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Conservation training in four-year-old children
JOURNAI.
OF EXPERIMENTAL
Conservation NANCY
CHILD
PSYCHOLOGY
Training
24, 129- 146 (1977)
in Four-Year-Old
WADSWORTH DENNEY, SEZEN AND S. CLAIRE SELZER Unil,ersity
Children
ZEYTINOGLU.
of‘k’onsas
In Experiment I two training procedures were used to teach four-year-olds to conserve. Verbal rule instruction consisted of providing verbal rules and demonstrations of the operations referred to by the rules. Feedback consisted of providing verbal feedback contingent upon the children’s responses. One week after training on conservation of number and length the children were given a posttest which included tests of conservation of number, length, and mass. Children who were given verbal rule instruction conserved significantly more on the number and length posttest problems than children who were not. However, this learning did not transfer to the mass problems. possibly because mass is not naturally acquired until some time after conservation of number and length. The feedback training procedure had no effect on conservation performance. In Experiment 2, the verbal rule instruction procedure was used to train four-year-olds on conservation of length and mass. One week after training the children were tested on both conservation of number, which is typically acquired before length and mass, and conservation of weight, which is typically acquired after length and mass, as well as on conservation of length and mass. Children who were given training conserved more on all four types of problems than children in the control group.
A number of investigators have attempted to teach nonconserving children to conserve. With some exceptions (e.g., Bucher & Schneider. 1973; Emrick, 1969; Rosenthal & Zimmerman, 19721, the children in most of the successful studies have been close to five years old or older. The purpose of the present research was to teach four-year-old children to conserve. In Experiment 1 the relative efficacy of two training procedures was investigated. One of them, the verbal rule instruction procedure, consisted of providing the children with verbal rules and demonstrations of the operations referred to by the rules. The other, the feedback procedure, involved providing the children with verbal feedback contingent upon their responses to conservation problems. A review of the conservation training literature reveals that, with some exceptions (e.g., Mermelstein & Meyer, 1969), verbal rule instrucExperiment I is based on a Master’s Thesis submitted by Sezen Zeytinoglu to the Department of Psychology at the University of Kansas. Requests for reprints should be sent to Nancy W. Denney. Department of Psychology. University of Kansas. Lawrence, Kan. 66045.
130
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tion training procedures usually have led to improved conservation behavior in children who are within the age range of five to seven (e.g., Beilin, 1971: Peters, 1970; Rosenthal & Zimmerman, 1972: Siegler & Liebert, 1972; Smith, 1968). Feedback procedures have also been widely employed in attempts to teach nonconservers to conserve. Some of these attempts have been successful in leading to improved conservation behavior(e.g.. Brainerd, 1974: Bucher& Schneider, 1973; Emrick, 1969: Gelman, 1969: Kinsley & Hall, 1967: Siegler & Liebert, 1972) while others have not (e.g.. Beilin. 1965: Christie & Smothergill. 1970: Smith. 1968). The rules for the verbal rule instruction condition were adapted from Beilin (1965). In Beilin’s procedure, although the rules referred to reversibility and addition/subtraction operations, only reversibility was actually demonstrated to the children. However. in the present research both addition/subtraction problems and standard conservation problems were presented along with the relevant rules. The feedback procedure employed in Experiment 1 was patterned after Gelman’s (1969) requirements of (a) systematically varying the irrelevant stimuli, and (b) feedback to inform the subjects of the conservation-relevant dimensions. Gelman claims that young children’s failure to conserve on classical conservation tasks is due to their attending to the irrelevant and ignoring the relevant attributes of the stimulus display. If this is the case, then giving feedback on conservation problems in which the irrelevant dimensions are varied on successive problems should force the subjects to attend to the relevant dimensions and thereby conserve. In Experiment 1, number and length problems were alternated to inform the subjects what quantity dimension was relevant to the particular conservation task. Furthermore, it was assumed that the alternated presentation of addition/subtraction problems and standard conservation problems would inform the children of the types of transformations that do and do not affect the relevant quantity dimension. EXPERIMENT
1
Method
The participants were 20 male and 20 female white. middle-class children between the ages of 4 years, 0 months and 4 years, 10 months. The children ranged in age from 4 years, 0 months to 4 years, 11 months. The mean age of the total sample was 4 years, 6 months. The children were selected from nursery schools and day-care centers in Lawrence, Olathe, and Kansas City, Kansas. The children were tested and trained individually by a 23-year-old, white female.
