Explicitness and Conservation: Social Class Differences

INTERNATIONAL JOURNAL OF BEHAVIORAL DEVELOPM ENT, 1997, 21 (1), 51–70

Explicitness and Conservation: Social Class Differences Antonio Roazzi Universidade Federal de Pernambuco, Recife, Brazil

Peter Bryant Oxford University, UK The performance of 5-, 6-, 7-, and 8-year-old children in liquid conservation tasks was studied in four conditions. In the Ž rst two conditions (Standard and Incidental) the initial comparison in the task was made perceptually. In the other two conditions (Quantity and Money) the child was not allowed to make a direct perceptual comparison and the initial comparison was made by measuremen t. The children did much better when they measured the quantities than when they simply made perceptual comparisons, and this effect was stronger with working class children than with middle class children. Contrary to previous reports, there was no difference between the Standard and the Incidental conditions. We conclude that children in general, and working class children in particular, are helped when the nature of the task is made more explicit.

The conservation task, devised by Piaget and his colleagues to test understanding of the principle of invariance (e.g. Piaget & Inhelder, 1959; Piaget & Szeminska, 1941), is one of the best known and most widely repeated techniques in development al psychology. However, there is some uncertainty about the status of this task. The original procedure has been criticised, but the evidence on which the criticisms are based also has its aws.

