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The empirical violation of conservation laws and its relation to structural change
JOURNAL
The
OF EXPERIMENTAL
Empirical
CHILD
Violation Relation SIDNEY
18, 464-479
PSYCHOLOGY
of
Conservation
to Structural STRAUSS Tel-Avzv
(1974)
AND
and
Its
Change1
Dov
Unived
Laws
LIBERMAN y
Concrete operational Ss were provided empirical evidence of nonconservation of discontinuous quantity and weight. The findings were that few Ss accepted this evidence. This was interpreted as supporting the organismicdevelopmental claim that lower forms of reasoning are transformed into structurally more advanced forms. It was also found t.hat (1) probing provides a more accurate assessment of Ss’ operational levels, (2) one can empirically distinguish between logicomathematical and physical knowledge, and (3) the former is understood by Ss to be nomically necessary and the latter, in the case of weight, may not be.
One of the basic tenets of organismic-developmental and structuralist theories addresses itself to the problem of directed sequential transformations of cognitive competences. Piaget (1970) has argued that structural transformation involves a qualitative reorganization to a more adaptive structure. Since a structure is transformed into a qualitatively different form, one would expect that a child would have difficulty retrieving previous forms. Consequently, this model would not predict the occurrence of regression. Experimental evidence supporting this hypothesis has been gathered in both the moral and intellectual domains. Turiel (1966) and Kuhn (1972) presented training conditions in which models provided S with reasoning one level above (+ 1)) two above ( +21, or one below ( - 1) his predominant level. It was found that being presented with a - 1 structure of reasoning did not significantly affect Ss’ reasoning. In addition, Rest (1969)) Rest, Turiel, and Kohlberg (1969)) and Kuhn (1972) presented data which suggested that Ss could comprehend -I reasoning yet they rejected it as inadequate. ‘This article is based upon an M.A. dissertation submitted by the second author to the Department of Education at Tel-Aviv University. We would like to express our appreciation to Matal-the Tel-Aviv University Elementary School Science Project-for its support, of this research. ’ Author’s address: Sidney Strauss, School of Education, Tel-Aviv University, Tel-Aviv (Ramat, Aviv), Israel. Copyright All rights
464 @ 1974 by Academic Press, Inc. of reproduction in any form reserved.
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Alternatively, other research evidence has shown considerable extinction of behaviors which are thought to be structural products; e.g., conservation concepts (Kingsley & Hall, 1967; Smith, 1968; Brison, 1966; Hall & Simpson, 1968 ; Hall & Kingsley, 1968 ; Sullivan, 1967). In summarizing their findings, Miller (1971) pointed out that conservation response extinction is ubiquitous, rather easy to obtain, and that a majority of Ss seem susceptible to such training. As Miller indicated, these studies are quite divergent and do not present LIP with a clearly formulated alternative to the structuralist model presented above. Consequently, the defining criterion of the “alternative model” presented below is t.he similar results from experiments which studied the feasibility of extinguishing conservation responses. The protot,ype alternate model experiment was conducted by Smedslund (1961). Subjects were administered an extinction procedure in which E surreptitiously removed clay from one of two objects which previously had been judged to be equivalent in weight. The results of interest for the present study were that six of 13 Xs successfully resisted extinction, which was defined as occurring when S suggested that clay was added or subtracted during the deformation. These alternate model experiments can be interpreted as being - 1 studies, since conserving Ss were shown empirical evidence of nonconservation. That is, concrete operational Ss saw empirical evidence which embodied a form of reasoning they had used in the ontogenetically prior intuitive stage. The discrepancy between the findings reported by investigators within the organismic-developmental model (i.e., no regression) and the alternate model (i.e., ubiquitous extinction) has been discussed elsewhere (Strauss, 1972) and served as a motivation for the following two experiments. EXPERIMENT
I
There are two types of issues which bear on the discrepancy just described: methodological and theoretical. The first methodological issue which could explain the discrepant findings was raised by Smedslund (1968)) where he argued that the use of probing questions would more accurately identify Ss who revert to the previous structure. Consequently, we hypothesized that., if one probed further into 8s reasoning about nonconservation, fewer Ss would be identified as having reverted to a previous stage. The second methodological issue concerns the criteria one uses in determining the acceptance or rejection of -1 experiences. With the possible exception of the Miller-Schwartz-Stewart (1973) study, only
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two answers were accepted as adequate indicators of the rejection of nonconservation: The scale was broken or some material was added to or subtracted from one of the objects. We hypot,hesieed that if one probed for reasoning underlying other judgments, evidence of rejection of nonconservation experiences would be found. The third methodological issue pertains to the acceptability of some, but not all, - 1 experiences. We hypothesized that more - 1 experiences against the direction of expectation (-cl) would be rejected than those in the direction of expectation (+d). The definition of -d and +d is relative to intuit.ive reasoning and can be illustrated with a discontinuous quantity conservation example. Intuitive Ss, when presented with such a problem, argue that the row which is spread out contains more objects. If in the - 1 experience we were to surreptitiously add an object to the longer row, the result would provide empirical evidence in the direction of expectation of an intuitive S ( +d) . Conversely, adding an object to the shorter row would be against an intuitive S’s direction of expectation ( -d) . The final methodological issue concerns the short term versus long term and generality of regression. Hall and Simpson (1968)) Miller and Lipps (19731, and Smit’h (1968) provided delayed posttest measures of long-term cognitive change, while Miller (1973 1 provided posttest, measures immediately after the - 1 experiences. In the remaining studies cited above, the acceptance or rejection of -1 experiences was determined only during the t’reat,ment condition. We hypothesized that the acceptance of - 1 experiences during the treatment condition would be short term. With respect to generalization, in the three cases where delayed posttests were used, the concept assessed on the posttest was the same concept. as in the treatment condition. In the present study, the generality of nonconservation judgments after the treatment conditions was tested by administering posttests for several conservation concepts. It was hypothesized that Ss who accepted - 1 experiences for one concept would not generalize this to the others. The theoretical argument concerns structural elaboration and its relation to the level of the concept being presented. We hypot.hesized that a relatively more elaborated structure (one which is being applied to discontinuous quantity, length, and weight concepts’) is less susceptible to - 1 experience at its lower limits (i.e., with discontinuous quantity conservation) than at its upper limits (i.e., weight). Similarly, we hypothesized t’hat a relatively less elaborated structure-one which is applied to discontinuous quantity only-is susceptible to assimilating - 1 experiences at its own level or upper limits of it,s application, i.e., for discontinuous quantity conservation.
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Method There were three phases to the research: posttest phases.