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Procedure
The study consisted of three phases: (a) a pretest for conservation of number, length, and mass, (b) a training session involving conservation of number and length, and (c) a posttest for conservation of number, length, and mass. Pretest. The pretest consisted of three subtests: one for conservation of number, one for conservation of length, and one for conservation of mass, in that order. Each subtest included two conservation problems. The materials used were two rows of five checkers (for the number conservation problems), two 12-in. strips of cardboard (for the length conservation problems), and two round balls of Plasticine (for the mass conservation problems). Each child was seated at a table directly opposite the experimenter and was told that he was going to play a number of games with the experimenter. At the start of each problem, the two stimuli were presented so that they were both perceptually and quantitatively equal. That is, the two rows of checkers were placed in one-to-one correspondence, the two strips of cardboard were placed side-by-side on a vertical plane with their ends matching, and the clay was shaped into two equal round balls. Then the child was asked if the two stimuli had the same or a different amount of the relevant attribute (number, length, or mass). Stimuli were changed until the child agreed that they were equal. Then the experimenter rearranged or altered the form of one of the two objects. The rearrangement only disturbed the perceptual equality, not the quantitative equality. For example, in a number conservation problem one of the rows was spread to look longer than the other row: in a length conservation problem one cardboard was placed perpendicular to the other one; and in a mass conservation problem one of the balls was made into a sausage shape while the other remained in a ball shape. The experimenter then questioned the child regarding the equivalence of the two stimuli. For the number conservation problems, the child was asked, “Do these two rows have the same number of checkers or does one row have more?” For the length conservation problems, the child was asked, “Do these two papers have the same length or is one of them longer?” For the mass conservation problems, the child was asked, “Do these two objects have the same or a different amount of play dough?” If the child answered that the two stimuli were not the same the experimenter asked him or her which had more (or was longer) and why. If the child answered that the stimuli were the same the experimenter asked, “Why do you think so?” The following were the actual stimulus rearrangements used for the
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DENNEY.
pretest problems. following order:
These problems
Conservation subtest Numbet-
Length
Mass
ZEYTINOGLU
AND
were
SELZER
presented
to each child in the
Problem I
One row was spread in both directions longer than the other row.
2
One row was placed other row.
I
One cardboard on the vertical plane was moved toward the subject so the ends of the two strips of cardboard were no longer in correspondence.
?
One cardboard perpendicular
I
One ball was made into a sausage shape while the other remained unchanged.
2
One ball was made into a pancake the other remained unchanged.
perpendicular
to look
to the
was placed at the center to the other cardboard.
and
shape while
Two measures of conservation were obtained. Judgment scores were based upon the child’s judgments regarding the equality of the two objects after the transformation. A correct judgment was given a score of 1, while an incorrect judgment was given a score of 0. Since the pretest consisted of six conservation problems, each child received a pretest judgment score between 0 and 6. Explanation scores were based upon the experimenter’s rating of the child’s answers to “Why do you think so?” questions. A correct explanation was given a score of 1, while an incorrect explanation was given a score of 0. Again, each child received a pretest explanation score between 0 and 6. An explanation was rated correct if it referred to either the former equality of the stimuli, compensation, addition/subtraction, reversibility. or the irrelevancy of the transformation. Children who gave both correct judgments and correct explanations on both of the number and both of the length conservation problems were classified as conservers and were eliminated from the study. There was only one child who met this criterion and was thus eliminated from the study. Of the 40 children who remained in the study, one gave correct judgments on both of the number problems and on one of the mass problems, 11 gave correct judgments on only the two number problems. four gave a correct judgment on only one of the number problems, and one gave a correct judgment on only one of the length problems. Twutment condirions. Upon completion of the pretest the children were randomly assigned to one of the five treatment conditions, with the restriction that the same proportion of nonconservers (children who made no conservation judgments or conservation explanations on the pretest)
CONSERVATION
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and partial conservers (children who made one or more conservation judgments or explanations on the pretest) were included in each condition. Half of the children in each condition were male and half were female. The treatment conditions were the four cells of a 2 (presence or absence of verbal rule instruction during training) x 2 (presence of absence of feedback during training) factorial design and an additional no-training-trials control group. Children in every treatment condition except the no-training-trials control group received six number conservation problems and six length conservation problems. Three of the six problems involved changing the spatial arrangements of the stimuli and thus disturbing their perceptual equality but not their quantitative equality. One problem involved the addition of some stimulus substance to one of the stimuli but not to the other. Another problem involved the subtraction of some stimulus substance from one of the stimuli but not from the other. Still another involved the addition of the same amount of the stimulus substance to both of the stimuli. The six number conservation problems were presented to every child in the following order: 1. One row spread in both directions to look longer than the other row. 2. A checker added to one row but not to the other. 3. One row made into a ring shape while the other row remained unchanged. 4. A checker taken away from one row but not from the other. 5. One row placed perpendicular to the other row. 6. A checker added to the end of both of the rows. The six length conservation the following order:
problems
were presented to each child in
1. One cardboard on the vertical plane moved toward the child so the ends of the two strips of cardboard were no longer in correspondence. 2. A small strip of cardboard added to the end of one of the cardboards but not to the other. 3. One cardboard placed at the center and perpendicular to the other cardboard. 4. A small strip of cardboard cut from the end of one of the cardboards but not from the other. 5. One cardboard placed at the top and perpendicular to the other cardboard in an L shape. 6. Two equal strips of cardboard added to the ends of both of the stimulus cardboards. These six different problems were each presented different sets of stimuli. For conservation of number.