Requests for reprints should be sent to Peter Bryant, University of Oxford, Department of Experimental Psychology, South Parks Road, OX1 3UD Oxford, UK; e-mail: PEBRYANT 6 psy.ox.ac.uk. We acknowledge with thanks the efforts of Ana Coelho Vieira and Carlos Eduardo F. Monteiro in collecting the data. We are extremely grateful to Annalucia Schliemann for the discussions that we had with her about the design of the project. We are also grateful for the care taken by the anonymous reviewers of our paper and for their helpful suggestions. q 1997 The International Society for the Study of Behavioural Developmen t Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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In the traditional conservation task, children are asked to compare two quantities which are identical in appearance and which they must judge to be equal. The experimenter then transforms the perceptual appearance of one and asks the child to compare the two quantities again. Before they are about 7 years old, children usually say that the two quantities are now unequal. This incorrect response led Piaget to claim that young children have not grasped the principle of invariance of quantity. They wrongly treat a mere perceptual change as a real quantitative change. However, slight variations on this original procedure led young children to show use of the invariance principle more frequently than in the traditional conservation task. McGarrigle and Donaldson (1974/75) originally suggested that the intentional nature of the experimenter’s actions when transforming the quantity of the conservation task might mislead the child by making him/her think that he/she ought to change his/her judgem ent. This hypothesis about the importance of the context led to some strikingly successful new techniques, including those of McGarrigle and Donaldson (1974/75) and Light, Buckingham , and Robbins (1979), in which the perceptual transformation happens as though by accident or by incident. The contrast between children’s relative success in these new procedures and their failure in the traditional task led to hypotheses about the importance of context. Both Donaldson (1978) and Gelman (1982) argued that young children do have a basic understandin g of invariance, but that the nature of the standard conservation task sometimes prevents them from using this understanding. However, the new procedures have themselves encountered some criticism. One problem is that, although the results of the new experim ents were repeated with some groups of young children (Dockrell, Campbell, & Neilson, 1980; Samuel & Bryant, 1984), they were not replicated with others (Dockrell et al., 1980; Miller, 1982). A second problem is that there is a possibility of “false positives” in these new techniques, as these may distract children from attending to the transformation. This would mean that the modiŽ ed tasks are not a proper test of the understandin g of invariance. Light et al. (1979) warned of this danger and a study by Moore and Frye (1986) seems to demonstrate, at least with McGarrigle and Donaldson’s (1974/75) “accidental” task, that false positives do occur. However, Nunes-Carraher and Schliemann (1985) devised a less wellknown but probably more successful variation of the conservation task which provided good results among children, when compared to those obtained via the traditional Piagetian task. In traditional Piagetian tasks, children are Žrst asked whether the two quantities are the same on the basis of a perceptual comparison. Later, the perceptual equality is destroyed and the question about the quantities’ equality is repeated. This sequence may lead children to interpret that what the exam iner wants is a perceptual and not a quantitative comparison. If this is so, stress on the quantitative Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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comparison, from the beginning, should lead to more frequent conservation answers. To test this hypothesis, Nunes-Carraher and Schliemann (1985) examined four groups of 4- and 5-year-old children in two versions of the conservation of discrete quantities (number of tokens) task and two of the conservation of continuous quantities (length of pieces of string) task. Two groups were submitted to the traditional Piagetian versions of each task and, accordingly, Žrst established the equality between the quantities through perceptual comparison. The other two groups underwent the modiŽed version of each task where, instead of a perceptual comparison, the child was Žrst asked to make a quantitative comparison between the two quantities. The results revealed a signiŽ cantly higher performance in the modiŽed version among 5-year-olds (60% and 45% conservation answers for discrete and continuous quantity, respectively, in the modiŽ ed version vs. 27% and 0% in the traditional version). This result supports the hypothesis that wrong answers in the traditional conservation task may be due to misinterpretation of the conservation question. Thus far we have discussed procedural issues. However, there is another variable that clearly affects children’s performance in the conservation task and this is social class (Perret-Clermont, 1980). The disadvantage that working class (WC) children show in comparison to middle class (MC) children in conservatio n tasks raises a question which is directly relevant to the issues that we have just discussed. If the conservation task is presented in different contexts will we Žnd any difference across social classes? Roazzi and Dias (1987) compared children of different social classes in two types of conservation tasks, liquid and length. The results indicated the ways in which the subject’s socio-cultural background interacts with types of presentation that stress either perceptual or quantitative comparisons in the conservation task. In the conservation of liquid task, where a perceptual comparison of the two quantities was asked in the Žrst phase of the task, middle class children performed better than working class children. In the length conservation task, which laid more emphasis, at the beginning, on a quantitative comparison, no class differences were found. Many studies have shown that working class children tend to perform at lower levels in intelligence tests as well as in some Piagetian tasks [e.g. see Amann Gainotti, 1979; Amann Gainotti, De Murtas, & Casale, 1982; Barolo, 1979; Barolo & Albanese, 1981; Carotenuto & Casale, 1981; Nunes-Carraher & Schliemann, 1982; Perret-Clermont and Leoni (described in Doise & Mugny, 1984); Roazzi & Dias, 1992]. The fact that the children in Roazzi and Dias’ study did not differ from middle class children when the aim of the task—a quantitative comparison—was made explicit from the beginning, suggests that the class difference usually found may be due to misunderstandings Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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about what it is that the examiner wants and not to a deŽ cit in logical reasoning. Thus, we still need to know whether differences between social classes in the conservation task can be explained in terms of differences in the need for explicitness. How do children with different social class backgrounds perform in a conservation task when the degree of explicitness of the task is varied? A closely related problem concerns the criterion that one should adopt to consider that a child understands invariance. On the whole, the experim enters who devised the new procedures were satisŽ ed with a correct response. Piaget and his followers, on the other hand, required a correct answer and a verbal justiŽ cation that explicitly appealed to the invariance principle. Bovet, Parat-Dayan, and Deshusses-Addor (1981) and Bovet, Parrat-Dayan, and Kamii (1986) showed that children who were successful in the task devised by Light et al. (1979) could not always justify their responses in terms of the principle of invariance when questioned after the task was completed. Opinions are still divided on the signiŽ cance of such justiŽ cations (Bryant, 1994; Smith, 1993). False negatives are certainly a danger, because children who understand the principle may nevertheless still be unable to put it into words explicitly. However, when a child does justify his/her answer by appealing to the principle, one can be sure of having eliminated the possibility of a false positive, and so it seems appropriate to ask children to justify their responses in any versions of the conservation experim ent. There is, we believe, a third point to be made about techniques for studying children’s understanding of invariance that is based largely on work on a different topic. It has been shown that children are more likely to solve mathem atical problem s in meaningful situations (Hughes, 1986), particularly when Žnancial transactions are involved (Nunes-Carraher, Carraher, & Schliemann, 1985). These results suggest that children might be more successful in conservation tasks if similar manoeuvres were introduced in these tasks. For these reasons we conducted a large-scale study of the understanding of the principle of invariance in middle and working class Brazilian children. The main aim of the study was to analyse the impact of different versions of the conservatio n tasks on the performance of children from different social classes. In particular, we were interested in the effects of introducing the incidental procedure and of making children measure the quantities in the initial comparison. Two scores were chosen to be analysed: (1) the number of correct responses; and (2) the children’s success in justifying these responses. We expected that: (1) the children would perform better when the initial comparison was based on measurem ent rather than on perceptual Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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judgem ents; (2) the differences between working class and middle class children would be more marked in the perceptual conditions than in the measurem ent conditions; (3) the children in the Incidental condition would perform better than those in the Standard condition; and (4) there would be more correct answers than adequate verbal justiŽ cations.