the pretest,
treatment,
and
Pretest All Ss were tested for the understanding of the terms “more,” “less,” and LLsame” for discontinuous quantity and weight and “longer,” “shorter,” and “same” for length (see Langer & Strauss, 1972, for a description of these tasks). Subjects who did not understand these terms were eliminated from the experiment,. Those who understood these terms were administered conservation of discontinuous quantity, length, and weight problems. (A balance scale was used when administering the weight conservation t,asks, and Ss were trained in the use of the balance scale.) Each S received two items per conservation toncept. We shall present an example of one discontinuous quantity conservation item as an illustration of the general procedure: (a) Two perfectly aligned rows of five identical buttons in parallel formation were presented to S for ordinal comparison. (b) As S watched, the buttons in one row were compressed in order to deform the spatial alignment. (c) The S was asked to judge whether or not there were the same number of buttons in the two rows. (d) The S was asked to justify his judgment. (e) A verbal countersuggestion, varying according to whether or not S judged equivalence, was offered: “Someone before told me that this one had more (they were the same) because it sticks out farther (they were the same before). Do you think that’s right or are they the same (is this one more) ?” Parts (c) and (d) will henceforth be referred to as the standard question. The types of deformations for the two items per concept were as follows: (i) For one item in discontinuous quantity, one row was compressed while, in the second it,em, one row was expanded. (ii) For one item in length, one of two parallel sticks in an ends aligned configuration was moved so that the ends were no longer aligned but the parallel arrangement was maintained; in the second item, one of the sticks was deformed into a V shape. (iii) For one weight item, one of t,wo equivalentweight clay balls was deformed into a ring while in the second item one of the balls was broken up into five balls. The three forms of deformation (discontinuous quantity, length, and weight) and the two items of each form permitted the following assessment of each S’s structural profile. For each test item the scoring resulted in one of two st,age assessments: (a) intuitive-marked by two
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STRAUSS
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behavioral features: an equal or unequal judgment and no ability to produce at least one logical operational reason (e.g., identity, compensation, or reversibility justifications) for the judgment; and (b) concrete operational-marked by three behavioral features: an equal judgment, a logical operational reason, and resistance to the countersuggestion. The cumulative score for two items within a concept also yielded two stage assessments: (a) intuitive-& who were intuitive on both test items, and (b) concrete operational-L% who were concrete operational on both test items. The only Ss included in the study were those who were pretested as (i) concrete operational on the cumulative score for discontinuous quantity and intuitive for the remaining tasks, and (ii) concrete operational on the cumulative score for all three concepts. Treatment
Conditions
According to S’s pretest structural profile, he was randomly assigned to a condition. Subjects who were pretested as concrete operational for discontinuous quantity only were randomly assigned to either a control group (in which Ss were administered pre- and posttests without any intervening training) or to one of two - 1 conditions: (a) discontinuous quantity +d or (b) discontinuous quantity -d. Subjects pretested as concrete operational for all of the concepts were randomly assigned to either a control group or to one of four - 1 conditions: (a) discontinuous quantity +d, (b) discontinuous quantity -d, (c) weight +d, and (d) weight -d. The discontinuous quantity and weight conditions contained three and five sections, respectively. The procedure was terminated at. the end of the section in which S rejected the - 1 experience (i.e., maintained weight or discontinuous quantity equivalence). For purposes of elucidation, we shall first describe the - 1 weight conditions. A. -1 weight +d. Section 1: E manipulated. (a) The S was presented with two balls of clay which were equivalent in weight. (b) The balls were placed on opposite sides of a pan balance scale and an equivalence judgment was obtained. (c) The balls were then taken off the balance. The experimenter deformed one of them into a ring shape and surreptitiously removed clay from t,he ring. (d) The standard question (SQ) was asked. (e) The subject was then told that the ball and ring would be placed on the pan balance scale and was asked to indicate where the weight indicator would be. (f) The experimenter then placed the ball and ring on the balance scale and asked, “What did we find?” (g) After S indicated weight nonequivalence, E asked, “How do you explain this?” (h) For those Ss who said that the ball weighs more,
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because the pointer indicated so, E asked, “But why does it weigh more now?” (i) If S said that E had added or subtracted clay, or that E had exchanged that ball for a heavier one, E asked, ‘(HOW do you know? Did you see me add (subtract) clay (exchange balls?) ” (j ) If S said that, the scale was broken, E asked, “If I fixed the scale, where would the pointer be?” (k) The subject was asked to justify his judgment. If S maintained that the ball and ring should weigh the same, the training was terminated. If this argument was not produced, the training continued. Section 2: S gave heaviness judgments. At this point a terminological change was int.roduced. Based upon findings in a pilot study, S’s were asked about the heaviness of the clay ball and ring. Previously, Ss had been asked about their weight. (a) The experimenter asked, “Are these t,wo the same heaviness or is one heavier?” (1~) The subject was then asked to justify his judgment. (c) The experimenter then posed the following situation, ‘Suppose I would take this ball and put it on a regular (bathroom) scale and I find out that. it weighs 50 g. Now I’ll take it off and put the ring on the same scale. Will the ring weigh less than 50 g, 50 g, or more than 50 g?” (d) If S said that the ring is the same heaviness as the ball and/or that the ring would weigh 50 g, he was asked to explain why the balance scale indicated that the ball weighed more, and the training was terminated. For Ss who argued that the ball and ring were not equivalent in heaviness, the training continued to Section 3. Section 3: E showed contradiction. (a) The experimenter told S, “A couple of minutes ago (in the pretest) you said that they should weigh the same because . . . (E provided S with his previous justification for equivalence). Now you say that the ball should weigh more. Which do you think is really right?” (b) If S said that he was correct before (i.e., that they should be equivalent in weight), he was asked, “Then how do you explain that the point.er leans to the side of the ball?” If S gave a correct answer, the training was terminated. (c) If X said that he had been wrong before, or provided no explanation, the training continued to Section 4. SeeCon 4: X predicted and manipulated. (a) The experimenter said, “Let’s play again.” (b) The experimenter then presented S with two new clay balls which were equivalent in weight. The balls were put on the pan balance scale and an equivalence judgment was obtained. (c) The subject. was then told, “Now it’s your turn. I would like you to make a ring out of one of the balls just as I did.” (d) Before X did this, E asked, “After you finish, do you think that one will weigh more than the other or that they will weigh the same?” (e) The experimenter then
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asked for a justification. (f) If S said that they will weigh the same, he was asked, ‘(How do you explain that when I played, the indicator went to the side of the ball?” Both this type of S and Ss who predicted that they would not weigh the same continued. (g) The subject S then deformed one of the balls into a ring. (11) The standard question was asked. (i) If S said that they weighed the same, he was asked, “How do you explain that when I played the game, the ball weighed more?” The training was then terminated. Section 5: S observed equivalence of weight. (a) If S said that one of the pieces weighed more, he was asked to indicate both the side to which the pointer would go and the levels of the pans when t,he ball and ring would be placed on opposite sides of the scale. (b) The ball and ring were then placed on the scale and S observed that the pointer indicated equality. The experimenter asked, “What do you see?” (c) The experimenter asked, “How do you explain that when I played the game the pointer moved to the side of the ball and now it moved to the center?” B. - 1 weight -d. This training procedure was identical to the procedure described above except that E surreptitiously added, rather than removed, clay to t,he ring. C. - 1 discontinuous quantity +d and -d. These treatment conditions followed the same format as the - 1 weight conditions for three sections, which were present.ed in t.he following order: (1) E manipulated, (2) E showed contradiction, and (3) S predicted and manipulated. The manipulations for the +d condition were stretching out and surreptitiously adding a button to the longer row. As both rows initially had five buttons each, the longer row had six buttons after the manipulation. For the -d condition, the manipulation involved compressing one row and adding to it so that the shorter row would have more buttons. Posttests The posttests were administered 2 weeks to 1 month after the treatment conditions. They were identical to the pretests except that no balance scale was used in the weight, conservation tasks. The experimenters were unaware as to the treatment. condition to which Ss had been assigned. Subjects The Xs were predominantly middle class from mixed suburban areas in and around the city of Netanya, ranges and mean ages for the different groups were as who conserved for DQ only: (a) DQ + d, 4;10-7;0, DQ - d, 5;4-6;9, a = 6;0, (c) control, 5;2-6;1, x
urban, Israel. follows. J?Y= = 5;7.
rural, and The age For those 5;11, (b) For those
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who conserved through weight: (a) W + d, 7;11-9;4, x = 8;6, (b) W - d,8;2-9;10, x = 8;9, (c) DQ + d, 8;4-9;4, z = 8;10, (d) DQ - d, 8;7-9;4, a= 9;0, (e) control, 8;&9;4, 2 = 8;lO. A total of 151 Ss were administered the pretest. Of these, 71 Ss were eliminated from the study. Two were eliminated due to failure to understand terms, 31 Ss for not having conserved on DQ, and 38 Xs for having conserved on DQ and L but not W. Eighty Ss remained in the experiment. Ten Ss were assigned to each of the six treatment or two control groups.
Results and Discussion Before analyzing the data relevant t.o the above hypotheses, we shall first determine the adequacy of the deceptions involved in the surreptitious addition or removal of clay (for - 1 W) and addition of a button (for - 1 DQ). This can be measured at two points in the procedure. The first point occurred immediately after the deceptive deformat.ion in Treatment Section 1. If, after the surreptitious addition or removal, S judged weight or number equivalence, it could be safely argued that he did not observe the deception. This occurred for all Ss in the - 1 W conditions and for 22 of 40 Ss in the - 1 DQ conditions. The second point in the procedure in the above determination occurred for the remaining 18 Ss in the - 1 DQ conditions, all of whom argued that E must have added a button. Of these Ss, (a) 11 said that t.hey did not see E add a button. (b) Six said that they saw E add a button to one row by taking a button from a surplus pile and adding it to the row that had more; however, when asked where the button had been placed, all Ss pointed to the end of the row closest to the surplus pile, which was not the end to which E had added. (c) Only one S reported the decept.ion as it had occurred (i.e., E held a button in his hand and added it to one of the rows) ; but subsequent questioning indicated that this was a guess and not an observation on S’s part. Having established the adequacy of the deceptions, we can now proceed to the hypotheses. The first hypothesis, that probing would reduce the number of Ss identified as accepting -1 experiences, was confirmed. Data relevant to this hypothesis can be found in Table 1. The results were that (a) in the - 1 DQ + d condition, all three Ss who would have been assessed as intuitive without probing were assessed as operational by the end of the treatment condition. (b) Of the four intuitive Ss in the -1 W + d condition, two produced operational judgments, one remained intuitive, and one could not produce any explanations for the phenomena. (c) Of the three intuit.ive Ss in the - 1 W - d condition, one produced operational judgments and t,wo provided no answers. The no-explanations category for DQ Ss was rvidence of concrete
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FREQUENCY
Treatment sections
OF TYPES
Operational
TABLE OF JUDGMENTS OF THE: TRAINING
No explanations
Intuitive
AND
Operational
LIBERMAN
1 PRODIJCKD I~RING CONDITIONS No explanations
Int,uit,ive Experiment,
-1 1. Before After 2. After 3. After
DQ
10 7 8 10
+da 0 3 2 0
-1 0 0 0 0
10 9 9 9
Experiment
DQ
Operational -.-___
SFXTION
-da 0 0 0 0
-1 0 1 1 1
DQ
+d
20 2oc
and
W -d*
-Q
0 0
Experiment -1
No expla nations
Intuitive
I
I
-lW+db
EACH
0 0
II
-1WfdA
1. Before Afkr 2. After 3. After 4. After 5. After
10 G 7 8 8 8
0 4 3 2 2 1
0 0 0 0 0 1
10 5 5 G 7 8
0 3 3 3 2 0
u Subjects b Subjects c Training point.