four times with the four sets of
134
DENNEY.ZEYTINOGLU
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stimuli were determined by the four possible combinations of color of the checkers (red or blue) and number of the checkers (two rows of five checkers or two rows of six checkers). For length conservation, the four sets of stimuli were determined by the four possible combinations of color of the cardboard (red or blue) and length of the cardboard (9-in. strips or 12-in. strips). All six of the number conservation problems were presented with one of the four sets of number stimuli, then all six of the length conservation problems were presented with one of the four sets of length stimuli, then all six of the number conservation problems were presented with a second set of number stimuli, and so forth until all six of the number and length problems had been presented with each of the four sets of stimuli. The order of presentation of the sets of stimuli was randomly determined with the restriction that number and length stimulus sets were alternated. The conservation problems were presented with the various stimulus sets in the following order: 1. 2. 3. 4. 5. 6. 7. 8.
Two Two Two Two Two Two Two Two
rows of five blue checkers 12-in., red strips of cardboard rows of six red checkers 9-in., blue strips of cardboard rows of six blue checkers 9-in.. red strips of cardboard rows of five red checkers 12-in., blue strips of cardboard
At the beginning of each problem the two stimuli were equalized and the child was asked if they had the same amount of the relevant attribute (i.e., “Do these two rows have the same number of checkers or does one row have more’?” or “Do these two papers have the same length or is one of them longer’?“). If necessary, stimuli were adjusted until the child agreed that they were equal. Then the experimenter made the appropriate rearrangement of the stimuli. What happened subsequent to the stimulus rearrangement varied with the treatment condition. In the feedback and verbal rule instruction condition the experimenter then asked the child. “Now do these two rows have the same number of checkers or does one row have more?” (for the number conservation problems) or “Now do these two papers have the same length or is one of them longer?” (for the length conservation problems). If the child responded correctly. the experimenter said, “That’s the right answer.” and provided the child with the relevant conservation rule depending on the particular trial. If the child’s response was not correct the experimenter said, “That’s not the right answer,” and again provided him or her with the relevant rule. The following rules were given for the standard conservation of num-
CONSERVATION
TRAINING
135
ber, the unequal addition of number, the unequal subtraction of number. and the equal addition of number problems, respectively, while the operations referred to by the rules were demonstrated: 1. “Whenever we start with two rows of the same number of checkers, and we don’t add any checkers or take away any checkers, but only move them, they will still have the same number even if they now look different. See, I can put them back the way they were, so you see. they still have the same number.” 3-. “Whenever we start with two rows of the same number of checkers and we add a checker only to this row (pointing) and not to the other, there will be more checkers in this row. They don’t have the same number anymore, because I added a checker only to this row.” 3. “Whenever we start with two rows of the same number of checkers, and take away a checker only from this row (pointing), and not from the other, there will be fewer checkers in this row. They don’t have the same number anymore. because I took away a checker only from this row.” 4. “Whenever we start with two rows of the same number of checkers and we add the same number of checkers to both of the rows (pointing), the rows still have the same number of checkers.” Similar rules were given for the standard conservation of length, the unequal addition of length, the unequal subtraction of length, and the equal addition of length problems. In the verbal rule instruction condition, the children were HOG asked if the two stimuli were “same” or “different” after the rearrangement. Instead. the experimenter immediately provided the child with the relevant conservation rules and demonstration depending on the particular trial. The rules were the same ones provided to children in the feedback and verbal rule instruction condition. The children in this condition were not asked to make a judgment concerning the equality of the two stimuli because the provision of a rule following a child’s judgment would provide him or her with feedback. In the feedback condition, after the experimenter made the appropriate stimulus rearrangement, she then asked the child if the two stimuli were the “same” or “different” in number (for number conservation problems) or in length (for length conservation problems). If the child responded correctly. the experimenter said, “That’s the right answer.” If the child’s response was not correct, the experimenter said, “That’s not the right answer.” The conservation rules were not given to the children. In the no feedback and no verbal rule instruction condition the experimenter asked the child if the two stimuli were the “same” or “different” in number (for number conservation problems) or in length (for
136
DENNEY.