METHOD Subjects The subjects were 256 children from Recife, Brazil, half of them from working class families (WC) and the other half from middle class families (MC). The criteria selected for deŽ ning social classes concerned the type of school (state or private, respectively) attended by the children, a criteria that has already proved to be adequate in most Brazilian large towns (for more information about the bases for this criterion see Roazzi & Monteiro, 1991). Each social class group was divided into four age groups of 32 children. The mean ages for WC age groups were: 5;5 years (range 5;2–5;9); 6;4 years (range 6;0–6;8), 7;6 years (range 7;1–7;9), and 8;6 years (range 8;2–8;9). The mean ages for MC children age groups were: 5;4 years (range 5;1–5;7); 6;4 years (range 6;0–6;8), 7;3 years (range 7;0–7;7), and 8;5 years (range 8;0–8;8). The children were initially given a standard nonverbal intelligence test, the Raven’s Special Scale Progressive Matrices. The distribution of percentiles in this test in the different social class groups and in the different experim ental conditions is shown in Table 1. In all age groups and in all four conditions MC children obtained higher scores than WC ones. The mean difference between WC and MC children percentiles was 30 with WC children located, on average, in the 44th percentile and MC children in the 74th percentile.

Materials In all four conditions the following were used: one jug full of lemonade, two identical glasses, A and A 9 , and one narrower and taller glass, B. In the Standard condition all glasses were clean whereas in the other three TABLE 1 Mean Percentiles in the Raven’s Matrices Test according to Social Class and Conservation Condition

Conservation Condition

Perceptual

Social Class Working Class (WC) Middle Class (MC)

Measurement

Standard

Incidental

Quantity

Money

48 72

41 72

49 75

40 77

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conditions glass A 9 was dirty. For the two measurement conditions (Quantity and Money) a ladle and a box were used. The glasses A and A 9 were placed inside the box so that the child could not see and compare the levels of lemonade inside the glasses.

Procedure The Raven’s test and conservation task were administered individually by an exam iner. The tests took place in a quiet room of the school attended by the children. All interviews were tape-recorded. The children were assigned to the four conditions random ly. In all four conditions the exam iner suggested to each child that he/she should play a vendor-purchaser game in which the experim enter takes the role of the purchaser and the subject adopts the role of a vendor. The instructions were:

“Let’s play a game. I am a customer and you are selling lemonade. Your lemonade is in this jug. Here is the jug with the lemonade and the glasses (A and A 9 ). All right. You sell the lemonade to me in these glasses and after I have drunk it I’ll give the glass back to you.” Perceptual Conditions In the two perceptual conditions (Standard and Incidental) the examiner then asked: “How much does the lemonade in this glass cost?” The price stated by the child was then adopted throughout the session which proceeded as a sale interaction. The examiner said: “Hello! I would like to have a lemonade. How much is it? Give me one, please.” After the child had poured lemonade into one of the glasses (A), the experim enter said: “I want to buy another lemonade for a friend of mine. Please pour the same amount of lemonade here into this glass (A 9 ) .” At this point the exam iner put the two glasses (A and A 9 ) next to each other and asked: “Do you think that my friend and I are going to drink the same amount of lemonade, or is one going to drink more than the other? . . . How do you know? How did you guess?” If the child replied that one glass contained more lemonade than the other, the examiner said: “So, pour more lemonade into the one with less lemonade, so that the two glasses have the same amount of lemonade. And now is there the same amount of lemonade in the two glasses?” When the child agreed that the two glasses had the same amount the experim enter asked: “How much does this lemonade cost (showing glass A) and how much does this one cost (showing glass A 9 )?”

Standard Condition. In this condition the examiner than proceeded: “All right. Now I am going to pour the lemonade from this glass (A 9 ) into this Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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one (B). And now do my friend and I still have the same amount to drink or is one going to drink more lemonade than the other? How do you know? (or) How did you guess? (or) Why? And about the price (amount question). Do my friend and I pay the same price or is one going to pay more than the other? (price question). Why?” In this condition and in all the other three conditions the child was always asked the amount question Žrst and the price question second. Incidental Condition. In this condition, the Žrst two sentences were changed: “All right. Now I am going to pour the lemonade from this glass (A 9 ) to this other one (B).” The experim enter pretended to be surprised to Žnd that glass A 9 was dirty, and searching for an alternative glass which was clean (B), said: “All right. Ah, wait a moment, this glass is dirty (A 9 ): it’s no use. Let’s change it for this other one which is clean (B).” The rest of the statement was identical to that in the Standard condition. Measurement Conditions In the two measurem ent conditions (Quantity and Money) the examiner started by saying:

“Let’s play a game. I am a customer and you are selling lemonade. Your lemonade is in this jug. Here is the jug with the lemonade and the glasses (A and A 9 ). Each glass of lemonade that you are going to sell must be Žlled four times with this ladle and the ladle must always be full. All right. You sell the lemonade in these glasses and after I have drunk it I will give the glass back.” Quantity Condition. In this condition the exam iner then proceeded: “For how much are you going to sell me the lemonade in this glass? I would like to have some lemonade. Pour four ladles of lemonade into this glass for me, please. How much is it?” After the child had poured the required amount into one of the glasses (A), the experimenter said: “All right. How many ladles of lemonade did you put in?” After that the experim enter put the glass (A) inside a box and continued: “I want to buy another lemonade for a friend of mine. Put the same amount of lemonade here in this glass (A 9 )” (the experim enter put this glass inside the box). How many ladles of lemonade did you put in the other glass? Pour the same number of ladles into this glass (A 9 ) .” After the child had put the four ladles of lemonade into the second glass, the experimenter asked: “Do you think that my friend and I are going to Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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drink the same amount of lemonade, or is one going to drink more than the other? How do you know? How did you guess?” “How much does this lemonade cost? (indicating glass A inside the box). And how much does this one cost?” (indicating glass A 9 which in the meantime has been put inside the box before Žlling). If the child replied that one glass contained more lemonade than the other, the experim enter said: “But didn’t you put four ladles of lemonade in each one?” If the child said that the price of one lemonade is different from the price of the other, the experim enter said: “But are my friend and I going to have the same amount of lemonade? Why is one going to pay more than the other?” If the child did not admit that the two glasses had the same amount of lemonade and that they cost the same, the test ended. If the child said that the two glasses had the same amount of lemonade and that they cost the same, the conservation task was continued. “All right. Ah, wait a moment, this glass is dirty (A 9 ), it is of no use. Let’s change it for this other one which is clean (B)”. The experimenter poured the lemonade from glass A 9 to B, took the other glass (A) from the box, put it next to B and asked the child: “And now? Do my friend and I still have the same to drink or is one going to drink more lemonade than the other? How do you know? (or) How did you guess? (or) Why? And about the price. Do my friend and I pay the same price or is one going to pay more than the other? Why?” Money Condition. This condition was similar to the Quantity condition, except that the child had to state the price of each ladle of lemonade, as well as the price for each full glass. The questions about this took the following form: “Each glass of lemonade that you are going to sell must be Žlled four times with this ladle and the ladle must always be full. All right. You sell the lemonade in these glasses and after I have drunk it I will give you the glass back. Each full ladle of lemonade costs 1 cruzado (Brazilian currency). How much will the lemonade in this glass cost? Hello! I would like to have a lemonade. Pour 4 cruzados-worth of lemonade for me into this glass, please. How much is it?” After the child had poured four ladles of lemonade in one of the glasses (A) and after saying that the price was 4 cruzados, the experim enter asked: “All right. How many ladles of lemonade did you pour?” After that the experim enter put the glass (A) inside a box and continued: “I want to buy another lemonade for a friend of mine. Pour the same amount of lemonade into this glass (A9 ) (the experimenter put the glass A 9 inside the box). “How many cruzados-worth of lemonade did you put in the other glass? Pour 4 cruzados-worth of lemonade into this glass (A 9 ) too.” Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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After the child has put the four ladles of lemonade into the second glass, the experimenter asked: “Do you think that my friend and I are going to drink the same amount of lemonade, or is one going to drink more than the other? How do you know? How did you guess? How much does this lemonade cost? (showing glass A). And how much does this one cost?” (indicating glass A 9 ). If the child replied that one glass contains more lemonade than the other, the experim enter said: “But didn’t you put 4 cruzados-worth in each one?” If the child said that the price of one lemonade was different from the price of the other, the experim enter said: “But are my friend and I going to have the same amount of lemonade? Why is one going to pay more than the other?” If the child did not admit that the two glasses had the same amount of lemonade and that they cost the same, the test ended. If the child said that the two glasses had the same amount of lemonade and that they cost the same price, the conservation task continued. If the child gave the correct answer and the correct price to the amount question, the experimenter drew his/her attention to the different levels of liquids in the two glasses: “But here (showing glass A) the lemonade is only up to here . . . don’t you think that the person who is going to drink from this glass is going to drink less lemonade and that the glass has to be cheaper?” The test ended after the child had given a logical justiŽ cation for his/her answers. If the child gave a wrong answer but the correct price to the amount question, the exam iner asked: “Didn’t you say before that this one has less lemonade? Why does it cost the same now?” If he/she changed his/her incongruent judgement to the correct one, the experim enter posed the question given to children who produced the right answer (see earlier). If the child did not change his/her judgem ent, the experim enter asked for a justiŽ cation and ended the session. If the child gave the right answer to the amount question but the wrong price, the experimenter asked: “Didn’t you say before that both had the same amount of lemonade? So why does one cost more than the other now?” If the child gave the wrong answer and the wrong price, the experimenter said: “But before, when you poured the lemonade in these glasses (A and A 9 ), didn’t you say that my friend and I were going to drink the same amount of lemonade? Why does this glass (B) now have more lemonade than this one (A)?”

