A Follow‐up Study of Some Aspects of the Work of Piaget and Inhelder on the Child's Conception of Space

Abstract

SUMMARY.In their book, The Child's Conception of Space, Piaget and Inhelder suggest that a child's first spatial concepts are topological ones and that these later lead to projective and euclidean concepts. A number of experiments from five chapters of their book were undertaken with some 140 children of nursery school age. Part of the evidence presented agrees with that of the authors' and some is at variance with theirs. It is suggested that much more experimentation is needed before the main thesis of Piaget and Inhelder is accepted.~.-INTRODUCTION. THE Child's Conception of Space, by J. Piaget and B. Inhelder, is divided into three main sections which deal with Topological* Space, Projective Space, and the transition from Projective to Euclidean Space, respectively. In the opening pages a clear distinction is made between perception on the one hand, and imaginal or representational space on the other. As early as six months of age an ordinary child can distinguish between a circle and a triangle when they are visually presented, but it is much later before he can represent these figures to himseli, that is, before he has the concept of the figures. Almost the whole of the book is devoted to the conception of space, not perception as such. The study reported here deals with experiments described in four of the five chapters devoted to Topological Space and the first of the five chapters on Projective Space.In the opening chapter dealing with Topological Space, the authors deal with ' haptic perception,' or the manner in which the child recognises various objects by touch alone. This is followed by an examination of the drawing of geometrical figures by children, and from the findings, Piaget and Inhelder conclude that in the very early years children construct their space by building up and using certain primitive relationships such as order and enclosure, proximity and separation. These relationships, the authors argue, are topological ones, and they claim that a child's first concepts of space are topological rather than projective or euclidean.To substantiate their hypothesis Piaget and Inhelder then study linear and circular order through the threading of beads on wires (this involves proximity and separation) in chapter 3 of the first section of their book. This is followed by a number of experiments involving a working knowledge of knots, and in these the child is concerned with surroundings and enclosure. Then, in the last chapter devoted to Topological Space, the authors study the problem of continuity through the gradual subdivision of lines and surfaces into small units and ultimately into points. Now topological relationships are independent of changes in size of the figure and they do not conserve distance, angles, straight lines, etc., during changes in shape. Thus, topological space allows that kind of analysis which starts from the position of each figure considered in isolation ; it is not a space * Topology is the science of that group of spatial relations which remain constant in any spatial ...

A comparison of the performance of intellectually gifted and average-ability children on four spatial tasks

“…Of the studies of a variety of Piagetian spatial competencies reviewed here, all imply some developmental aspect associated with chronological age, though not all report ages of mastery of given tasks that agree with the predictions of Inhelder in 1956 (Laurendeau andPinard, 1970;Lovell, 1959). Mental age was found to be a significant factor in the success at spatial tasks reported by Dodwell (1963), Stephens et al (1972), andDeVries (1974).…”

“…The "three mountains" task, in particular, has been fairly extensively 6 researched, though not always with corroborative results (Fishbein, Lewis, and Keiffer, 1971;Lovell, 1959;Shantz, 1971). Other spatial tasks of Piaget and Inhelder that have reappeared in various adaptations and repli cations have been the water level task, the projection of a straight line, and various paper-folding tasks (McGee, 1979).…”

“…Only two studies (Laurendeau and Pinard, 1970;Lovell, 1959) looked at performance of preschoolers, and these two did not consider the IQ as a variable of interest. Giftedness was a factor considered only in the work of DeVries (1974) and Lehman and Erdwins (1982), neither of whom used pre schoolers .…”

Bringing van Hiele and Piaget Together: A Case for Topology in Early Mathematics Learning

“…It should be noted that the Piaget-Inhelder experiments were conducted by other researchers such as Lovell [9] and Martin [10] resulting in different conclusions. While these researchers observed some understanding of topological notions in the children, these children also demonstrated some competence with geometric concepts, casting doubt on Piaget and Inhelder's claim that topological concepts precede geometric concepts.…”

Experimental modification of the lag between perceiving and performing

“…This has been observed in speech (Berko & Brown, 1960;Metcalfe, 1962), where a child may misarticulate words he discriminates in others' speech, and in drawing (Piaget & Inhelder, 1956;Maccoby & Bee, 1965;Lovell, 1960), where a child is able to make discriminations between simple geometric figures such as circles and triangles before he is able to draw the figures accurately.…”