ZEYTINOGLL
AND
SELZER
length conservation problems) after the rearrangement. Neither the feedback nor the rules were given to the children. The experimenter proceeded to the next problem regardless of the child’s response. All of the children in the above four training conditions received the training in the same day on which they were pretested. The children in the no-training-trials control group received only the pre- and posttests. They were not presented with the training problems at all. This group was added in order to control for possible repeated testing effects. Posttesr. The posttest was administered one week after the pretest. The procedure, the problems, the order of presentation of the problems, and the scoring of the children’s responses were identical to those employed in the pretest. Results The explanations given by the children in the pre- and posttests were recorded on tape and transcribed. A random selection of 240 explanations were scored independently by two raters as either conserving or nonconserving. The interrater reliability, calculated from the Index of InterCoder Agreement for Nominal Scale Judgements (Scott & Wertheimer, 1962, p. 194) was .95. Because of the lack of variability in both judgment and explanation scores in the no feedback, no verbal rule instruction, and no training trials control groups, a nonparametric test had to be used to compare the pre- and posttest scores for these two groups. The children’s responses were divided into those in which there was improvement from pre- to posttest and those in which there was no improvement from pre- to posttest. A child’s response was classified as exhibiting improvement if it changed either from zero to one or two, or from one to two conservation responses from pre- to posttest. None of the children in these two groups gave more than two correct conservation judgments on either the pre- or posttest. A 2 (no feedback and no verbal rule instruction vs. no training trials control group) X 2 (improvement vs. no improvement) Fisher’s Exact Test was then performed. The differences were nonsignificant for both the judgment and the explanation scores. Therefore, neither the additional experience with the stimuli and the experimenter nor the questioning that took place during training had any effect. Consequently, the no training trials control group was excluded from further analyses. The means of the judgment and explanation scores for the four remaining experimental groups are presented in Table 1. Since these experimental groups were equated for pretest performance before training, only the posttest scores were analyzed. A 3 (verbal rule instruction vs. no
CONSERVATION TABLE MEANS
OF BOTH
JGDGMENT
AND
137
TRAINING 1
EXPLANATION
SCORES
Type Training
conditions Judgment
Feedback and verbal rule instruction Verbal rule instruction Feedback No feedback and no verbal rule instruction
EXPERIMENT
1
of conservation
Number
Length
Mass
2.00 2.00 2.00 1.00
2.00 1.25 .X8 .25
.LO .50 .25 .oo
2.00 1.88 1.25 .88
I .88 1.00 .25 .oo
.75 .SO .25 .oo
scores
Feedback and verbaf rule instruction Verbal rule instruction Feedback No feedback and no verbal rule instruction Explanation
FOR
scores
-
verbal rule instruction) x 2 (feedback vs. no feedback) x 3 (number vs. length vs. mass) x 2 (judgment vs. explanation) analysis of variance was performed on the posttest scores. Verbal rule instruction and feedback were between-subjects variables, while concept and type of response were within-subject variables. A significant effect was obtained for verbal rule instruction, F(1,28) = 22.72, p < .Ol, indicating that children who were given the rules conserved more after training than children who were not given the rules. Type response was a significant source of variance, F( 1,28) = 7.61,~ < .05: judgments were more often correct than explanations. Concept was also a significant source of variance. A Tukey B test yielded significant differences, p < .Ol, between all three concepts. with mass, length, and number the order of decreasing difficulty. Both the interaction between verbal rule instruction and concept, F(2,56) = 4.50,~ < .05. and the interaction between concept and type of response, F(2,56) = 3.71,~ < .05, were significant. A simple main effects test indicated that the interaction between verbal rule instruction and concept was obtained because while performance on both length, F( 1,56) = 17.86, p < .Ol, and number, F(1,56) = 36.46, p < .Ol, problems was better in the verbal rule instruction condition, performance on the mass problems did not differ as a function of verbal rule instruction. A simple main effects test also indicated that the interaction between concept and type of response occurred because, although there were no differences in the number of correct judgments and number of correct explanations given on either number or mass problems, more correct judgments than correct explanations were given on length problems, F( 1.56) = 14.29, p < .Ol .