RESULTS In the analysis of our results we made three main comparisons. These were between: (1) the perceptual and the measurement conditions; (2) the incidental and the standard condition; and (3), the two measurement Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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conditions. In each of these three comparisons we looked at possible interactions with social class. We looked at two kinds of score: (a) the number of children who produced the correct conservation answer, and (b) the number of children who were classiŽed as conservers or as intermediate conservers on the basis of the justiŽ cations that they offered for their correct responses. Two trained judges classiŽ ed the verbal justiŽ cations independentl y. They evaluated the protocols without knowing the children’s identity, ages, or performance in the Raven’s Matrices. Interjudge reliability for the two judges was 86%. Where disagreement occurred, a third judge was asked to classify the justiŽ cation. This third evaluation in all cases coincided with one of the Žrst two judges, and was taken as Žnal. The judges put the children into three categories, using the method elaborated by Inhelder, Sinclair, and Bovet (1974). The three categories were: (1) Nonconservers; (2) Intermediate conservers who were inconsistent or who gave the correct answer but could not justify it properly; and (3) Conservers who gave the correct answer and produced the correct explanation for it. Our analysis took two forms. First, we made direct comparisons between the social class groups in the four conditions and used the chi-square statistic to see where there were signiŽ cant differences. Second, we carried out logistic analyses (using generalised linear interactive modelling, GLIM, Healy, 1988 and Payne, 1977) to see whether the differences between different groups were signiŽ cant even when the effects of variations in the children’s intelligence were controlled. 1. Is there a Difference between the Perceptual and the Measurement Conditions? Table 2 gives the combined scores for the two perceptual conditions and for the two measurement conditions and it shows that the difference between the two was quite striking. On the whole, many more children were counted as conservers when the Žrst question was a quantitative one (measurement) than when it was not (perceptual). This general pattern of results conŽrmed previous studies (Gelman, 1982; Nunes-Carraher & Schliemann, 1985) on the effect of making the Žrst question an explicitly quantitative one. The only exception to this pattern was the scores of the MC children when justiŽ cations were not taken into account for the amount question (Z 5 0.555, P 5 .289; hypothesis test for proportion). Slightly more MC children were counted as conservers under this criterion when the Žrst question was a quantitative one. However, when MC children were asked about price, and when the WC children were asked about amount and price, the measurement conditions produced much better scores than the perceptual conditions. The WC group performed better in the measurement condition than in the perceptual condition for the amount question (for the verbal Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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TABLE 2 Number of Conserving, Intermediate, and Nonconserving Judgements (With JustiŽ cation and Without JustiŽcation: First Answer) in the Perceptual and Measurement Conditions of the Conservation Task According to Social Class and Type of Question

Question/Social Class With justiŽcation Amount WC MC Price WC MC

Perceptual (Standard + Incidental)

Measurement (Quantity + Money)

N

I

C

N

I

C

40 30

17 13

7 21

20 15

28 31

16 18

30 26

24 17

10 a 20

14 9

25 22

25 33

10 21

36 40

28 24

22 a 29

19 17

45 47

Without justiŽcation: First answer Amount WC 54 MC 43 Price WC 42 MC 34

Note: N, non-conserving; I, intermediate; C, conserving. a These particular Žgures are out of 63. The data from one subject were lost.