who were operational for DQ only. who were fully operat,ional. was terminated for all Ss after Section
0 2 2 1 1 2
15 6 7 11 11 11
1, since all rejected
0 9 5 4 4 1
-1
0 0 3 0 0 3
DQ at that
operational reasoning, since all of these Ss, without explanation, maintained that there should be equivalence and predicted equivalence in the next section. In contrast, t,he no explanations category for W Ss was evidence of intuitive reasoning since they maintained that nonequivalence should have occurred yet had no explanation when it did occur. They also predicted nonequivalence in the next section. Consequently, the DQ and W no-explanations categories could not be combined. It was found that a significant number of the above-mentioned Xs who would have been assessed as intuitive at the end of Section 1 produced operational reasoning during probing (binomial test N = 6; 9 = 0; p = .016). It was also found that more DQ than W treatment Ss changed to operational judgments during the treatment (Fisher exact p = .OlSj . Here we have seen that the rejection of empirical nonconservation was
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almost complete when taking into account both Ss’ spontaneous (Section 1) and elicited (other sections) judgments. An interesting point is that the percentage of Ss spontaneously rejecting -1 W after Section 1 in the present study (55%) was similar to Smedslund’s (1961) findings (46%). The end of Section 1 in our study was procedurally similar to Smedslund’s entire study. The second hypothesis, that reasons other than addition/subtraction or a broken scale would, when probed, turn out to be operational reasoning answers, was confirmed. Table 2 contains the relevant data in both - 1 DQ columns and the - 1 W Expt I column. We anticipated the findings for the second hypothesis since apparent nonconservation judgments and justifications could have an underlying structure of reasoning more advanced than the intuitive struct,ure. For example, a Nobel prize-winning physicist has argued t.hat, in certain instances, nonconservation is an accept’ed empirical phenomenon (Feynman, 1965). One would clearly be reluctant to classify Feynman’s and intuitive 8s’ reasoning as equivalent on the basis that, both accept nonconservation and can justify it. It is somewhat more likely that Feynman uses a much more sophisticated structure of reasoning than an intuitive stage child. The implication of the findings from the first and second TABLE: 2 TYPES .~ND FREQUENCIES OF JUSTIFICATIONS ACCOMPANYING OPEMTTONAL JUDGMENTS -1
w
-1
DQ
-____ Types
of justifications
1. h’ added or subtracted clay (button) 2. E exchanged ball for a heavier one 3. Scale broken 4. Original balls (buttons) were not equivalent 5. Clay remained on B’s hand 6. When E performed manipulation, there were not more buttons in one of the rows 7. Moved buttons from one row to other 8. Weight concentration in ball pushed scale further down 9. Cannot explain why scale does not balance but not due to weight 10. Same weight but different shapes affect scale
Expt I ss
Expt II SS
P 7 I 1
.i 1 2
DQ
DQ,
only
L,W
13
17
2
I
1 2
2 4 1 1
1 _. .__
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hypotheses is that through probing one can obtain a clearer picture as to the structure of reasoning that Ss are using and, consequently, stage assessment can be more accurate. The third hypothesis, that -d experiences would he accepted by fewer Ss than +d experiences, was not confirmed since practically all Ss rejected both types of -1 experiences. However, when we analyzed Ss’ spontaneous reactions, a trend towards differences was found (Fisher exact p = .lO) Thirty-five percent of Ss accepted +d experiences, as opposed t,o 25% who accepted -d experiences. The relevant data can be found in Table 1. Differences can be attributed to the DQ conditions, since no Ss accepted -d while 30% accepted +d experiences. There were small differences between -d and + d conditions for W, where 50% and 40%) respectively, spontaneously accepted - 1 experiences. For DQ, this suggests that the more implausible an empirical violation of a conservation law, the more likely it is to be suspect. That this was not the case for W might be explained by the difficulty of assessing what -d or +d meant for Ss. We assumed intuitive Ss believe that the ball would be heavier than a ring, and, therefore, if the ball was surreptitiously made heavier, it was +d. However, we found in a pilot study that some intuitive Ss argued that the ring would be heavier. In our study, there was no way of determining in advance if a -1 W manipulation was +d or -d for a particular S. Consequently, the similar distribution of Ss spontaneously rejecting + d and -d treatments for weight might be a function of the distribution of “ball heavier” and “ring heavier” Ss in the treatment conditions. The data from the fourth and fifth hypotheses, that the effect of accepting -1 experiences would be short term and, for those who accepted - 1 W experiences, the effect would not generalize to other concepts, are not very meaningful since there was only one S who accepted - 1 experiences throughout the treatment condition. He accepted - 1 W and on the posttest tasks he was assessed as intuitive for weight conservation only. All other Ss, with one exception, did not change levels on the posttests. The one exception was an S who was assessed as intuitive for weight conservation on the posttest; she had spontaneously rejected - 1 W during the treatment. In the posttest., this S was assessed as intuitive for weight only on the task which was used in the treatment (ball-ring). she used the argument of nonconservation of air pressure (for the ring and not the ball) to justify her judgment. This type of reasoning was not found on the pretest. As a result, this case might have indicated the beginning of a higher-level concept which takes into account more variables. For more elaborate discussions of cases of this sort, see Werner and
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Kaplan’s (1963) discussions of t’he genetic principle of spirality and Cambon and Sinclair’s (1973) discussion of temporary “regression.” The data from the sixth hypothesis, that Ss with more elaborated structures are more likely to reject. - 1 information about DQ than W, cannot be analyzed meaningfully since only one S accepted - 1 for W and none accepted - 1 for DQ. However, if we look at Xs’ spontaneous judgments, we find significantly more Ss rejecting - 1 DQ than - 1 W (Fisher exact p = .0006). All 20 Xs spontaneously rejected -1 DQ experiences, while 11 of 20 Ss (55%) rejected -1 W experiences (see Table 1). Finally, the seventh hypothesis, that Xs with less elaborated structures would be susceptible to assimilating -1 DQ experiences, was not confirmed. None of the 20 Ss accepted -1 experiences by the end of the experimental conditions. Discussion of the sixth and seventh hypotheses will be deferred to the discussion of Expt II. EXPERIMENT
II
Due to findings from a pilot study, it was decided to examine the influence of stage consolidation on -1 W experiences. In Expt I we found Ss between 7;ll and 9;lO years of age with a mean age of &;7 able to conserve for all three conservation tasks. Experiment II Xs, who were from the same school, also conserved for all three tasks and their age range was from 11;6 to 12;9 and their mean age was 12;0. From this age difference we inferred that Ss in Expt II had more consolidated structures than those in Expt I. It was hypothesized that more Expt II than Expt I Ss would spontaneously reject - 1 W experiences. Method Twenty-five Ss who were completely concrete operational were randomly assigned to either the - 1 W + d condition or to a control group where 15 Se were in the treatment condition and 10 Ss were controls. All Ss were administered the same pre- and posttests as in Expt I. Results
alld Discussion
The major finding for the treatment condition was that all Ss did not spont.aneously produce operational judgments (see Table 1). Indeed, contrary to our expectations, only 40% produced such judgments spontaneously. This can be compared to 61% of the younger (Expt I) Xs’ spontaneous judgments. It was also found that 60% of the Ss produced spontaneous intuitive judgments as compared to 29% of the Expt I Xs. In addition, none produced no explanaticns as compared to 10% of the Expt I Ss.