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Ten children provided correct judgments on both of the pretest number conservation problems, while nine children provided correct explanations on both of the pretest number conservation problems. None of the children made correct judgments or correct explanations on both of the length or both of the mass pretest problems. The possible effects of conserving number on the pretest upon the overall posttest scores were investigated. Six separate point-biserial correlations were computed-one on the judgment scores of the total sample, one on the explanation scores of the total sample, one on the judgment scores of the verbal rule instruction groups. one on the explanation scores of the verbal rule instruction groups. one on the judgment scores of the no verbal rule instruction groups. and one on the explanation scores of the no verbal rule instruction groups. The continuous variable of the point-biserial correlations was the total posttest score, while the dichotomous variable was the pretest number conservation score. More specifically, any child who gave one or more correct pretest number conservation judgments was assigned a score of 1, while any child who did not give at least one correct pretest number conservation judgment was assigned a score of 0. Explanation responses were scored in the same fashion. To test the significance of each of these correlations, separate t tests were performed. The only significant correlation on the explanation scores was in the no verbal rule instruction groups, t( 14) = 2.91.1, < .O:! (rpb = + .61). None of the correlations on the judgment scores was significant. However, the correlation on the judgment scores of the no verbal rule instruction group approached significance. t( 14) 1.86. p < .lO (rpb = +.45). Therefore, conserving number on the pretest influenced the overall posttest conservation scores only in the no verbal instruction groups, the influence being stronger on the explanation scores than on the judgment scores. Therefore, the superior posttest conservation performance of the verbal rule instruction groups over that of the no verbal rule instruction groups appeared to be primarily due to the effects of the training rather than being due to the initial conservation levels of the subjects. In order to test for nonspecific transfer, the responses to the mass conservation problems were analyzed separately. In the verbal rule instruction groups, four children provided correct judgments and five children provided correct explanations on both of the posttest mass conservation problems. None of these children could provide correct judgments or correct explanations on any of the pretest mass conservation problems. On the other hand, only one child in the no verbal rule instruction groups could correctly judge and explain the conservation of mass on the two posttest mass conservation problems. It is interesting to note that this child was already able to correctly judge and explain one of the two mass conservation problems on the pretest. A 2 (verbal
CONSERVATION
TRAINING
139
rule instruction vs. no verbal rule instruction) x 2 (conservation on posttest mass problems vs. no conservation on posttest mass problems) ChiSquare test performed on the judgment scores did not reveal a significant difference, x2(1) = 2.13. A 2 (verbal rule instruction vs. no verbal rule instruction) x 2 (conservation on posttest mass problems vs. no conservation on posttest mass problems) Chi-Square test performed on the explanation scores approached significance, x’(1) = 3.28. p < .lO. Discussion
The results of the present study demonstrate the effectiveness of the verbal rule instruction procedure in teaching four-year-old children to conserve. Subjects who received the verbal rules obtained better posttest scores a week after training than the subjects who did not receive the verbal rules. Although no subject in the verbal rule instruction conditions recited verbatim the rules provided by the experimenter, many subjects referred to reversibility (“because you can put it back here”) or to the lack of either addition or subtraction operations (“because you did not add anything’* or “because you did not take away anything”) in explaining their judgments. From the explanations. it appears that many subjects learned to focus on the transformations and were able to discriminate the types of transformations that do and do not affect the quantitative equality of the objects. The feedback procedure employed in the present study was not effective in training four-year-olds to conserve. The disparity of the present results with those in which feedback was successful may be a result of procedural differences. In the present study the subjects were simply given verbal feedback contingent on their judgments of conservation problems, while in both Kingsley and Hall’s (1967) and Bucher and Schneider’s (1973) studies the subjects were trained on a graded series of subtasks related to conservation with the use of several different types of feedback. If the subjects of the present study had been trained in the attainment of a hierarchy of subtasks related to conservation of number and length with the employment of the various types of feedback, especially those employed by Kingsley and Hall, the feedback procedure may have been more effective. Gelman’s requirements of systematically varying the irrelevant dimensions together with feedback were met in the present feedback procedure. If, as Gelman claims, nonconserving responses were due to the lack of feedback and chances to try alternative cues in conservation problems, then it would be expected that with the present feedback procedure subjects would learn to attend to the relevant and ignore the irrelevant dimensions, and thereby conserve. However. the results did not support this prediction. The most probable reason for the disparity may be the employment of fewer training trials in the present study in com-
