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This is perhaps the most technical of the array of monographs that have issued from Piaget's schoolroom 'laboratory' since The Language and Thought of the Child. For even a fragmentary grasp of the concepts elucidated in the present volume, the reader should not only have a knowledge of Piaget's previous work, particularly
The Construction of Reality in the Child and, in collaboration with Bärbel Inhelder, The Child's Conception of Space, but also a fairly sophisticated mathematical comprehension of topological and Euclidean notions of space and their interrelations. The reviewer lacks this comprehension and thus lays claim to no more than an 'informed layman's' attempt to estimate critically the methods and conclusions set forth in this volume.
In the preceding study, The Child's Conception of Space, the authors show that contrary to the historical development of geometry, which begins with the Euclidean or 'metric properties' of objects, the child develops a 'topological' schema or 'network of dimensions' in which the spatial properties of objects are organized. Only at a more sophisticated level does he begin to concern himself with the 'metrics' of lines, angles, and areas. In the present work the development of geometrical concepts, from the measurement of length and notions about rectangular coördinates to areas and solids, is studied in children from early nursery to high school age. As usual in Piaget's reports, particularly those concerning preschool and early school-age children, one is struck by the unlimited ingenuity of the investigators in devising the means for organizing the familiar objects and activities of the everyday environment of the child into spatial problems that seem natural and familiar to him. The level of the subject's intuitive grasp of Euclidean relationships is abstracted from both his verbal response and his behavioral performance in response to the problems posed.
The study seems to serve two immediate purposes. It is a furt