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Another set of differences between Expt I and II Ss lies in their types of justifications. Six of 13 (46%) Expt II Ss who rejected - 1 argued that. E must have tricked them (justifications 1 and 2 in Table 2). Five of the same 13 Ss (38%) attempted to explain the situation as if no trick had been played and that the scale’s indications had to be explained. Their justifications were hypotheses about (a) weight concentration in the ball versus the ring and (b) different pressures on the scales due to different numbers of contact points on the pan balance which was a function of the shapes of the objects. An example of the latter type of justification was found in a child who argued t,hat the ball and ring were the same “heaviness” despite the positions of the pan balance which indicated t,hat the ball was heavier. She used the following arguments, “It’s like when I go swimming. If I’m straight up and down (analogy to the ball), I will sink but if I’m spread out (analogy to the ring’), I will float. And I didn’t change my weight.” These types of justifications accompanied operational judgments and made it clear that many Ss simply didn’t understand what the scale measures. Because the weight appeared to be different, these Ss created possible theories to explain the phenomenon. In contrast, 75% of Expt I Ss claimed that E had tricked them, and only one of 16 Ss (6%) attempted to find a possible hypothesis to explain the apparent nonconservation. Finally, the posttest was marked by the assessment of four experimental Ss as intuitive for weight only. None of the controls were assessed as intuitive. The findings from the sixth and seventh hypotheses of Expt I and from our hypothesis of Expt II provided t’he following picture: (a) 80% of Xs with less elaborated and 100% of Xs with more elaborated structures spontaneously rejected - 1 DQ experiences, and (b) older Xs who conserved through weight, were not more likely to reject, - 1 W experiences than younger Xs whose structures were elaborated to the same extent. In other words, an increase in age and structural elaboration resulted in total spontaneous rejection of - 1 DQ, while an increase in age and structural consolidation produced less spontaneous and provoked rejection of -1 W experiences. A similar pattern of findings was reported by Miller and Lipps (1973) where almost all of the younger Ss (83%) and even more of the older Ss (93%) rejected -1 empirical information for weight transitivity on a delayed posttest while only 53% and 60% of younger and older Xs, respectively, rejected - 1 W conservation experiences. This perhaps can be explained by the fact that older Xs, being more sophisticated, were able to draw upon a larger reservoir of knowledge and to generate alternative, albeit erroneous, hypotheses for the nonbalancing of the scale. The findings of the present study and those of Miller and Lipps
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(1973) can also he explained in terms of Piaget’s (1970) distinction between logicomathematical and physical concepts. The former are generalized abstractions from children’s actions upon objects, whose properties are essentially irrelevant. An example of such a concept is number. In contrast, physical concepts are abstractions about properties of objects. The emphasis here is upon extract.ing empirical information about the objects themselves, e.g., the weight of objects. This distinction becomes clearer if we compare how Ss may have interpreted -1 DQ and - 1 W experiences. In the case of DQ, the children used an internal counting or number system as a verification of nonequivalence. In contrast, the initial verification system for weight is the pan balance, which provides external, empirical information about the weight of the clay objects. When S’s who accepted - 1 W were asked for their justifications, they pointed to the pan balance as if it were selfevident that this was reason enough to explain nonconservation. This apparent difference between logicomathematical and physical concepts is complicated by the uniqueness of weight conservation among the conservation laws. Judgments about weight conservation require an inference from judgments about mass conservation. Weight is defined in physics as a relation between two objects, i.e., weight = mass X gravity. Consequent,ly, weight is a relational property of an object. The uniqueness of the weight concept can also be observed in its ontogenetic course. Children who are preoperational cannot conserve weight, while those who clre operational conserve only after they have constructed the concept of mass conservation. Yet, t,he present study found that many of these latter children apparently spontaneously accept weight nonconservation (- 1 W) at, age 8, and there is no improvement at, age 11. Dasen and Christie (1972) also reported an apparent weight “regression” phenomenon at approximately ages 10-11. In a similar vein, Miller et al. (1973) and Hall and Kingsley (1968) indicated t,hat college students are likely to accept -1 W experiences while providing sophisticated justifications to explain their nonconservation judgments. All of this attests to the complexity of the weight concept and suggests that Ss’ responses to its nonconservation may not be representative of other physical concepts. In sum, we obtained data which relate to several important issues in developmental psychology and cognition. First, it seems to be the case that Ss reject - 1 empirical experiences about nonconservation, which implies that they reject former levels of reasoning. While the presentation of one trial is insufficient to allow the claim that Ss cannot be trained to accept former levels of reasoning, the types of justifications offered for rejecting -1 experiences suggest that this rejection would continue. At the very least, this calls into question the claims based upon alternate
478
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model studies’ findings that regression had occurred. The present study’s findings support both the organismic-developmental claim of hierarchic integration of structures and the findings reported by Turiel f.1966 J and Kuhn (1972). Second, it was found that with probing questions one can provide an accurate picture of Ss’ underlying reasoning. This is especially important since we and others (Hall & Kingsley, 1968; Miller, 1973; Miller & Lipps, 1973) found that concrete operational Ss provide “sophisticated” justifications for what originally appeared to be nonconservation judgments in -1 conditions. These were not, like justifications produced by intuitive Ss when asked to justify nonconservation judgments in a standard conservation task; thus, the need for probing. Third, our evidence suggested that one can empirically distinguish between logicomathematical and physical knowledge. This stat’ement must be qualified by the unique status of the weight concept among physical concepts. Fourth, t.he above findings speak to the relations between intellectual structures and nomic necessity. Nomic necessity is distinguished from logical necessity in contemporary epistemology, and this distinction seems a useful one to make here, as well (Nagel, 1961). Logical necessity concerns propositions of the following sort: “Either it will or will not rain tomorrow.” This proposition, although logically necessary, says nothing about, whet.her or not it will rain tomorrow. Nomic necessity, which is a product of model logic, pertains to the necessity of the occurrence of physical laws in the “real” world. ,4s a consequence, empirical studies such as ours, Smedslund’s (1961), and Miller’s (1973) were concerned with nomic and not logical necessity. The results of our study combined with others’ findings suggest that logicomathematical knowledge, which is a structural product, is understood by young children as nomically necessary. Physical knowledge, which is also a structural product, may not be understood as nomically necessary in the case of weight. REFEREKCES BRISON, D. W. Acceleration of conservation of substance. Jownnl of Genetic Psychology, 1966, 109, 311-322. CAMBON, J., & SINCLAIR, H. Relations between syntax and semantics: Are they “easy to see?” Unpublished manuscript, 1973. DASEN, P. R., & CHRISTIE, R. D. A regression phenomenon in the conservation of weight. Archives de Psychologie, 1972, 41, 145-152. FEYNMAN, R. The character of physical kzz(r, Cambridge, MA: MIT Press. 1965. HALL, V. C., & KINGSLEY. R. Conservation and equilibration theory. JOTLI,& of Genetic Psychology, 1968. 113, 195-213.
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G. J. Factors influencing extinction of weight conservaQuarterly, 1968, 17, 319-334. KINGSLEY, R., & HALL, V. C. Training conservation through the use of learning Sets. Child Development, 1967, 38, 1111-1126. KUHN, D. Mechanisms of change in the development of cognitive structures. Child Development, 1972, 43, 833844. reality and identity. Cognition, 1972, 1, LANCER, J., & STRAUSS, S. Appearance, 105128. MILLER, S. A. Extinction of conservation: A methodological and theoretical analgsis. Merrill-Palmer Quarferly, 1971, 17, 319334. MILLER. 8. A. Contradiction, surprise, and cognitive change: The effects of disconfirmation of belief on conservers and nonconservers. Journal of Experimental Child Psychology, 1973, 15, 47-62. MILLER, S. A., & LIPPS, L. Extinction of conservation and transitivity of weight. Journal of Experimerctal Child Psychology, 1973, 16, 388402. MILLER, S. A., SCHWARTZ, L. C., AND STEWART, C. An attempt to extinguish conservation of weight in college students. Developmental Psychology, 1973, 8, 316. Problems in the logic of scientific explanation. NAGEL, E. The structure oj science: New York: Harcourt, Brace, and World, 1961. PIAGET, J. Piaget’s theory. In P. H. Mussen (Ed.), Carmichael’s mawal of child psychology. Sew York: Wiley, 1970. REST, J. Hierarchies of comprehension and preference in a developmental stage model of moral thinking. Unpublished doctoral dissertation, University of Chicago, 1969. REST, J.. T~RIEL, E., & KOHLBERG, I,. Level of moral development as a determinant of preference and comprehension of moral judgments made by others. JolLrnal of Personality, 1969, 37, 226252. SMEDSLUND, J. The acquisition of conservation of substance and weight in children. III. Extinction of conservation of weight acquired “normally” and by means of empirical controls on a balance scale. Scandanavian Journal of Psychology, 1961, 2, 85-87. SMEDSLUND, J. Conservation and resistance to extinction: A comment on Hall and Simpson’s article. &fed/-Palmer Quarterly, 1968, 14, 211-214. SMITH. I. D. The effects of training procedures on the acquisition of conservation of weight. Child Development, 1968, 39, 515-526. STRAUSS. S. Inducing cognitive development and learning: A review of short-term training experiments. I. The organismic-developmental approach. Cognition, 1972. 1, 329-357. STRAUSS. S.. & LANCER, J. Operational thought inducement. Child Development, 1970, 41, 163-175. SULLIVAN. E. V. Acquisition of conservation of substance through film modeling techniques. In D. W. Brison and E. V. Sullivan (Eds.), Recent research on the acquasition of conservation of substance. Ontario Institute for Studies in Education, 1967. Pp. 11-23. HALL,
V. C., & SIMPSON, tion. Merrill-Palmer
E. An experimental test the child’s moral development. 1966. 3, 611-615.
of
TURIEL,
WERNER,
H. Comparative
national WERNER,
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psychology
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the sequentialitp of Journal of Personality
of mental
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developmental and Social New
stages in Psychology, York:
1948. formafion.
