, in the arts, in science. What is of interest for my purposes in this book are its manifestations in the processes of con cept formation as they occur in the humanities, broadly conceived. Here the following methodological approaches seem to dominate the scene. 1. A tendency to apply semiotic concepts in various fields of research. 2. Attempts to introduce metrical concepts and measurement, even into disciplines tra ditionally considered as unamenable to mathematical treatment, like aesthetics and theory of art. 3. Efforts to fmd ways of formulating empirically testable, operational criteria for the application of concepts, especially concepts which refer to objects directly not observable, like dispositions, attitudes, character or personality traits. Care is also taken to take advantage of the conceptual apparatus of methodology to express problems in the humanities with the highest possible degree of clarity and precision. 4. Analysis of the p~rsuasive function oflanguage and its possible uses in science and in everyday life. The above tendencies are present in this book. It is divided into two parts: I. Methods of Concept Formation, and II. Applications. In the first part some general methods of concept formation are presented and their merits discussed.

Essays in Memory of Imre Lakatos

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Essays in Memory of Imre Lakatos by Robert S. Cohen,P.K. Feyerabend,Marx W. Wartofsky Book Resume:

The death of Imre Lakatos on February 2, 1974 was a personal and philosophical loss to the worldwide circle of his friends, colleagues and students. This volume reflects the range of his interests in mathematics, logic, politics and especially in the history and methodology of the sciences. Indeed, Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as well as his humane warmth and his quick wit. He was a person to love and to struggle with. PAUL K. FEYERABEND ROBERT S. COHEN MARX W. WARTOFSKY TABLE OF CONTENTS Preface VII JOHN WORRALL / Imre Lakatos (1922-1974): Philosopher of Mathematics and Philosopher of Science JOSEPH AGASSI / The Lakatosian Revolution 9 23 D. M. ARMSTRONG / Immediate Perception w. W. BAR TLEY, III/On Imre Lakatos 37 WILLIAM BERKSON / Lakatos One and Lakatos Two: An Appreciation 39 I. B. COHEN / William Whewell and the Concept of Scientific Revolution 55 L. JONATHAN COHEN / How Can One Testimony Corroborate Another? 65 R. S. COHEN / Constraints on Science 79 GENE D'AMOUR/ Research Programs, Rationality, and Ethics 87 YEHUDA ELKANA / Introduction: Culture, Cultural System and Science 99 PA UL K.

Causality in Sociological Research

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Causality in Sociological Research by Jakub Karpinski Book Resume:

The general treatment of problems connected with the causal conditioning of phenomena has traditionally been the domain of philosophy, but when one examines the relationships taking place in the various fields, the study of such conditionings belongs to the empirical sciences. Sociology is no exception in that respect. In that discipline we note a certain paradox. Many problems connected with the causal conditioning of phenomena have been raised in sociology in relatively recent times, and that process marked its empirical or even so-called empiricist trend. That trend, labelled positivist, seems in this case to be in contradiction with a certain type of positivism. Those authors who describe positivism usually include the Humean tradition in its genealogy and, remembering Hume's criticism of the concept of cause, speak about positivism as about a trend which is inclined to treat lightly the study of causes and confines itself to the statements on co-occurrence of phenomena.

The Structure of Appearance

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The Structure of Appearance by Nelson Goodman Book Resume:

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do.

Phenomenological Aspects of Wittgenstein’s Philosophy

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Phenomenological Aspects of Wittgenstein’s Philosophy by B.-C. Park Book Resume:

In his writings around 1930, Wittgenstein relates his philosophy in different ways to the idea of phenomenology. He indicates that his main philosophical project had earlier been the construction of a purely phenomenological language, and even after having given up this project he believed that "the world we live in is the world of sense-data,,,l that is, of phenomenological objects. However, a problem is posed by the fact that he does not appear ever to have given a full, explicit account of what he means by his 'phenomenology', 'phenomenological language', or 'phenomenological problems'. In this book, I have tried to unravel the nature of Wittgenstein's phenomenology and to examine its importance for his entire work in philosophy. Phenomenology can be characterized as philosophy whose primary concern is what is immediately given in one's experience. This 'immediately given' is not merely impressions inside one's mind, but includes also the part of objective reality that impinges upon one's consciousness. Thus, an aim of phenomenological enterprise is to grasp this objective reality by attending to immediate experience. Husserl's phenomenology is in fact a case in point.

