Child’s Conception of Space Selected Works vol 4 1st edition by Piaget Jean – Ebook PDF Instant Download/Delivery: 0415846462, 9780415846462
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ISBN 10: 0415846462
ISBN 13: 9780415846462
Author: Piaget Jean
First published in 1997. This Volume 4 of Jean Piaget’s selected works and explores the study of the concept of space, or rather, of the innumerable ideas involved in the concept of space, which Piaget sees is for many reasons an indispensable part of child psychology.
Child’s Conception of Space Selected Works vol 4 1st Table of contents:
Part One Topological Space
Chapter I. Perceptual Space, Representational Space, and the Haptic Perception of Shape
Section I—Perceptual or Sensori-Motor Space
§1 Spatial perception prior to representation
§2 Perception and movement: the role of ‘perceptual activity’
Section II—The Recognition of Shapes (‘Haptic Perception’)
§3 The recognition of shapes by means of ‘haptic’ perception. Technique and general results
§4 Stage I. The recognition of familiar objects, then of topological, but not of euclidean shapes
§5 Stage II. The progressive recognition of euclidean shapes
§6 Stage III. Operational co-ordination
§7 Conclusions
Chapter II. The Treatment of Elementary Spatial Relationships in Drawing. ‘Pictorial Space’
Section I—Space in Spontaneous Drawings
§1 Stage I. ‘Synthetic Incapacity’
§2 Stage II. ‘Intellectual Realism’
§3 Stage III. ‘Visual Realism’
Section II—The Drawing of Geometrical Figures
§4 Technique and general results
§5 Stage 0, simple rhythmic movements. Stage I, beginnings of discrimination (IA), then appearance of closed curved shapes (IB)
§6 Stage II. Differentiation of euclidean shapes
§7 Stage III and Conclusions
Chapter III. Linear and Circular Order
§1 Technique and general results
§2 Stage L Simple intuitive correspondence without order through resemblance between objects
§3 Stage II. Intuitive representation of order when correspondence is visible
§4 Stage II. Intuitive correspondence of order substage IIB. Transposition from circular to linear order. Failure to reverse the order
§5 Stage II. Intuitive representation of order. Examples of transition from Substage IIB to Stage III. Construction of reverse order by trial and error
§6 Stage III. Operational correspondence. Conclusions
Chapter IV. The Study of Knots and the Relationship of ‘Surrounding’
§1 Technique and general results
§2 Stage L Learning to tie knots
§3 Stage II. Partial intuitive correspondence between knots which can be reproduced in practice
§4 Stage III. Operational correspondence between simple knots. Right and left hand ‘clover’ knots distinguished
Chapter V. The Idea of Points and the Idea of Continuity
§1 Technique and general results
§2 Stage II. Pre-operational notions
§3 Stage III. Operational synthesis within finite limits. Transitional reactions with respect to continuity
§4 Stage IV. Abstract operations of thought and the synthesis of continuity
Part Two Projective Space
SUMMARY
Chapter VI. Projective Lines and Perspective
Section I—Construction of the Projective Straight Line
§1 Technique and general results
§2 Stage I and Substage IIA. Inability to form straight lines parallel with the table edge (I), or independently of it (IIA)
§3 Substage IIB, intermediate reactions. Stage III, operational construction of straight lines by the method of ‘sighting’ or ‘aiming’.
Section II—Perspective
§4 Technique and general results
§5 Stage II. Inability to discriminate (first total then partial) between different viewpoints. Representation without perspective.