justiŽ cation: N 1 I vs. C: Z 5 2.072, P 5 .0171 and N vs. I 5 C: Z 5 1.776, P , .037; and for the Žrst answer: Z 5 3.482, P , .001) as well as for the price question (for the verbal justiŽ cation: N 1 I vs. C: Z 5 2.975, P , .001 and N vs. I 1 C: Z 5 2.978, P 5 .0014; and for the Žrst answer: Z 5 4.070, P , .001). Similarly, the MC group performed better in the measurement condition than in the perceptual condition with the amount question for the answers with verbal justiŽ cation only contrasting nonconserving versus intermediate and conserving answers (N 1 I vs. C: Z 5 .576, P 5 .2823 and N vs. I 1 C: Z 5 2.777, P , .0027). For the price question signiŽ cant differences were found for the answer with verbal justiŽ cation (N 1 I vs. C: Z 5 2.26, P , .0118 and N vs. I 1 C: Z 5 3.431, P , .0003), and also for the Ž rst answer (Z 5 3.150, P , .0008). 2. Is the Incidental Condition Easier than the Standard Condition? Table 3a presents the scores for the Standard and Incidental conditions. It can be seen that there were only small differences between the two conditions and that these differences went both ways. Test of proportion comparisons of both types of score (the number of correct responses and the number judged as conservers or intermediate conservers on the basis of their justiŽ cation) Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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produced no signiŽ cant differences between the two conditions. We conclude that an incidental transformation does not always lead to better performance in the conservation task. On the other hand, chi-square comparisons did show some signiŽ cant differences between the two social class groups. When we classiŽed children on the basis of their justiŽ cations, the difference between social classes reached signiŽ cance in the Incidental condition for the amount question (c 2 5 6.93 with 2 df, P , .05). When the answers were classiŽed on the basis of only their correctness, the difference between social classes reached 2 signiŽ cance in the Standard condition for the amount question (c 5 4.73 with 1 df, P , .05) and in the Incidental condition for the price question (c 2 5 4.64 with 1 df, P , .05). Three points need to be made about these results. First, the absence of a signiŽ cant difference between social classes in the Standard condition when the children’s justiŽ cations were taken into account was unusual. Previous evidence on social class comparisons in the standard conservation task shows MC children signiŽ cantly outscoring WC children (e.g. NunesCarraher & Schliemann, 1982; Perret-Clermont, 1980). It is difŽ cult to explain the discrepancy between our results and that of earlier studies. Second, WC children seem to be helped by having to justify their answers in the Standard condition. Third, the signiŽ cant difference between social classes in their justiŽ cations in the Incidental condition is basically due to the fact that the WC children’s performance improved very little in the Incidental condition as compared with the Standard condition for the amount question (their correct answers were 9.4% vs. 12.5% ), whereas MC children were positively affected by this change in context. Their correct answers were 25% and 40.6% , respectively, in the two conditions. Moreover, when they gave the Žrst answer without justiŽ cation for the price question in the Incidental condition they performed worse than the MC children, and their level of performance was actually worse than in the Standard condition. Thus, contrary to our hypothesis, the Incidental condition affected MC children more positively than it did WC children. 3. Are there Differences between the Two Measurement Conditions? As shown in Table 3b, in all four comparisons the children gave more correct answers when they had worked with the price of each ladleful (Money task) than when they had simply measured the quantity in ladles (Quantity task). However, this difference was not signiŽ cant for the justiŽ cation responses. There was one signiŽ cant difference between the two conditions on the measure of simple responses. For the WC children there were more correct answers on amount for the money than for the quantity question (Z 5 2.0052, P , .005). Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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EXPLICITNESS AND CONSERVATION TABLE 3a and b Number of Conserving, Intermediate, and Nonconserving Judgements (With JustiŽ cation and Without JustiŽ cation: First Answer) in the Two Perceptual Conditions (a) and in the Two Measurement Conditions (b) of the Conservation Task According to Social Class and Type of Question a)

Perceptual Conditions

With JustiŽcation

Standard

Question/Social Class

Amount WC MC Price WC MC

Without JustiŽcation

Incidental

Standard

Incidental

N

I

C

N

I

C

N

C

N

C

22 16

7 8

3 8

18 14

10 5

4 13

29 22

3 10

25 21

7 11

14 15

12 9

6 8

16 11

12 8

4 12

19 20

13 12

23 14

9 17

b)

Measurement Conditions

With JustiŽcation

Quantity

Amount WC MC Price WC MC a

Without JustiŽcation

Money

Quantity

Money

N

I

C

N

I

C

N

C

N

C

10 9

17 17

5 6

10 6

11 14

11 12

23 22

9 10

13 18

19 14

8 5

14 14

10 13

6 4

11 8

15 20

12 12

20 20

7 5

25 a 27

This particular Žgure is out of 31. The data from one subject were lost.

Summary The only difference that we found between the Standard and Incidental conditions was in the MC children’s answers to questions about quantity. Otherwise, this difference between conditions did not appear to have an effect. However, there was a striking difference between the combined scores for the two perceptual conditions on the one hand and the two measurem ent conditions on the other. The measurement conditions were a great deal easier. This supports the idea that young children can apply the principle of invariance in a conservation task when they understand that the task concerns quantity. There were also signs of differences within the two measurem ent conditions. The Money condition was easier than the Quantity condition for the WC children with the amount questions (although not with the price questions). Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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Logistic Analysis (GLIM) Although there were consistent differences between the two social class groups in the results that we have just reported, there were also differences between these two groups in the test of nonverbal intelligence (Ravens) administered at the start of the experim ent. It is interesting to see whether the differences that we have reported would still hold if the effect of these differences in intelligence scores were partialled out. This cannot be done in chi-square comparisons, but it is possible in a logistic analysis. A logistic analysis works in much the same way as a Ž xed-order multiple regression, except that in a logistic analysis the dependent variable can be dichotomous. In a logistic analysis, as in a Žxed-order multiple regression, you enter in the extraneous variables that you wish to control before the other variables. This means that you have accounted for, and have removed, the variance due to the extraneous variables before you deal with the variable that you consider to be the relevant one. We carried out two logistic analyses, each with three steps. The Žrst two steps were Age and IQ, because we needed to control for differences in Age and IQ. The other independent variable, Conditions—the variable that interested us most—we entered at the end. This variable dealt with the differences between the four conditions. In a logistic analysis, the statistic that indicates whether each independent variable has a signiŽ cant effect is the chi-square. As GLIM works on dichotomous scores for the dependent variables when the variables are not continuous, the children performing at an intermediate and conserving level were put together in one category and children who did not conserve at all into the other. We entered the independent variables in the same order in two analyses for both social classes. The Žrst analysis treated performance on the amount question as the dependent variable; the second analysis treated performance on the price question as the dependent variable. The results of these Žxed-order logistic analyses considering the children’s answer with and without verbal justiŽ cation are presented in Table 4. The children’s answers with justiŽ cation appear to have a considerable and impressive connection between context conditions and the level of performance (the dependent variable) in the conservation task for the 2 2 amount question (for MC c 5 11.27 with 3 df, P , .02 and for WC c 5 16.54 2 with 3 df, P , .001) and for the price question (for MC c 5 14.13 with 3 df, P , .01 and for WC c 2 5 12.27 with 3 df, P , .01). Moreover, although age played a signiŽ cant role in the regression for both social classes, the level of performance in Raven’s matrices (IQ) only affected the children’s performance signiŽ cantly in the case of the middle class children’s Žrst answer to the price question (c 2 5 5.32 with 1 df, P , .01). Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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EXPLICITNESS AND CONSERVATION TABLE 4 Fixed-order Logistic Analysis (GLIM) of the Dependent Variables Amount and Price Questions Taking into Account the Two Social Classes Separately