Collected Papers on Epistemology, Philosophy of Science and History of Philosophy

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Collected Papers on Epistemology, Philosophy of Science and History of Philosophy by W. Stegmüller Book Resume:

These two volumes contain all of my articles published between 1956 and 1975 which might be of interest to readers in the English-speaking world. The first three essays in Vol. 1 deal with historical themes. In each case I have attempted a rational reconstruction which, as far as possible, meets con temporary standards of exactness. In The Problem of Universals Then and Now some ideas of W.V. Quine and N. Goodman are used to create a modem sketch of the history of the debate on universals beginning with Plato and ending with Hao Wang's System :E. The second article concerns Kant's Philosophy of Science. By analyzing his position vis-a-vis I. Newton, Christian Wolff, and D. Hume, it is shown that for Kant the very notion of empirical knowledge was beset with a funda mental logical difficulty. In his metaphysics of experience Kant offered a solution differing from all prior as well as subsequent attempts aimed at the problem of establishing a scientific theory. The last of the three historical papers utilizes some concepts of modem logic to give a precise account of Wittgenstein's so-called Picture Theory of Meaning. E. Stenius' interpretation of this theory is taken as an intuitive starting point while an intensional variant of Tarski's concept of a relational system furnishes a technical instrument. The concepts of model world and of logical space, together with those of homomorphism and isomorphism be tween model worlds and between logical spaces, form the conceptual basis of the reconstruction.

Theory and Experiment

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Theory and Experiment by Diderik Batens,Jean-Paul van Bendegem Book Resume:

This is not "another collection of contributions on a traditional subject." Even more than we dared to expect during the preparatory stages, the papers in this volume prove that our thinking about science has taken a new turn and has reached a new stage. The progressive destruction of the received view has been a fascinating and healthy experience. At present, the period of destruction is over. A richer and more equilibrated analysis of a number of problems is possible and is being cru'ried out. In this sense, this book comes right on time. We owe a lot to the scholars of the Kuhnian period. They not only did away with obstacles, but in several respects instigated a shift in attention that changed history and philosophy of science in a irreversible way. A c1earcut example - we borrow it from the paper by Risto Hilpinen - concerns the study of science as a process, Rnd not only as a result. Moreover, they apparently reached several lasting results, e.g., concerning the tremendous impact of theoretical conceptions on empirical data. Apart from baffling people for several decades, this insight rules out an other return to simple-minded empiricism in the future.

Relativism Refuted

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Relativism Refuted by H. Siegel Book Resume:

Download or read Relativism Refuted book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

An Architectonic for Science

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An Architectonic for Science by W. Balzer,C.U. Moulines,J.D. Sneed Book Resume:

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness.

Justice, Law, and Argument

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Justice, Law, and Argument by Ch. Perelman Book Resume:

This collection contains studies on justice, juridical reasoning and argumenta tion which contributed to my ideas on the new rhetoric. My reflections on justice, from 1944 to the present day, have given rise to various studies. The ftrst of these was published in English as The Idea of Justice and the Problem of Argument (Routledge & Kegan Paul, London, 1963). The others, of which several are out of print or have never previously been published, are reunited in the present volume. As justice is, for me, the prime example of a "confused notion", of a notion which, like many philosophical concepts, cannot be reduced to clarity without being distorted, one cannot treat it without recourse to the methods of reasoning analyzed by the new rhetoric. In actuality, these methods have long been put into practice by jurists. Legal reasoning is fertile ground for the study of argumentation: it is to the new rhetoric what mathematics is to formal logic and to the theory of demonstrative proof. It is important, then, that philosophers should not limit their methodologi cal studies to mathematics and the natural sciences. They must not neglect law in the search for practical reason. I hope that these essays lead to be a better understanding of how law can enrich philosophical thought. CH. P.