NFIV
York:
Wiley,
1963.
Inter-
The
OF EXPERIMENTAL
Empirical
CHILD
Violation Relation SIDNEY
18, 464-479
PSYCHOLOGY
of
Conservation
to Structural STRAUSS Tel-Avzv
(1974)
AND
and
Its
Change1
Dov
Unived
Laws
LIBERMAN y
Concrete operational Ss were provided empirical evidence of nonconservation of discontinuous quantity and weight. The findings were that few Ss accepted this evidence. This was interpreted as supporting the organismicdevelopmental claim that lower forms of reasoning are transformed into structurally more advanced forms. It was also found t.hat (1) probing provides a more accurate assessment of Ss’ operational levels, (2) one can empirically distinguish between logicomathematical and physical knowledge, and (3) the former is understood by Ss to be nomically necessary and the latter, in the case of weight, may not be.
One of the basic tenets of organismic-developmental and structuralist theories addresses itself to the problem of directed sequential transformations of cognitive competences. Piaget (1970) has argued that structural transformation involves a qualitative reorganization to a more adaptive structure. Since a structure is transformed into a qualitatively different form, one would expect that a child would have difficulty retrieving previous forms. Consequently, this model would not predict the occurrence of regression. Experimental evidence supporting this hypothesis has been gathered in both the moral and intellectual domains. Turiel (1966) and Kuhn (1972) presented training conditions in which models provided S with reasoning one level above (+ 1)) two above ( +21, or one below ( - 1) his predominant level. It was found that being presented with a - 1 structure of reasoning did not significantly affect Ss’ reasoning. In addition, Rest (1969)) Rest, Turiel, and Kohlberg (1969)) and Kuhn (1972) presented data which suggested that Ss could comprehend -I reasoning yet they rejected it as inadequate. ‘This article is based upon an M.A. dissertation submitted by the second author to the Department of Education at Tel-Aviv University. We would like to express our appreciation to Matal-the Tel-Aviv University Elementary School Science Project-for its support, of this research. ’ Author’s address: Sidney Strauss, School of Education, Tel-Aviv University, Tel-Aviv (Ramat, Aviv), Israel. Copyright All rights
464 @ 1974 by Academic Press, Inc. of reproduction in any form reserved.
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Alternatively, other research evidence has shown considerable extinction of behaviors which are thought to be structural products; e.g., conservation concepts (Kingsley & Hall, 1967; Smith, 1968; Brison, 1966; Hall & Simpson, 1968 ; Hall & Kingsley, 1968 ; Sullivan, 1967). In summarizing their findings, Miller (1971) pointed out that conservation response extinction is ubiquitous, rather easy to obtain, and that a majority of Ss seem susceptible to such training. As Miller indicated, these studies are quite divergent and do not present LIP with a clearly formulated alternative to the structuralist model presented above. Consequently, the defining criterion of the “alternative model” presented below is t.he similar results from experiments which studied the feasibility of extinguishing conservation responses. The protot,ype alternate model experiment was conducted by Smedslund (1961). Subjects were administered an extinction procedure in which E surreptitiously removed clay from one of two objects which previously had been judged to be equivalent in weight. The results of interest for the present study were that six of 13 Xs successfully resisted extinction, which was defined as occurring when S suggested that clay was added or subtracted during the deformation. These alternate model experiments can be interpreted as being - 1 studies, since conserving Ss were shown empirical evidence of nonconservation. That is, concrete operational Ss saw empirical evidence which embodied a form of reasoning they had used in the ontogenetically prior intuitive stage. The discrepancy between the findings reported by investigators within the organismic-developmental model (i.e., no regression) and the alternate model (i.e., ubiquitous extinction) has been discussed elsewhere (Strauss, 1972) and served as a motivation for the following two experiments. EXPERIMENT
I
There are two types of issues which bear on the discrepancy just described: methodological and theoretical. The first methodological issue which could explain the discrepant findings was raised by Smedslund (1968)) where he argued that the use of probing questions would more accurately identify Ss who revert to the previous structure. Consequently, we hypothesized that., if one probed further into 8s reasoning about nonconservation, fewer Ss would be identified as having reverted to a previous stage. The second methodological issue concerns the criteria one uses in determining the acceptance or rejection of -1 experiences. With the possible exception of the Miller-Schwartz-Stewart (1973) study, only
466
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two answers were accepted as adequate indicators of the rejection of nonconservation: The scale was broken or some material was added to or subtracted from one of the objects. We hypot,hesieed that if one probed for reasoning underlying other judgments, evidence of rejection of nonconservation experiences would be found. The third methodological issue pertains to the acceptability of some, but not all, - 1 experiences. We hypothesized that more - 1 experiences against the direction of expectation (-cl) would be rejected than those in the direction of expectation (+d). The definition of -d and +d is relative to intuit.ive reasoning and can be illustrated with a discontinuous quantity conservation example. Intuitive Ss, when presented with such a problem, argue that the row which is spread out contains more objects. If in the - 1 experience we were to surreptitiously add an object to the longer row, the result would provide empirical evidence in the direction of expectation of an intuitive S ( +d) . Conversely, adding an object to the shorter row would be against an intuitive S’s direction of expectation ( -d) . The final methodological issue concerns the short term versus long term and generality of regression. Hall and Simpson (1968)) Miller and Lipps (19731, and Smit’h (1968) provided delayed posttest measures of long-term cognitive change, while Miller (1973 1 provided posttest, measures immediately after the - 1 experiences. In the remaining studies cited above, the acceptance or rejection of -1 experiences was determined only during the t’reat,ment condition. We hypothesized that the acceptance of - 1 experiences during the treatment condition would be short term. With respect to generalization, in the three cases where delayed posttests were used, the concept assessed on the posttest was the same concept. as in the treatment condition. In the present study, the generality of nonconservation judgments after the treatment conditions was tested by administering posttests for several conservation concepts. It was hypothesized that Ss who accepted - 1 experiences for one concept would not generalize this to the others. The theoretical argument concerns structural elaboration and its relation to the level of the concept being presented. We hypot.hesized that a relatively more elaborated structure (one which is being applied to discontinuous quantity, length, and weight concepts’) is less susceptible to - 1 experience at its lower limits (i.e., with discontinuous quantity conservation) than at its upper limits (i.e., weight). Similarly, we hypothesized t’hat a relatively less elaborated structure-one which is applied to discontinuous quantity only-is susceptible to assimilating - 1 experiences at its own level or upper limits of it,s application, i.e., for discontinuous quantity conservation.
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Method There were three phases to the research: posttest phases.
