Child's Conception of Movement and Speed

Jean Piaget

• Publisher: Routledge
• Year: 2013
• eBook ISBN: 9781135658472
• Edition: 1
• Topic: Psychology
• Subtopic: Developmental Psychology
• Index: Psychology

This book was first published in 1970.

Part 1
Successive Order or Placing

The two chapters which form this first part are devoted to the study of the order of succession, linear or recurring in cycles, by way of introduction to the analysis of change of location itself. The idea of movement implies in fact the idea of order first of all, in both mathematics and psychology: viewed fundamentally, a change of position is of necessity related to a system of positions, i.e. to be precise, positions conforming to a particular order. That is why we shall begin the analysis of the development of the conceptions of movement and speed with the evolution of the idea of order. But as we are not examining the child's relation to geometry, but solely his relation to movement, we shall here choose as examples of succession not points on a static line, but objects transported by one and the same movement whether linear or cyclic. From the point of view of operations of order or disposition this comes to the same thing, and from the psychological point of view, there will be the benefit of placing these operations in an intuitive context of movement from the outset.

Chapter One
The Problem of Alternative Directions of Travel

Let us consider three elements A, B and C, such that A precedes B, and B precedes C, during a movement from right to left A← B←C. We achieve this in three different ways: Technique 1. Three beads, A=red, B=black, and C=blue are threaded on a small piece of wire; this is then placed within one's half-closed hand with the two ends of the wire projecting, then the beads are made to reappear on the other side in the same order ABC, then to retrace their path in inverse order CBA etc. Technique 2. Three small wooden balls A=red, B—brown and C=yellow are placed in a chute made of cardboard in the order ABC and are guided with A leading, into a tunnel occupying the central part of the slide to emerge in the same order or to return in inverse order. Technique 3. Three little wooden dolls A=blue, B = green, and C—yellow, are strung on a wire and pass in the same order of A←B←C behind a screen. The following questions are asked systematically, although giving way to free conversation in so far as may be profitable, depending on the child's reactions.

Q 1. In what order will the objects emerge at the other side of the hand, tunnel or screen?

Q 2. In what order will the objects reappear, on travelling through the tunnel (or passing behind the screen) in the opposite direction?

Note: The child draws the objects with suitably coloured pencils in the direct order (either after or before Q 1.) so as to serve as a reminder. To solve Q 2. then, he has only to look at his paper and read off the colours in reverse order. In this way the problem of reasoning is quite separate from memory.

Q 3. When the first two questions are solved (and if they are not at the first trial, the experiment is repeated until the child is sure of the answer), one then presents Q 3 and 4, (Q 3 applies only to the Technique 2). The objects are inserted in the direct order ABC into the tunnel, after which the child is asked to change places and sit at the other side of the table. If in his starting position the movement took place from right to left, it will now appear from left to right in the subject's new position: he is then asked in what order the balls will emerge on the right hand side and he should realize that this will be the direct order though he himself has changed his place in relation to the tunnel and so the balls seem to retrace their path. In other words the child must judge their order of progress from the starting point of the balls and not according to the left and the right of the tunnel. This question involves the two ways in which the child may judge the direction of travel when faced with the same objective order.

Q 4. The three objects are put back, in view of the child, in the order ABC, whether within the hand or into the tunnel or behind the screen, and a rotary movement 180° is described either with the hand and the wire jointly (Technique 1), or with the cardboard tunnel (Technique 2) or by the wire alone (Technique 3). Care is taken that the movement is fully visible, describing what is being done¹ and drawing attention, in Technique 1 and 3 to the ends of the wire visible in the process of turning on itself. This semi-rotation completed, one asks in what order the objects will emerge, in the same place as that where in Q 1 they came out in the direct order. This Q 4, thus bears, like Q 2 on the inverse order, but owing to the rotation of the apparatus, and no longer to a simple sending back as in Q 2.

Q 5. Same question as 4 but with two successive semi-rotations (in the same direction), either in two moves, 180°+180°, or in one move: 360°.

Q 6. Same questions for a random number of semi-rotations, either uneven (=emerging in inverse order) or even (=emerging in direct order).

Q 7. if up till now the child has not spontaneously thought that the middle object B could come out in first place, in any of the preceding situations, the question is then put as follows. A random number of semi-rotations is described (about 10 but without counting) and one asks which object 'might emerge first? Could it be A? or C? or B?' Each time one asks why, or why not, and in the case of an affirmative for B, 'How could that happen?' (it should be stated that the tunnel in Technique 2 is of a diameter hardly greater than the balls, to avoid any leap frogging).

Finally, the same Q 1 to 7 may be asked in relation to four or five objects, and not merely to three.