Language, Mind, and Art

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Language, Mind, and Art by D. Jamieson Book Resume:

This book is a collection of essays in honor of Paul Ziff written by his col leagues, students, and friends. Many of the authors address topics that Ziff has discussed in his writings: understanding, rules and regularities, proper names, the feelings of machines, expression, and aesthetic experience. Paul Ziff began his professional career as an artist, went on to study painting with J. M. Hanson at Cornell, and then studied for the Ph. D. in philosophy, also at Cornell, with Max Black. Over the next three decades he produced a series of remarkable papers in philosophy of art, culminating in 1984 with the publica tion of Antiaesthetics: An Appreciation of the Cow with the Subtile Nose. In 1960 he published Semantic Analysis, his masterwork in philosophy of lan guage. Throughout his career he made important contributions to philosophy of mind in such papers as "The Simplicity of Other Minds" (1965) and "About Behaviourism" (1958). In addition to his work in these areas, his lec tures at Harvard on philosophy of religion are an underground classic; and throughout his career he has continued to make art and to search for the meaning of life in the properties of prime numbers. Although his interests are wide and deep, questions about language, art, and mind have dominated his philosophical work, and it is problems in these areas that provide the topics of most of the essays in this volume.

Body, Mind, and Method

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Body, Mind, and Method by Donald F. Gustafson,B.L. Tapscott Book Resume:

Simple seeing. Plain talking. Language in use and persons in action. These are among the themes of Virgil Aldrich's writings, from the 1930's onward. Throughout these years, he has been an explorer of conceptual geography: not as a foreign visitor studying an alien land, but close up 'in the language in which we live, move, and have our being'. This is his work. It is clear to those who know him best that he also has fun at it. Yet, in the terms of his oft-cited distinction, it is equally clear that he is to be counted not among the funsters of philosophy, but among its most committed workers. Funsters are those who attempt to do epistemology, metaphysics, or analysis by appealing to examples which are purely imaginary, totally fictional, as unrealistic as you like, 'completely unheard of'. Such imaginative wilfullness takes philosophers away from, not nearer to, 'the rough ground' (Wittgenstein) where our concepts have their origin and working place. In the funsters' imagined, 'barely possible' (but actually impossible) world, simple seeing becomes transformed into the sensing of sense-data; plain talk is rejected as imprecise, vague, and misleading; and per sons in action show up as ensouled physical objects in motion. Then the fly is in the bottle, buzzing out its tedious tunes: the problem of perception of the external world; the problem of meaning and what it is; the mind-body problem. Image-mongering has got the best of image-management.

Communication and Meaning

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Communication and Meaning by A.J Jones Book Resume:

This essay contains material which will hopefully be of interest not only to philosophers, but also to those social scientists whose research concerns the analysis of communication, verbal or non-verbal. Although most of the topics taken up here are central to issues in the philosophy of language, they are, in my opinion, indistinguishable from topics in descriptive social psychology. The essay aims to provide a conceptual framework within which various key aspects of communication can be described, and it presents a formal language, using techniques from modern modal logic, in which such descriptions can themselves be formulated. It is my hope that this framework, or parts of it, might also turn out to be of value in future empirical work. There are, therefore, essentially two sides to this essay: the development of a framework of concepts, and the construction of a formal language rich enough to express the elements of which that framework is composed. The first of these two takes its point of departure in the statement quoted from Lewis (1972) on the page preceding this introduction. The distinction drawn there by Lewis is accepted as a working hypothesis, and in one sense this essay may be seen as an attempt to explore some of the consequences of that hypothesis.