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E-raamat: Origin of the Idea of Chance in Children (Psychology Revivals) [Taylor & Francis e-raamat]

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  • Formaat: 270 pages
  • Sari: Psychology Revivals
  • Ilmumisaeg: 19-Mar-2014
  • Kirjastus: Psychology Press Ltd
  • ISBN-13: 9781315766959
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Origin of the Idea of Chance in Children (Psychology Revivals)Suurem pilt
  • Formaat: 270 pages
  • Sari: Psychology Revivals
  • Ilmumisaeg: 19-Mar-2014
  • Kirjastus: Psychology Press Ltd
  • ISBN-13: 9781315766959
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781315766959

Although originally published in France in 1951 this English translation was not published until 1975. The book supplements the authors’ previous publications on the development of thought in the child and is the result of two preoccupations: how thought that is in the process of formation acts to assimilate those aspects of experience that cannot be assimilated deductively – for example, the randomly mixed; and the necessity of discovering how the mental processes work in the totality of spontaneous and experimental searchings that make up what is called the problem of ‘induction’. Induction is a sifting of our experiences to determine what depends on regularity, what on law, and what on chance.

The authors examine the formation of the physical aspects of the notion of chance; they study groups of random subjects and of ‘special’ subjects; and they analyse the development of combining operations which contributes to determining the relationship between chance, probability, and the operating mechanisms of the mind.

Translators' Preface xi
Foreword xiii
Introduction. The Intuition of Probabilities xv
PART ONE Chance in Physical Reality
Chapter I Notions of Random Mixture and Irreversibility
1(25)
1 Technique of the experiment and general results
2(2)
2 The first stage (four to seven years): Failure to understand the random nature of the mixture
4(8)
3 The second stage (seven to eleven years): Beginning of the idea of combinatorics
12(11)
4 The third stage (from eleven to twelve years): Permutations and interaction of trajectories
23(3)
Chapter II Centered Distributions (Normal Curves) and Uniform Distributions
26(31)
1 Centered distributions: Experimental technique and general results
28(3)
2 The first stage: Absence of a distribution of the whole
31(9)
3 The second stage: Beginnings of structuring a distribution of the whole and generalization from one experiment to the next
40(6)
4 The third stage: Symmetrical dispersion of the whole with immediate quantification
46(3)
5 Uniform distribution of drops of rain on square tiles
49(8)
Chapter III The Discovery of a Constant Relationship in Conflict with a Fortuitous Uniform Distribution
57(38)
1 Technique of the experiment and general results
59(2)
2 The first stage: I. Illusory predictions of isolated results
61(6)
3 The first stage: II. The reaction to the magnet
67(7)
4 The second stage: I. Gradual establishment of successive fortuitous results
74(7)
5 The second stage: II. Reactions to the magnet
81(7)
6 Third stage: The beginnings of formal reasoning in the discovery of the relationships of variability and constancy
88(7)
PART TWO Random Drawings
Chapter IV Chance and “r;Miracle”r; in the Game of Heads and Tails
95(21)
1 The first stage: Intuition of rarity, but not of random mixture
97(6)
2 The second stage: Chance and total possibilities
103(3)
3 The third stage: Quantification of probability
106(3)
4 The experiments with marbles
109(7)
Appendix
114(2)
Chapter V The Random Drawing of Pairs
116(15)
1 The first stage: Absence of systematic probability
117(7)
2 The second stage: Beginnings of quantified probability
124(3)
3 The third stage and conclusions
127(4)
Chapter VI The Quantification of Probabilities
131(30)
1 Technique and general results
132(2)
2 The first stage. Level I A: Absence of logical and arithmetical comparisons
134(10)
3 The first stage: Level I B: Reactions intermediary between stages I and II
144(5)
4 The second stage: The general success of comparisons with a single variable. Level II A: Systematic failure with questions of proportion
149(4)
5 The second stage. Level II B: Progressive empirical solution of questions of proportionality
153(4)
6 The third stage: Solution of questions with two variables
157(4)
PART THREE Combinatoric Operations
Chapter VII The Development of Operations of Combination
161(12)
1 The first stage: Empirical combinations
164(2)
2 The second stage: Search for a system
166(4)
3 The third stage: Discovery of a system
170(3)
Chapter VIII Operations of Permutation
173(22)
1 Technique and general results
175(1)
2 The first stage: Absence of a system
176(4)
3 The second stage: The empirical discovery of partial systems
180(9)
4 The third stage: The discovery of a system
189(6)
Chapter IX Operations of Arrangement
195(17)
1 Technique and general results
196(1)
2 The first stage: Empirical arrangements and failure to understand random mixture
197(3)
3 The second stage: Search for a system and the beginning of the idea of chance
200(4)
4 The third stage: Understanding of the system of arrangements and of the laws of random mixture tending toward large numbers
204(3)
5 The quantification of probabilities based on arrangements
207(5)
Chapter X Conclusion: Chance, Probability, and Operations
212(35)
1 The three stages of the development of the idea of chance
213(3)
2 The first period: Failure to differentiate between the possible and the necessary
216(6)
3 The second period: Discovery of chance as a noncom-posable reality as an antithesis to operations
222(8)
4 The third period: Probabilistic composition, a synthesis of chance and the deductive operations
230(6)
5 Chance and probabilities
236(11)
Glossary 247
Authored by Piaget, Jean; Inhelder, Barbel
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