the pretest,
treatment,
and
Pretest All Ss were tested for the understanding of the terms “more,” “less,” and LLsame” for discontinuous quantity and weight and “longer,” “shorter,” and “same” for length (see Langer & Strauss, 1972, for a description of these tasks). Subjects who did not understand these terms were eliminated from the experiment,. Those who understood these terms were administered conservation of discontinuous quantity, length, and weight problems. (A balance scale was used when administering the weight conservation t,asks, and Ss were trained in the use of the balance scale.) Each S received two items per conservation toncept. We shall present an example of one discontinuous quantity conservation item as an illustration of the general procedure: (a) Two perfectly aligned rows of five identical buttons in parallel formation were presented to S for ordinal comparison. (b) As S watched, the buttons in one row were compressed in order to deform the spatial alignment. (c) The S was asked to judge whether or not there were the same number of buttons in the two rows. (d) The S was asked to justify his judgment. (e) A verbal countersuggestion, varying according to whether or not S judged equivalence, was offered: “Someone before told me that this one had more (they were the same) because it sticks out farther (they were the same before). Do you think that’s right or are they the same (is this one more) ?” Parts (c) and (d) will henceforth be referred to as the standard question. The types of deformations for the two items per concept were as follows: (i) For one item in discontinuous quantity, one row was compressed while, in the second it,em, one row was expanded. (ii) For one item in length, one of two parallel sticks in an ends aligned configuration was moved so that the ends were no longer aligned but the parallel arrangement was maintained; in the second item, one of the sticks was deformed into a V shape. (iii) For one weight item, one of t,wo equivalentweight clay balls was deformed into a ring while in the second item one of the balls was broken up into five balls. The three forms of deformation (discontinuous quantity, length, and weight) and the two items of each form permitted the following assessment of each S’s structural profile. For each test item the scoring resulted in one of two st,age assessments: (a) intuitive-marked by two
468
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behavioral features: an equal or unequal judgment and no ability to produce at least one logical operational reason (e.g., identity, compensation, or reversibility justifications) for the judgment; and (b) concrete operational-marked by three behavioral features: an equal judgment, a logical operational reason, and resistance to the countersuggestion. The cumulative score for two items within a concept also yielded two stage assessments: (a) intuitive-& who were intuitive on both test items, and (b) concrete operational-L% who were concrete operational on both test items. The only Ss included in the study were those who were pretested as (i) concrete operational on the cumulative score for discontinuous quantity and intuitive for the remaining tasks, and (ii) concrete operational on the cumulative score for all three concepts. Treatment
Conditions
According to S’s pretest structural profile, he was randomly assigned to a condition. Subjects who were pretested as concrete operational for discontinuous quantity only were randomly assigned to either a control group (in which Ss were administered pre- and posttests without any intervening training) or to one of two - 1 conditions: (a) discontinuous quantity +d or (b) discontinuous quantity -d. Subjects pretested as concrete operational for all of the concepts were randomly assigned to either a control group or to one of four - 1 conditions: (a) discontinuous quantity +d, (b) discontinuous quantity -d, (c) weight +d, and (d) weight -d. The discontinuous quantity and weight conditions contained three and five sections, respectively. The procedure was terminated at. the end of the section in which S rejected the - 1 experience (i.e., maintained weight or discontinuous quantity equivalence). For purposes of elucidation, we shall first describe the - 1 weight conditions. A. -1 weight +d. Section 1: E manipulated. (a) The S was presented with two balls of clay which were equivalent in weight. (b) The balls were placed on opposite sides of a pan balance scale and an equivalence judgment was obtained. (c) The balls were then taken off the balance. The experimenter deformed one of them into a ring shape and surreptitiously removed clay from t,he ring. (d) The standard question (SQ) was asked. (e) The subject was then told that the ball and ring would be placed on the pan balance scale and was asked to indicate where the weight indicator would be. (f) The experimenter then placed the ball and ring on the balance scale and asked, “What did we find?” (g) After S indicated weight nonequivalence, E asked, “How do you explain this?” (h) For those Ss who said that the ball weighs more,
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because the pointer indicated so, E asked, “But why does it weigh more now?” (i) If S said that E had added or subtracted clay, or that E had exchanged that ball for a heavier one, E asked, ‘(HOW do you know? Did you see me add (subtract) clay (exchange balls?) ” (j ) If S said that, the scale was broken, E asked, “If I fixed the scale, where would the pointer be?” (k) The subject was asked to justify his judgment. If S maintained that the ball and ring should weigh the same, the training was terminated. If this argument was not produced, the training continued. Section 2: S gave heaviness judgments. At this point a terminological change was int.roduced. Based upon findings in a pilot study, S’s were asked about the heaviness of the clay ball and ring. Previously, Ss had been asked about their weight. (a) The experimenter asked, “Are these t,wo the same heaviness or is one heavier?” (1~) The subject was then asked to justify his judgment. (c) The experimenter then posed the following situation, ‘Suppose I would take this ball and put it on a regular (bathroom) scale and I find out that. it weighs 50 g. Now I’ll take it off and put the ring on the same scale. Will the ring weigh less than 50 g, 50 g, or more than 50 g?” (d) If S said that the ring is the same heaviness as the ball and/or that the ring would weigh 50 g, he was asked to explain why the balance scale indicated that the ball weighed more, and the training was terminated. For Ss who argued that the ball and ring were not equivalent in heaviness, the training continued to Section 3. Section 3: E showed contradiction. (a) The experimenter told S, “A couple of minutes ago (in the pretest) you said that they should weigh the same because . . . (E provided S with his previous justification for equivalence). Now you say that the ball should weigh more. Which do you think is really right?” (b) If S said that he was correct before (i.e., that they should be equivalent in weight), he was asked, “Then how do you explain that the point.er leans to the side of the ball?” If S gave a correct answer, the training was terminated. (c) If X said that he had been wrong before, or provided no explanation, the training continued to Section 4. SeeCon 4: X predicted and manipulated. (a) The experimenter said, “Let’s play again.” (b) The experimenter then presented S with two new clay balls which were equivalent in weight. The balls were put on the pan balance scale and an equivalence judgment was obtained. (c) The subject. was then told, “Now it’s your turn. I would like you to make a ring out of one of the balls just as I did.” (d) Before X did this, E asked, “After you finish, do you think that one will weigh more than the other or that they will weigh the same?” (e) The experimenter then
470
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asked for a justification. (f) If S said that they will weigh the same, he was asked, ‘(How do you explain that when I played, the indicator went to the side of the ball?” Both this type of S and Ss who predicted that they would not weigh the same continued. (g) The subject S then deformed one of the balls into a ring. (11) The standard question was asked. (i) If S said that they weighed the same, he was asked, “How do you explain that when I played the game, the ball weighed more?” The training was then terminated. Section 5: S observed equivalence of weight. (a) If S said that one of the pieces weighed more, he was asked to indicate both the side to which the pointer would go and the levels of the pans when t,he ball and ring would be placed on opposite sides of the scale. (b) The ball and ring were then placed on the scale and S observed that the pointer indicated equality. The experimenter asked, “What do you see?” (c) The experimenter asked, “How do you explain that when I played the game the pointer moved to the side of the ball and now it moved to the center?” B. - 1 weight -d. This training procedure was identical to the procedure described above except that E surreptitiously added, rather than removed, clay to t,he ring. C. - 1 discontinuous quantity +d and -d. These treatment conditions followed the same format as the - 1 weight conditions for three sections, which were present.ed in t.he following order: (1) E manipulated, (2) E showed contradiction, and (3) S predicted and manipulated. The manipulations for the +d condition were stretching out and surreptitiously adding a button to the longer row. As both rows initially had five buttons each, the longer row had six buttons after the manipulation. For the -d condition, the manipulation involved compressing one row and adding to it so that the shorter row would have more buttons. Posttests The posttests were administered 2 weeks to 1 month after the treatment conditions. They were identical to the pretests except that no balance scale was used in the weight, conservation tasks. The experimenters were unaware as to the treatment. condition to which Ss had been assigned. Subjects The Xs were predominantly middle class from mixed suburban areas in and around the city of Netanya, ranges and mean ages for the different groups were as who conserved for DQ only: (a) DQ + d, 4;10-7;0, DQ - d, 5;4-6;9, a = 6;0, (c) control, 5;2-6;1, x
urban, Israel. follows. J?Y= = 5;7.
rural, and The age For those 5;11, (b) For those
COK’SERVATION
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who conserved through weight: (a) W + d, 7;11-9;4, x = 8;6, (b) W - d,8;2-9;10, x = 8;9, (c) DQ + d, 8;4-9;4, z = 8;10, (d) DQ - d, 8;7-9;4, a= 9;0, (e) control, 8;&9;4, 2 = 8;lO. A total of 151 Ss were administered the pretest. Of these, 71 Ss were eliminated from the study. Two were eliminated due to failure to understand terms, 31 Ss for not having conserved on DQ, and 38 Xs for having conserved on DQ and L but not W. Eighty Ss remained in the experiment. Ten Ss were assigned to each of the six treatment or two control groups.
Results and Discussion Before analyzing the data relevant t.o the above hypotheses, we shall first determine the adequacy of the deceptions involved in the surreptitious addition or removal of clay (for - 1 W) and addition of a button (for - 1 DQ). This can be measured at two points in the procedure. The first point occurred immediately after the deceptive deformat.ion in Treatment Section 1. If, after the surreptitious addition or removal, S judged weight or number equivalence, it could be safely argued that he did not observe the deception. This occurred for all Ss in the - 1 W conditions and for 22 of 40 Ss in the - 1 DQ conditions. The second point in the procedure in the above determination occurred for the remaining 18 Ss in the - 1 DQ conditions, all of whom argued that E must have added a button. Of these Ss, (a) 11 said that t.hey did not see E add a button. (b) Six said that they saw E add a button to one row by taking a button from a surplus pile and adding it to the row that had more; however, when asked where the button had been placed, all Ss pointed to the end of the row closest to the surplus pile, which was not the end to which E had added. (c) Only one S reported the decept.ion as it had occurred (i.e., E held a button in his hand and added it to one of the rows) ; but subsequent questioning indicated that this was a guess and not an observation on S’s part. Having established the adequacy of the deceptions, we can now proceed to the hypotheses. The first hypothesis, that probing would reduce the number of Ss identified as accepting -1 experiences, was confirmed. Data relevant to this hypothesis can be found in Table 1. The results were that (a) in the - 1 DQ + d condition, all three Ss who would have been assessed as intuitive without probing were assessed as operational by the end of the treatment condition. (b) Of the four intuitive Ss in the -1 W + d condition, two produced operational judgments, one remained intuitive, and one could not produce any explanations for the phenomena. (c) Of the three intuit.ive Ss in the - 1 W - d condition, one produced operational judgments and t,wo provided no answers. The no-explanations category for DQ Ss was rvidence of concrete
472
STRAUSS
FREQUENCY
Treatment sections
OF TYPES
Operational
TABLE OF JUDGMENTS OF THE: TRAINING
No explanations
Intuitive
AND
Operational
LIBERMAN
1 PRODIJCKD I~RING CONDITIONS No explanations
Int,uit,ive Experiment,
-1 1. Before After 2. After 3. After
DQ
10 7 8 10
+da 0 3 2 0
-1 0 0 0 0
10 9 9 9
Experiment
DQ
Operational -.-___
SFXTION
-da 0 0 0 0
-1 0 1 1 1
DQ
+d
20 2oc
and
W -d*
-Q
0 0
Experiment -1
No expla nations
Intuitive
I
I
-lW+db
EACH
0 0
II
-1WfdA
1. Before Afkr 2. After 3. After 4. After 5. After
10 G 7 8 8 8
0 4 3 2 2 1
0 0 0 0 0 1
10 5 5 G 7 8
0 3 3 3 2 0
u Subjects b Subjects c Training point.