The following stages were observed among the responses made by about fifty children between 4 and 8 years of age. In stage I the child is able to answer Q 1 (which is without doubt the case from the second year on) but not Q 2, i.e. simple inverse order. In the course of stage II, Q 2 is solved, but not 3 to 5, at least not at the first attempt; during the second half of this stage (sub-stage IIB), by contrast, Q 3 and 4 produce an immediate reply while 5 and 6 as yet only produce wavering attempts. During a third stage, finally, Q 1 to 5 are solved at once and soon after lead to a generalization in the form of a solution to Q 6. As for Q 7 which is concerned with the central object, at the start of stage I, the child spontaneously allows that B could come out first or last as well as staying between A and C; towards the end of this stage he is seldom inclined to think of such a transformation himself, but it is enough for the question to be asked in the form already observed, for him to accept it without more being said. From stage II on he thinks it impossible for the order to be broken in the case of three objects, B staying in the middle in both directions of travel; for five elements, however, it still happens in the course of this stage that objects not at either end may spontaneously be thought capable of coming out first.

§1. The first stage: Path retraced without inverting the order and displacement of middle object

This first stage ends on average towards 5 years of age but it is not unusual for examples to be found up to 5½ years. Here are some examples.

AN (4 years). Technique 2. Which will come first out of the tunnel? The red one (A). And then? The brown one (B) and the yellow (C). (dem). And now they are coming back, which one will come out first? The red one, the brown, and the yellow one, Look! (dem). Oh, no, it's the yellow, then the brown and the red. Why? Because coming back it's the yellow one. Fine. And now, look, I'm turning the tunnel, (Q 4). Which will be first this time? The red, then the brown, then the yellow one. Look! (dem). It's the yellow one. Why? Because I didn't know. We'll start again. It will be the yellow one. (dem). Why? Don't know.

Right then, look: I am going to turn it twice, you see, one, two. Which will come first now? The brown one (B). Why? Because you turned it two times. But why is it the brown one first if it's turned twice? . . . (dem). Look! The red one! (A). Why? Don't know. And now I'm going to turn it three times, look. This will be? The yellow one, no, the brown! Why? Because you did it three times, (dem). Well? Oh, the yellow one! Why? Don't know. And now? (Five to six half turns). The brown one (B). Why? Because you turned it lots of times. Can the balls in the tunnel jump over each other? No. Why? The hole is too little. Good. And where is the brown one? In the middle. Then which is going to come out first? The brown one. Look! Oh, dear no, it's the yellow one. What does it mean when the brown one is in the middle? That it is behind the red one and behind the yellow one. Fine. Now look (several turns). Which will be first? It's the yellow one. And now? (several more turns). The red. And now (rep.)? The yellow. And now (rep.)? And now it's the brown one! Why? Because you turned it I don't know how many times! Look! Oh, no, still not that one.

Technique 3. Can these little fellows hop over each other? No, because there's a wire. Right; then which one will be first out there? (Q 1). The blue (A). And after that? The green (B) and the yellow (C). Is that right? (dem). Yes. And now, coming back? The yellow one (dem). And if I turn the wire this way? (Q 4). The blue one. (dem). Oh, no, it's the yellow one because you turned the wire round. And now, if I turn it twice? The blue one. And if I turn three times? The blue (dem). No, the yellow one. And if I turn it four times? That will be the green one (B) first. Why? Because the green one (B) is after the blue one (A), (dem). Is that right? No, it's the blue. And now? (turning some more) The green one! (B).

ROS (4; 6). Technique 2. Which one will come out first? The red one (A). And then? The brown (B) and yellow (C) ones. Now you see? (dem). The journey's over. They're going back into the tunnel and will come out this side. Which will be first? The red (A). Why? Because there it is (pointing to the first in direct order) and Look! (dem). That's not right. Why? . . . And now? (first direction). The red (dem). Yes. And this way? (back)? The yellow, (dem). Yes. And now I am going to turn the tunnel. (Q 4). Which will be first? The red one. Look! (dem). No, the yellow. Once more (going back to the starting point). The red one. (dem). No, again it's the yellow. Why? Because it always goes this way (pointing to the pathway travelled). And why is the red one last? Because it stayed back there.