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parison with Gelman’s (1969). Another reason may be that the subjects in the present study were younger than those used in Gelman’s study. However, Emrick (1969) reported successful learning of conservation in four-year-olds using a similar procedure. A third reason for the disparity may be that the feedback procedure of the present study differed from both Gelman’s and Emrick’s in the employment of conservation rather than three-element oddity problems during training. Oddity problems may be more conducive to the discrimination of the relevant dimension than conservation problems. In each oddity problem, the subject is asked to respond with reference to a dimension such as “length.” Positive feedback confirms the subject’s prediction of the relevant dimension while negative feedback eliminates one of the dimensions. However, with conservation problems, the situation demands the subjects’s awareness of the relevant dimension ~1~s his judgment of what transformations do and do not affect that dimension. Consequently, while positive feedback confirms both of his predictions. negative feedback does not tell the subject precisely where he has gone wrong. Brainerd’s (1974) training procedure was very similar to that employed in the present study; training was given only on standard conservation problems and only verbal feedback was given. However, since “they are the same” was the correct answer on all of his pretest, training, and posttest trials, it could be that his subjects simply learned to say “the same” regardless of the question asked. Thus, we cannot conclude that his subjects actually learned anything about conservation. Although the subjects in the verbal rule instruction groups gave significantly more conservation responses to the length and number problems than the subjects in the no verbal rule instruction groups, they did not give more conservation responses on the mass problems. Thus, training children on number and length did not foster nonspecific transfer to mass conservation problems. This is not too surprising since children naturally acquire conservation of both number and length prior to conservation of mass. Generalization to types of conservation which are acquired prior to those on which training is given would be more likely to be obtained. Experiment 2 was designed to test this hypothesis. EXPERIMENT
2
In Experiment 2 four-year-olds who were trained on both length and mass conservation were tested for generalization on both number, which is naturally acquired before length and mass, and weight, which is naturally acquired after length and mass. Only the verbal rule instruction training method was used since the feedback training method used in Experiment 1 was not found to be effective.
CONSERVATION
141
TRAINING
Method
Participants were 32 white, middle-class, four-year-old children who attended day-care centers or nursery schools in Lawrence, Kansas. Half of the participants were male and half were female. Each child was tested and trained by one of two undergraduate male experimenters.
The study consisted of three phases: (a) a pretest for conservation of number. length, mass, and weight, (b) a training session which included conservation of length and mass tasks, and tc) a posttest identical to the pretest. Prefest. The pretest consisted of four subtests: one for conservation of number, one for conservation of length, one for conservation of mass, and one for conservation of weight. Each subtest was composed of two actual conservation problems and one addition/subtraction problem. The materials used were two rows of eight checkers each for number conservation tasks, two 12-in. strips of cardboard for length conservation tasks, two ball-shaped portions of red cfay for mass conservation tasks. and two round balls of clay and a balance for weight conservation tasks. Each child was seated directly opposite the experimenter at a table and was tested in the same manner as in Experiment 1 (i.e., equality of the stimuli was established in the same manner, and the format of the questions was the same). The exact stimulus rearrangements were as follows: Conservation subtest
Problem
Number
1
One
row
longer 2
One
One
I
the
was
placed
in both other
was
other
row
One cardboard toward the
perpendicular
removed
to look
to the
were
A small strip of cardboard the end of one of the
3
One
the
perpendicular
one
rev+
while
unchanged.
on the vertical plane child so that the end
2
cardboard
from
remained
strips of cardboard spondence.
from
directions
row.
row.
checker
the Length
spread
row
other 3
was than
was moved of the two
no longer
was cut cardboards
in correoff from but not
other. was
placed
to the
other
at the
center
cardboard.
and
142
DENNEY.
ZEYTINOGLU
AND
I
One ball uai; formed the other remained
2
A small amount hall while the
3
One
ball
the Weight
SELZER
wax
other
for-med
2
One
3
A small while
into
remained
One hall wa\ formed the other remained ball
wa\
fol-med
remained amount the
other
while
of clay wa5 added to one other remained unchanged.
I
other
into a su~sage unchanged.
a pancake
while
unchanged. into a snake unchanged. into
;L cube
while
while
the
unchanged. of clay remained
was
added
to one
ball
unchanged.