who were operational for DQ only. who were fully operat,ional. was terminated for all Ss after Section
0 2 2 1 1 2
15 6 7 11 11 11
1, since all rejected
0 9 5 4 4 1
-1
0 0 3 0 0 3
DQ at that
operational reasoning, since all of these Ss, without explanation, maintained that there should be equivalence and predicted equivalence in the next section. In contrast, t,he no explanations category for W Ss was evidence of intuitive reasoning since they maintained that nonequivalence should have occurred yet had no explanation when it did occur. They also predicted nonequivalence in the next section. Consequently, the DQ and W no-explanations categories could not be combined. It was found that a significant number of the above-mentioned Xs who would have been assessed as intuitive at the end of Section 1 produced operational reasoning during probing (binomial test N = 6; 9 = 0; p = .016). It was also found that more DQ than W treatment Ss changed to operational judgments during the treatment (Fisher exact p = .OlSj . Here we have seen that the rejection of empirical nonconservation was
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almost complete when taking into account both Ss’ spontaneous (Section 1) and elicited (other sections) judgments. An interesting point is that the percentage of Ss spontaneously rejecting -1 W after Section 1 in the present study (55%) was similar to Smedslund’s (1961) findings (46%). The end of Section 1 in our study was procedurally similar to Smedslund’s entire study. The second hypothesis, that reasons other than addition/subtraction or a broken scale would, when probed, turn out to be operational reasoning answers, was confirmed. Table 2 contains the relevant data in both - 1 DQ columns and the - 1 W Expt I column. We anticipated the findings for the second hypothesis since apparent nonconservation judgments and justifications could have an underlying structure of reasoning more advanced than the intuitive struct,ure. For example, a Nobel prize-winning physicist has argued t.hat, in certain instances, nonconservation is an accept’ed empirical phenomenon (Feynman, 1965). One would clearly be reluctant to classify Feynman’s and intuitive 8s’ reasoning as equivalent on the basis that, both accept nonconservation and can justify it. It is somewhat more likely that Feynman uses a much more sophisticated structure of reasoning than an intuitive stage child. The implication of the findings from the first and second TABLE: 2 TYPES .~ND FREQUENCIES OF JUSTIFICATIONS ACCOMPANYING OPEMTTONAL JUDGMENTS -1
w
-1
DQ
-____ Types
of justifications
1. h’ added or subtracted clay (button) 2. E exchanged ball for a heavier one 3. Scale broken 4. Original balls (buttons) were not equivalent 5. Clay remained on B’s hand 6. When E performed manipulation, there were not more buttons in one of the rows 7. Moved buttons from one row to other 8. Weight concentration in ball pushed scale further down 9. Cannot explain why scale does not balance but not due to weight 10. Same weight but different shapes affect scale
Expt I ss
Expt II SS
P 7 I 1
.i 1 2
DQ
DQ,
only
L,W
13
17
2
I
1 2
2 4 1 1
1 _. .__
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STRAUSS
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hypotheses is that through probing one can obtain a clearer picture as to the structure of reasoning that Ss are using and, consequently, stage assessment can be more accurate. The third hypothesis, that -d experiences would he accepted by fewer Ss than +d experiences, was not confirmed since practically all Ss rejected both types of -1 experiences. However, when we analyzed Ss’ spontaneous reactions, a trend towards differences was found (Fisher exact p = .lO) Thirty-five percent of Ss accepted +d experiences, as opposed t,o 25% who accepted -d experiences. The relevant data can be found in Table 1. Differences can be attributed to the DQ conditions, since no Ss accepted -d while 30% accepted +d experiences. There were small differences between -d and + d conditions for W, where 50% and 40%) respectively, spontaneously accepted - 1 experiences. For DQ, this suggests that the more implausible an empirical violation of a conservation law, the more likely it is to be suspect. That this was not the case for W might be explained by the difficulty of assessing what -d or +d meant for Ss. We assumed intuitive Ss believe that the ball would be heavier than a ring, and, therefore, if the ball was surreptitiously made heavier, it was +d. However, we found in a pilot study that some intuitive Ss argued that the ring would be heavier. In our study, there was no way of determining in advance if a -1 W manipulation was +d or -d for a particular S. Consequently, the similar distribution of Ss spontaneously rejecting + d and -d treatments for weight might be a function of the distribution of “ball heavier” and “ring heavier” Ss in the treatment conditions. The data from the fourth and fifth hypotheses, that the effect of accepting -1 experiences would be short term and, for those who accepted - 1 W experiences, the effect would not generalize to other concepts, are not very meaningful since there was only one S who accepted - 1 experiences throughout the treatment condition. He accepted - 1 W and on the posttest tasks he was assessed as intuitive for weight conservation only. All other Ss, with one exception, did not change levels on the posttests. The one exception was an S who was assessed as intuitive for weight conservation on the posttest; she had spontaneously rejected - 1 W during the treatment. In the posttest., this S was assessed as intuitive for weight only on the task which was used in the treatment (ball-ring). she used the argument of nonconservation of air pressure (for the ring and not the ball) to justify her judgment. This type of reasoning was not found on the pretest. As a result, this case might have indicated the beginning of a higher-level concept which takes into account more variables. For more elaborate discussions of cases of this sort, see Werner and
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Kaplan’s (1963) discussions of t’he genetic principle of spirality and Cambon and Sinclair’s (1973) discussion of temporary “regression.” The data from the sixth hypothesis, that Ss with more elaborated structures are more likely to reject. - 1 information about DQ than W, cannot be analyzed meaningfully since only one S accepted - 1 for W and none accepted - 1 for DQ. However, if we look at Xs’ spontaneous judgments, we find significantly more Ss rejecting - 1 DQ than - 1 W (Fisher exact p = .0006). All 20 Xs spontaneously rejected -1 DQ experiences, while 11 of 20 Ss (55%) rejected -1 W experiences (see Table 1). Finally, the seventh hypothesis, that Xs with less elaborated structures would be susceptible to assimilating -1 DQ experiences, was not confirmed. None of the 20 Ss accepted -1 experiences by the end of the experimental conditions. Discussion of the sixth and seventh hypotheses will be deferred to the discussion of Expt II. EXPERIMENT
II
Due to findings from a pilot study, it was decided to examine the influence of stage consolidation on -1 W experiences. In Expt I we found Ss between 7;ll and 9;lO years of age with a mean age of &;7 able to conserve for all three conservation tasks. Experiment II Xs, who were from the same school, also conserved for all three tasks and their age range was from 11;6 to 12;9 and their mean age was 12;0. From this age difference we inferred that Ss in Expt II had more consolidated structures than those in Expt I. It was hypothesized that more Expt II than Expt I Ss would spontaneously reject - 1 W experiences. Method Twenty-five Ss who were completely concrete operational were randomly assigned to either the - 1 W + d condition or to a control group where 15 Se were in the treatment condition and 10 Ss were controls. All Ss were administered the same pre- and posttests as in Expt I. Results
alld Discussion
The major finding for the treatment condition was that all Ss did not spont.aneously produce operational judgments (see Table 1). Indeed, contrary to our expectations, only 40% produced such judgments spontaneously. This can be compared to 61% of the younger (Expt I) Xs’ spontaneous judgments. It was also found that 60% of the Ss produced spontaneous intuitive judgments as compared to 29% of the Expt I Xs. In addition, none produced no explanaticns as compared to 10% of the Expt I Ss.