Technique 3. Which? Blue (A) then green (B) then yellow (C). And coming back? Blue, green, yellow (going to dem). No, yellow, green, blue. Look, now, I'm turning it. (Q 4), Which will be out first? Blue. (dem). Right? No. Why not? Because it's behind the yellow one. The bit of wire turned round. (New try). Yellow, (dem). Yes. Why? Because it turned the other way. And after it? Green. Why? Because that's behind the yellow one. (turning several times) Which will be first? Blue (A) or yellow (C) or green (B). Can the green one be first? Yes. How would it do that? . . . (turning five or six times). Which do you think? Green. What's that?... Look (showing the wire stem and the three dolls). It can't. Why? Because of the wire. And now (turning more than ten times)? The green one this time! Why? It turned. Was it at the front? In the middle. And if you turn it, can that one come first? Yes. Look! No. And this time (five more turns). Can the green one be first? Yes.

JAC (4; 8). Technique 2. Direct order, correct. Inverse order: first, confusion with direct order, then correction by experience and three correct answers in a row. Could the black come first (B? It probably could. (Return to direct order and child moves to other side of table: Q 3). That will be the yellow one (C). Why? That's the way it goes (judging from left to right without taking into account that the tunnel's opening, for balls travelling in inverse order, is no longer on the right. Look! (dem). No, the red one (A). And now (rep)? The red one (dem). Right. And now? (same) Yellow (C). Look! (dem). No red again. Look, now, I'm turning it. (Q 4). Red (then points out alternately the three colours). With five colours, direct order successful, but again not in the case of inverse order.

FRAN (4; 10). Technique 2. Direct order: right. Inverse order: expects direct order again. Red (A) then brown (B) and yellow (C). (dem). Is that right? No, because the red one came out first here (far left) and there (to the right) it came down another way. Look again, (direct order). Red. And now (inverse order). Yellow. That's right. Now I am going to turn the tunnel round. (4). Which will come out first? Red, because it's there (showing left end of tunnel). Right? (dem). No, because it was turned round, (another try) Yellow (correct). And now I'm turning it twice. Yellow. Look. Is that right? No, because it got turned the other way. How many times did I turn it for red? Twice. And when I turned it once? Yellow. And if I turn three times? The yellow one again. And four times? (dem). The brown (B). Why? Because it turned four times. Look! (dem). Oh, no, red again!

Technique 3. Direct order correct and inverse order at first confused with direct. And if I turn the wire (Q 4)? Blue (A). Look. Oh, no, yellow (C). Why? And if I turn it twice (doing it but concealing result)? Green (B). Why? Because it was turned twice. Where was it? After the blue one, in the middle. And if I turn it twice, it will come first? Yes, because of it turning twice. But how will it come first? You make it move in front of the blue one. What has it got right through its middle? A wire. Then it's easy for it to hop across the blue one? No. Then if I turn it twice, which will come first? Green!

DER (5; 6) begins (Technique 2) by thinking that inverse order will be the same as direct order. Look! (dem). No, it's changed now. Why? Because when they came back, they didn't turn round. So it's yellow (C). (Another try correct). Look now! I'm turning the tunnel round (Q 4). Red (A) then brown (B) then yellow (C). Is that right? (dem). Oh, no, it's yellow! But over there (=on the right before the half turn) it was yellow last and now it's yellow first over there (=on the right after the half turn). How did it change? What do you think? Oh, it's because you turned the box round (= the tunnel) (Another try: right). Good. Now then I'll turn it several times. Which might be first? I think it will be red now because it was yellow before, (compensation!) And now look! They're the same as before. (ABC). I turn it twice. Which is first? It will be brown! (Confidently). Why? Because you did it twice. Why? Before that it was behind the red one and in front of the yellow one: in the middle. How can it get to one end if it's in the middle? Maybe this is the way it could happen: brown starts off in the middle and after that brown is at one end. Look! (dem). Oh, no, it's red. Again (dem). Yellow! Once more! (dem). Red! Again! (dem). Yellow! Again! (dem). Red! And now, one more time? It will be yellow. And why is it never brown? Because the brown one can't turn round and come out at this side. And now I'm turning it lots of times (seven to eight). Which one will be out first? Yellow (C) or else red (A) or else brown (B)!

Technique 3. Same commencement with confusion of inverse and direct order. Then Q 4: It will be blue (A) because coming this way (=from the left) it's blue. Look! (dem). Oh, no, it's changed because you turned it. On subsequent tries he forecasts by turns A or C. Why not green (B)? Because you'd have to take away the other ones. I'm going to turn it a bit faster. Which one first? Green (B). Why? Because you did it that way!

These responses in stage I are of some interest in connection with the psychology of the intuition of order, and fo...

Table of contents

• Cover
• Title
• Copyright
• Contents
• Preface
• PART I SUCCESSIVE ORDER OR PLACING
• PART II CHANGE OF LOCATION
• PART III QUALITATIVE SPEED
• PART IV THE QUANTIFICATION OF SPEED
• PART V CONCLUSIONS
• Index