§6 Stage III. Operational discrimination between viewpoints of subject and object: Substage IIIA (partial). Substage IIIB (complete). Spontaneous rendering of perspective
Chapter VII. The Projection of Shadows
§1 Technique and general results
§2 The projection of straight lines
§3 The shadow of the disc
§4 The shadow of the rectangle
§5 The projection of cones
Chapter XVIII. The Co-ordination of Perspectives
§1 Technique and general results
§2 Substage IIA. The child confined to reproducing his own point of view
§3 Substage IIB. Transitional reactions. Attempts to distinguish between different viewpoints
§4 Substage III A. Genuine but incomplete relativity
§5 Substage IIIB. Complete relativity of perspectives
§6 Conclusions. Co-ordination of viewpoints and elaboration of isolated perspective relationships
Chapter IX. Geometrical Sections
§1 Transverse and longitudinal section of the cylinder, the prism, the parallelepiped, and the hollow ball
§2 The conic sections
§3 The sections of complex objects
Chapter X. The Rotation and Development of Surfaces
§1 Technique and general results
§2 The cylinder and the cone
§3 Development of the cube and tetrahedron
§4 Conclusions. The nature of the symbolic image and the connection between projective and euclidean operations
Part Three The Transition from Projective to Euclidean Space
Summary
Chapter XI. Affinitive Transformations of the Rhombus and the Conservation of Parallels
§1 Technique and general results
§2 Substage IIA. Rhombus without definite shape. Figures produced by adjustment of the apparatus enlarged indefinitely
§3 Substage IIB. Gradual construction of the rhombus: beginnings of anticipation, but without conservation of parallelity or length of sides
§4 Stage III: Substage IIIA. Beginning of operational construction with conservation of parallelity and length of sides
§5 Substage IIB and Stage IV. Explicit formulation of the relationships
§6 Conclusions. The conservation of parallelity
Chapter XII. Similarities and Proportions
Section I Similar Triangles
§1 Technique and general results
§2 Inscribed triangles. Substage IIA: no parallelism between corresponding sides. Substage IIB: the beginnings of parallelism
§3 Inscribed triangles. Substage IIIA: establishment of parallelism between sides. Substage IIIB: beginnings of dimensional relations
§4 Similarity of triangles based on equality of their angles. Substage IIA (slope of sides ignored). Substage IIB (first signs of analysis).
§5 Similarity of triangles based on equality of angles. Substages IIIA and IIIB. (Progressive analysis of angles ).
Section II The Similarity of Rectangles
§6 Technique and general results
§7 Stage II (4–5 to 7–8 years). Global comparison resulting in over-estimation of length
§8 Stage III. Intuitive transposition of dimensional relations in perceptual comparisons but not in drawings
§9 Stage IV. Proportions generalized operationally
§10 Conclusions
Additional Note: Proportionality in the Case of Open Figures
Chapter XIII. Systems of Reference and Horizontal-Vertical Co-ordinates
§1 Horizontal and vertical axes. Technique and general results
§2 Stage I. Inability to distinguish surfaces or planes, in the case of either fluids or solids
§3 Substage IIA. Water level shown parallel with the base of the jar and trees perpendicular to the mountainside
§4 Substage IIB. Intermediate types of response
§5 Stage III. The discovery of the vertical and horizontal
§6 The development of general systems of reference
§7 Conclusions: The construction of frames of reference
Chapter XIV. Diagrammatic Layouts and the Plan of a Model Village
§1 Locating the doll on the model landscape
§2 The layout of a model village. Technique and general results
§3 Stage I. No spatial correspondence except for a few elementary proximities
§4 Stage II. Partial co-ordination
§5 Substage IIIA. Beginning of general projective and euclidean co-ordination
§6 Substage IIIB. Mastery of distances and proportions
§7 The abstract plan with metric co-ordinates
Chapter XV. General Conclusions. The ‘Intuition’ of Space
§1 Perceptual and conceptual space. The function of the image
§2 Sub-logical operations and continuity
§3 The sub-logical operations constituting elementary topological relationships
I Partition of Sets and Addition of Sub-sets
II Order of Placement
III Reciprocity of Proximities
IV Symmetrical Interval Relations
V One-One Multiplication of Elements
VI One-One Multiplication of Relations
VII. and VIII —One-Many Multiplication, Either of Elements or Relationships
§4 Sub-logical operations constituting projective relationships
I Addition and Subtraction of Projective Elements
II Rectilinear Order
III Complementary Perspective Relations
IV Symmetrical Interval Relations
V One-One Multiplication of Elements
VI One-One Multiplication of Relations
VII and VIII One-Many Multiplication of Elements and Relations
§5 Sub-logical operations constituting euclidean space
I Addition and Subtraction of Elements
II Placement and Displacement of Objects
III Reciprocity of References
IV Inclusion of Intervals or Distances
V One-One Multiplication of Elements
VI One-One Multiplication of Placement and Displacement Relations
VII One-Many Multiplication of Elements
VIII One-Many Multiplication of Relations
§6 ‘Extensive’ operations, metric operations, and the question of their order of development
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