Middle Class

Steps

df

Amount

Price

Change in Scaled Deviance With justiŽcation 1. Age 2. IQ 3. Condition 4. Condition × Age 5. Condition × IQ 6. Age × IQ 7. Condition × Age × IQ

3 1 3 9 3 3 9

Without justiŽcation: First answer 1. Age 3 2. IQ 1 3. Condition 3 4. Condition × Age 9 5. Condition × IQ 3 6. Age × IQ 3 7. Condition × Age × IQ 9

Working Class

Amount

Price

Change in Scaled Deviance

25.45**** 2.80 11.27** 13.41 5.69 7.63 13.65

18.45**** 1.62 14.13** 15.78 10.24** 2.83 9.45

13.74*** 1.98 16.54**** 15.54 0.56 23.12**** 12.53

11.63*** 0.64 12.27*** 3.34 3.56 4.81 12.87

8.13* 2.07 1.43 16.41 1.33 0.76 5.68

11.08** 5.32** 6.16*** 18.51* 2.24 1.34 8.94

1.69 0.50 20.79**** 23.43*** 2.80 12.20*** 2.90

0.35 0.15 19.96**** 10.32 8.57* 5.25 8.76

* signiŽ cant at .05; ** signiŽ cant at .02; *** signiŽ cant at .01; **** signiŽ cant at .001.

We also carried out other similar logistic analyses, which took into account only the child’s Žrst answer (without justiŽ cation) (see Table 4). The results show a strong connection between context conditions and level of performance in the conservation task for the quantity and the price question for WC children only (amount question c 2 5 20.79 with 3 df, P , .001 and price question c 2 5 19.96 with 3 df, P , .001). With the MC children we found a considerable connection between context condition and level of 2 performance in the price question only ( c 5 16.41 with 3 df, P , .01). In the amount question, this connection was not found (c 2 5 1.43 with 3 df, P 5 n.s.). It is also interesting to note that the age variable affected the performance of the MC children, but not of the WC children. The signiŽ cant relationship between context and level of performance in the conservation task (with the single exception of the MC children Žrst answers to the amount question) suggests that the context of the experiment is a powerful variable that can affect demonstration of children’s cognitive abilities. The connection cannot be a product of differences in intelligence or in age because these were the variables that we controlled for. All in all, this result is a striking one because it shows a more precise interrelationship between child and context. When the in uences of Age and IQ have been removed, a powerful connection between context and Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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conservation ability still continues to be found (these factors were not adequately controlled in previous studies of this topic). This suggests that context does play a considerable role with both social classes in determining the child’s performance in the conservation task and that modifying aspects of the context may improve performance. The fact that there is such a strong connection, even after the most stringent controls, is particularly important. Thus, our analysis provides some support for the importance of context in the assessment of conservation ability.