The experimenter obtained both a judgment measure and an explanation measure in the same manner as in Experiment I. A child who gave both a correct judgment and a correct explanation on any one of the nine actual conservation problems, i.e., those not dealing with addition or subtraction, was classified as a conserver and eliminated from the study. Treatment ~orzu’ifions. At the completion of the pretest the children were randomly assigned to one of the two treatment conditions-the verbal rule instruction condition or the control condition. An equal number of males and females were assigned to each condition. The children then were presented with six length conservation problems and six mass conservation problems. Three of the six problems involved changing the spatial arrangements of the stimuli and thus disturbing their perceptual equality, one problem involved the addition of some of the stimulus material to one of the stimuli but not to the other, one problem involved the subtraction of some of the stimulus material from one of the stimuli and not from the other, and one problem involved the addition of the same amount of stimulus material to both of the stimuli. The six length conservation problems were presented to each child in the following order: 1. One cardboard on the vertical plane was moved toward the child so that the two strips of cardboard were no longer in correspondence. 2. A small strip of cardboard was added to the end of one of the cardboards but not to the other. 3. One cardboard was placed at the center and perpendicular to the other cardboard. 4. A small strip of cardboard was cut from the end of one of the cardboards but not from the other. 5. One cardboard was placed at the top and perpendicular to the other cardboard in an L shape.
CONSERVATION
6. Two the stimulus
equal strips cardboards.
of cardboard
The six mass conservation the following order:
problems
143
TRAINING
were added to the ends of both of were
presented
to each child in
1. One ball was formed into a snake while the other remained unchanged. 3. A small, equal amount of clay was added to each ball. 3. One ball was formed into a ring while the other remained unchanged. 4. A small amount of clay was added to one ball while the other remained unchanged. 5. One ball was formed into a triangle while the other remained unchanged. 6. A small amount of clay was taken away from one ball while the other remained unchanged. These six different problems were each presented twice with different sets of stimuli. The conservation training problems were presented with the indicated stimulus sets in the following order: 1. 2. 3. 4.
Two 9-in. blue strips of cardboard (length conservation). Two equal balls of clay (mass conservation). Two 12-in. red strips of cardboard (length conservation). Two equal logs of clay (mass conservation).
At the beginning of each problem each child was asked if the two stimuli had the same amount of the relevant attribute. Equality of the two stimuli was estabiished in the same manner as in the pretest. Then the experimenter made the appropriate rearrangement ofthe stimuli. What happened subsequent to the stimulus transformation varied with the treatment condition. In the verbal rule instruction condition, the child was asked if the two stimuli were the “same” or “different” after the rearrangement. Following this the experimenter indicated the correct answer, then immediately provided the child with the appropriate conservation rule and demonstration in the same manner as in Experiment 1. In the control condition, the experimenter asked the child if the two stimuli were the “same” or “different” after each transformation. The experimenter did not give the child any feedback about the correctness of his or her answer or provide the child with any of the conservation rules, but instead proceeded directly to the next problem. Posttrst. A posttest was administered to each child approximately one week after the pretest. The procedure, the problems, the order of
144
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AND
SELZER
presentation of the problems, and the scoring of the children’s were identical to those employed in the pretest.
responses
Results
The means of the judgment and explanation scores are presented in Table 2. Because performance on the pretest was equated by eliminating from the study all participants who gave a correct judgment and a correct explanation on any of the conservation questions, only the posttest results were analyzed. A 2 (training vs. no training) x 2 (male vs. female) x 2 (judgment vs. explanation scores) x 4 (number, length, mass, and weight conservation subtests) mixed analysis of variance was computed on the posttest scores. Training and sex were between-subjects variables: type of response and type of conservation were within-subject variables. This analysis revealed a highly significant main effect for training, F( 1.28) = 33.78,~ < .OOl. The children who received training had significantly higher posttest judgment and explanation scores than the children who did not receive training. The main effect for type of response was also significant, F( 1,28) = 8.18, /j < .Ol, indicating that participants made more correct judgment responses than explanation responses. The main effect for type of conservation was significant, F(3,84) = 5.95, /I < ,001, indicating that the children’s posttest scores differed significantly among the four subtests. A Tukey B comparison of the means of the four conservation subtests revealed that the children conserved more frequently on the length than on the mass or weight subtests. No other differences between subtests were significant. The interaction between training and type of conservation was significant. F-(3,84) = 2.89, (7 < .05, suggesting that the training differentially influenced posttest performance on the four subtests. The simple main TABLE MEANS
ot
Bo-FH JUDGMENT
2
4~11 EXPLANATION Type
Training
Verbal Control
Verbal Control
conditions
Number
Length
Judgment
score\
Explanation
xores
SCORES toR EXPNUMENI
7
of conservation Substance
Weight
rule instruction
rule instruction
I.75 .50
2.00 .x1
I .50 .?