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Another set of differences between Expt I and II Ss lies in their types of justifications. Six of 13 (46%) Expt II Ss who rejected - 1 argued that. E must have tricked them (justifications 1 and 2 in Table 2). Five of the same 13 Ss (38%) attempted to explain the situation as if no trick had been played and that the scale’s indications had to be explained. Their justifications were hypotheses about (a) weight concentration in the ball versus the ring and (b) different pressures on the scales due to different numbers of contact points on the pan balance which was a function of the shapes of the objects. An example of the latter type of justification was found in a child who argued t,hat the ball and ring were the same “heaviness” despite the positions of the pan balance which indicated t,hat the ball was heavier. She used the following arguments, “It’s like when I go swimming. If I’m straight up and down (analogy to the ball), I will sink but if I’m spread out (analogy to the ring’), I will float. And I didn’t change my weight.” These types of justifications accompanied operational judgments and made it clear that many Ss simply didn’t understand what the scale measures. Because the weight appeared to be different, these Ss created possible theories to explain the phenomenon. In contrast, 75% of Expt I Ss claimed that E had tricked them, and only one of 16 Ss (6%) attempted to find a possible hypothesis to explain the apparent nonconservation. Finally, the posttest was marked by the assessment of four experimental Ss as intuitive for weight only. None of the controls were assessed as intuitive. The findings from the sixth and seventh hypotheses of Expt I and from our hypothesis of Expt II provided t’he following picture: (a) 80% of Xs with less elaborated and 100% of Xs with more elaborated structures spontaneously rejected - 1 DQ experiences, and (b) older Xs who conserved through weight, were not more likely to reject, - 1 W experiences than younger Xs whose structures were elaborated to the same extent. In other words, an increase in age and structural elaboration resulted in total spontaneous rejection of - 1 DQ, while an increase in age and structural consolidation produced less spontaneous and provoked rejection of -1 W experiences. A similar pattern of findings was reported by Miller and Lipps (1973) where almost all of the younger Ss (83%) and even more of the older Ss (93%) rejected -1 empirical information for weight transitivity on a delayed posttest while only 53% and 60% of younger and older Xs, respectively, rejected - 1 W conservation experiences. This perhaps can be explained by the fact that older Xs, being more sophisticated, were able to draw upon a larger reservoir of knowledge and to generate alternative, albeit erroneous, hypotheses for the nonbalancing of the scale. The findings of the present study and those of Miller and Lipps
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(1973) can also he explained in terms of Piaget’s (1970) distinction between logicomathematical and physical concepts. The former are generalized abstractions from children’s actions upon objects, whose properties are essentially irrelevant. An example of such a concept is number. In contrast, physical concepts are abstractions about properties of objects. The emphasis here is upon extract.ing empirical information about the objects themselves, e.g., the weight of objects. This distinction becomes clearer if we compare how Ss may have interpreted -1 DQ and - 1 W experiences. In the case of DQ, the children used an internal counting or number system as a verification of nonequivalence. In contrast, the initial verification system for weight is the pan balance, which provides external, empirical information about the weight of the clay objects. When S’s who accepted - 1 W were asked for their justifications, they pointed to the pan balance as if it were selfevident that this was reason enough to explain nonconservation. This apparent difference between logicomathematical and physical concepts is complicated by the uniqueness of weight conservation among the conservation laws. Judgments about weight conservation require an inference from judgments about mass conservation. Weight is defined in physics as a relation between two objects, i.e., weight = mass X gravity. Consequent,ly, weight is a relational property of an object. The uniqueness of the weight concept can also be observed in its ontogenetic course. Children who are preoperational cannot conserve weight, while those who clre operational conserve only after they have constructed the concept of mass conservation. Yet, t,he present study found that many of these latter children apparently spontaneously accept weight nonconservation (- 1 W) at, age 8, and there is no improvement at, age 11. Dasen and Christie (1972) also reported an apparent weight “regression” phenomenon at approximately ages 10-11. In a similar vein, Miller et al. (1973) and Hall and Kingsley (1968) indicated t,hat college students are likely to accept -1 W experiences while providing sophisticated justifications to explain their nonconservation judgments. All of this attests to the complexity of the weight concept and suggests that Ss’ responses to its nonconservation may not be representative of other physical concepts. In sum, we obtained data which relate to several important issues in developmental psychology and cognition. First, it seems to be the case that Ss reject - 1 empirical experiences about nonconservation, which implies that they reject former levels of reasoning. While the presentation of one trial is insufficient to allow the claim that Ss cannot be trained to accept former levels of reasoning, the types of justifications offered for rejecting -1 experiences suggest that this rejection would continue. At the very least, this calls into question the claims based upon alternate
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model studies’ findings that regression had occurred. The present study’s findings support both the organismic-developmental claim of hierarchic integration of structures and the findings reported by Turiel f.1966 J and Kuhn (1972). Second, it was found that with probing questions one can provide an accurate picture of Ss’ underlying reasoning. This is especially important since we and others (Hall & Kingsley, 1968; Miller, 1973; Miller & Lipps, 1973) found that concrete operational Ss provide “sophisticated” justifications for what originally appeared to be nonconservation judgments in -1 conditions. These were not, like justifications produced by intuitive Ss when asked to justify nonconservation judgments in a standard conservation task; thus, the need for probing. Third, our evidence suggested that one can empirically distinguish between logicomathematical and physical knowledge. This stat’ement must be qualified by the unique status of the weight concept among physical concepts. Fourth, t.he above findings speak to the relations between intellectual structures and nomic necessity. Nomic necessity is distinguished from logical necessity in contemporary epistemology, and this distinction seems a useful one to make here, as well (Nagel, 1961). Logical necessity concerns propositions of the following sort: “Either it will or will not rain tomorrow.” This proposition, although logically necessary, says nothing about, whet.her or not it will rain tomorrow. Nomic necessity, which is a product of model logic, pertains to the necessity of the occurrence of physical laws in the “real” world. ,4s a consequence, empirical studies such as ours, Smedslund’s (1961), and Miller’s (1973) were concerned with nomic and not logical necessity. The results of our study combined with others’ findings suggest that logicomathematical knowledge, which is a structural product, is understood by young children as nomically necessary. Physical knowledge, which is also a structural product, may not be understood as nomically necessary in the case of weight. REFEREKCES BRISON, D. W. Acceleration of conservation of substance. Jownnl of Genetic Psychology, 1966, 109, 311-322. CAMBON, J., & SINCLAIR, H. Relations between syntax and semantics: Are they “easy to see?” Unpublished manuscript, 1973. DASEN, P. R., & CHRISTIE, R. D. A regression phenomenon in the conservation of weight. Archives de Psychologie, 1972, 41, 145-152. FEYNMAN, R. The character of physical kzz(r, Cambridge, MA: MIT Press. 1965. HALL, V. C., & KINGSLEY. R. Conservation and equilibration theory. JOTLI,& of Genetic Psychology, 1968. 113, 195-213.
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G. J. Factors influencing extinction of weight conservaQuarterly, 1968, 17, 319-334. KINGSLEY, R., & HALL, V. C. Training conservation through the use of learning Sets. Child Development, 1967, 38, 1111-1126. KUHN, D. Mechanisms of change in the development of cognitive structures. Child Development, 1972, 43, 833844. reality and identity. Cognition, 1972, 1, LANCER, J., & STRAUSS, S. Appearance, 105128. MILLER, S. A. Extinction of conservation: A methodological and theoretical analgsis. Merrill-Palmer Quarferly, 1971, 17, 319334. MILLER. 8. A. Contradiction, surprise, and cognitive change: The effects of disconfirmation of belief on conservers and nonconservers. Journal of Experimental Child Psychology, 1973, 15, 47-62. MILLER, S. A., & LIPPS, L. Extinction of conservation and transitivity of weight. Journal of Experimerctal Child Psychology, 1973, 16, 388402. MILLER, S. A., SCHWARTZ, L. C., AND STEWART, C. An attempt to extinguish conservation of weight in college students. Developmental Psychology, 1973, 8, 316. Problems in the logic of scientific explanation. NAGEL, E. The structure oj science: New York: Harcourt, Brace, and World, 1961. PIAGET, J. Piaget’s theory. In P. H. Mussen (Ed.), Carmichael’s mawal of child psychology. Sew York: Wiley, 1970. REST, J. Hierarchies of comprehension and preference in a developmental stage model of moral thinking. Unpublished doctoral dissertation, University of Chicago, 1969. REST, J.. T~RIEL, E., & KOHLBERG, I,. Level of moral development as a determinant of preference and comprehension of moral judgments made by others. JolLrnal of Personality, 1969, 37, 226252. SMEDSLUND, J. The acquisition of conservation of substance and weight in children. III. Extinction of conservation of weight acquired “normally” and by means of empirical controls on a balance scale. Scandanavian Journal of Psychology, 1961, 2, 85-87. SMEDSLUND, J. Conservation and resistance to extinction: A comment on Hall and Simpson’s article. &fed/-Palmer Quarterly, 1968, 14, 211-214. SMITH. I. D. The effects of training procedures on the acquisition of conservation of weight. Child Development, 1968, 39, 515-526. STRAUSS. S. Inducing cognitive development and learning: A review of short-term training experiments. I. The organismic-developmental approach. Cognition, 1972. 1, 329-357. STRAUSS. S.. & LANCER, J. Operational thought inducement. Child Development, 1970, 41, 163-175. SULLIVAN. E. V. Acquisition of conservation of substance through film modeling techniques. In D. W. Brison and E. V. Sullivan (Eds.), Recent research on the acquasition of conservation of substance. Ontario Institute for Studies in Education, 1967. Pp. 11-23. HALL,
V. C., & SIMPSON, tion. Merrill-Palmer
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