DISCUSSION One of the two main results of this study was positive and the other negative. We found a large and consistent difference between the two perceptual conditions (Standard and Incidental) and the measurem ent conditions (Quantity and Money). The children did better when they measured the quantities in the initial comparisons than when they compared them perceptually . It should also be remembered that one of the two measurem ent conditions, the Money condition, was easier for the working class children than the Quantity condition. In contrast, we found no signiŽ cant differences between the children’s performance in the Incidental and in the Standard tasks. The clear difference between the two nonmeasurem ent conditions and the two measurem ent conditions conŽrms the suspicion voiced by many other researchers that we cannot take for granted that children always understand the quantitative or logical nature of quantitative and logical tasks. The fact that the children are more likely to answer the posttransformation conservation question correctly when the quantitative nature of the initial comparison has been stressed demonstrates that they are helped by being shown that the questions are about quantity and not about perceptual appearance. The similarity between our results with liquid and those of Nunes-Carraher and Schliemann (1985) with number is impressive, and suggests that the importance for children of an explicit emphasis on quantity is a general one. Thus, children’s failures to give conserving answers may not be caused by their concentration on a particular perceptual feature, such as the different levels of lemonade in the two different glasses (this is the position defended by Piaget, 1950), but by the experim enter’s failure to take into account the child’s assumptions about the task and by the interaction of these assumptions and the linguistic and communicative aspects of the task. They may also re ect a failure by the child to understand the real intention of the experim enter. We also found evidence for differences in the effects of context on different social groups. Our idea was that these effects might be more Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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important for working class than for middle class children. We thought that working class children might be particularly handicapped by the limitations of the traditional context in which cognitive problem s are usually given. Our results give some support to this idea. They suggest a difference between working class and middle class children. Neither group was much affected by our making the task an incidental one, although there were signs that this manoeuvre might have helped the middle class more than the working class children. But the introduction of measurement and the consequent increase in the explicit stress on quantity appeared to have an appreciably stronger effect on working class children than on middle class children. The working class children seemed to beneŽ t most from this explicitness, particularly when money was involved. This result highlights the importance of experience and of the material that children have to deal with in experimental tasks. It is well known that in Brazil, working class children deal with money in commercial transactions during working activities at a young age. In other studies (Ceci & Roazzi, 1994; Nunes-Carraher et al., 1985; Roazzi, 1986a,b, 1987; Roazzi, Almeida, & Spinillo, 1991; Roazzi & Bryant, 1992) in which cognitive problem s are presented embedded in commercial transactions where money is involved, working class children’s performance improved enormously, and in certain cases the usual social class differences disappeared. In our study, no differences were found in the comparisons of the two social classes in the two measurem ent conditions either with the quantity or with the price questions. One can speculate about the reasons for this difference between the social groups (we have already argued that the middle class children, being better prepared for the school environment, may also be more at home with tasks presented in unfamiliar contexts), but the practical implications of our results are clear. Children in general, and working class children in particular, are helped when the nature of the task that they are being given is clear and explicit. Finally, we must consider the lack of a signiŽ cant difference between the Standard condition and the Incidental condition. This was a surprise to us, as we expected to repeat the differences found between these two conditions in previous studies (Finn, 1979; Light et al., 1979; Miller, 1982). In order to explain this discrepancy, we need to look at the differences among these socially intelligible conservation tasks. Although Light et al.’s experiment (1979) and our own were both devised in such a way that the transformation of materials appeared to be merely incidental, there are three differences between their study and ours. In Light et al.’s experim ent, the children were tested in pairs, whereas in our experim ent children were tested alone. Second, our system of classiŽcation of children’s answers was based on justiŽ cations and consequently the answers were classiŽed as conserving, intermediate, or nonconserving: Light et al. classiŽed children only as Downloaded from jbd.sagepub.com at NANYANG TECH UNIV LIBRARY on June 4, 2015

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conserving or nonconserving on the basis of their post-transformation judgem ent (no explanations were required). Third, in both experim ents the conservation task was embedded in a game, but in our experiment the children knew that they were being tested, whereas in Light et al.’s experim ent children did not know about the test situation (or at least the test situation was much less clear) and, in particular, the game played during the task was of a competitive nature. This last factor alone may have encouraged the children to pay more attention and to put more effort into solving Light et al.’s task. Nevertheless , our results provide strong support for the idea of the importance of context on performance in the conservatio n task. The difference between the measurem ent and the perceptual conditions and the fact that the working class children beneŽ ted so clearly from the introduction of money into the task show how sensitive children, in general, and working class children, in particular, are to the circumstances of the task and the material used in it. One possible reason for this is that the introduction of measurement provides the child with a more efŽ cient way of representing the quantities. There is evidence that children’s performance in measurem ent tasks is considerably affected by the way in which they represent the tasks to themselves (Nunes, Light, & Mason, 1993). It is also likely that the effect of measuring the quantities either in terms of money or in terms of ladles encourages the child to represent these quantities in a way that makes it easier to understand their invariance. If a quantity is represented as 4 ladlesful or 4 cruzados-worth it should be easier to understand that rearranging its perceptual appearance does not affect its quantity, because the child might easily understand that these rearrangable measures retain their value whatever their perceptual arrangem ent. Our results suggest to us that children’s understandin g of quantity may be considerably affected by the way in which they are encouraged to represent it. Revised manuscript received July 1996

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