I.31 .3x
CONSERVATION
TRAINING
14.5
effects procedure (Wirier, 1962) was used to further investigate this interaction. This analysis indicated that children who received training conserved more frequently on the number, length, mass, and weight subtests than did children who did not receive training, F(1,90) = 18.72, 30.10, 22.54, and 12.87, respectively, p < .OOl. Since training produced significant increases in performance on all four subtests, the interaction between training and type of conservation was not investigated further. It clearly was obtained only because the training effects were stronger for some subtests than for others. Discussion
The results of Experiment 2 clearly demonstrate significant nonspecific transfer both to a type of conservation which is typically acquired prior to those on which training was given (i.e., number) and to a type of conservation which is typically acquired after those on which training was given (i.e., weight). Although significant nonspecific transfer was not obtained in Experiment 1, the results of Experiment 2 are not too surprising since the transfer effects in Experiment 1 approached significance, x’( 1) = 2.13, p < .20 and x2(1) = 3.28, p < .lO for judgments and explanations, respectively. Thus, the results indicate that the verbal rule instruction procedure employed in the present research is an effective method for increasing conservation performance among four-year-olds on tests of both specific and nonspecific transfer up to one week after training. From a Piagetian perspective, one would not expect successful conservation learning with a procedure based exclusively upon the verbal provision of the conservation principle. With respect to the role of verbal transmission upon concept acquisition, Piaget (1973) stated that: Adequate verbal transmission of information relative to the operatory structures is assimilated only on the levels where the operations are elaborated on the basis of actions themselves or operations as interiorized actions, and if language favors this interiorization, it neither creates nor transmits ready-made structures by an exclusively linguistic means. (p. 1191.
In other words, according to Piaget, the child must possess the relevant cognitive structures before he will be able to assimilate verbally transmitted information. However, the present research demonstrated that children who have not yet acquired conservation concepts, and who are too young to possess the relevant cognitive structures, nevertheless benefit from the verbal rule instruction procedure in conservation acquisition. The superior posttest performance of the subjects in the verbal rule instruction conditions indicated that they effectively learned the information conveyed by the verbal rules, and were able to apply this learning to conservation problems presented to them a week after the training. The success of the verbal rule instruction procedure with fouryear-old children can be interpreted as resulting from the joint function
146
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of the verbal rules and the demonstrations of the operations referred to by the verbal rules. The demonstrations of reversibility and addition/ subtraction operations performed on the objects during training may have served to make the verbal rules, which might otherwise be abstract, concrete and thus meaningful for the four-year-olds. Consequently, the understanding of the verbal rules as they apply to manipulable objects effectively served for the transfer of the information they conveyed to posttest conservation tasks. However, with the present experimental design the effects of the rule presentation and the demonstrations cannot be separated. In future research, verbal rule presentation and the demonstration of conservation-relevant information should be varied independently to assess the contribution of each upon conservation learning. REFERENCES
Beilin. H. Learnlng and
operational convergence in logical thought development. J~III.II(I/ c~f‘ErprprrifF7cv7rtrl Ciiild /?YKh,/0~~. 1965. 2, 653-660. Beilin. H. The training and acquisition of logical operations. In M. F. Rosskopf. L. P. Steffe. & S. Taback t Eds. t. Piqytiw7 c.o~:r2ili1.e-d~~,~/~)~~~~1~~~f cd rntrrhrn2trric.cll cdrrc-crtiort Washington: National Council of Teachers of Mathematics. 1971. Brainerd, C. J. Training and transfer of transitivity, conservation, and class inclusion of length. Clrild fIer~a/<~~nrerrt. 1974. 35, 324-334. Bucher. B.. & Schneider. R. E. Acquisition and generalization of conservation by preschoolers. using operant training. J~wrr~crl o~‘Er/~c,rimr,2/trl Cllild Pc,rc.lr~~/og\, 1973. 16, 187-204. Christie, J. F.. & Smothergill. D. W. Discrimination and conservation of length. ~.~~c~/roflOF77iC Scicn~~e. 1970. 21, 3366337. Emrick. J. A. The acquisition and transfer of conservation skills by four-year-old children. Dksrrtutiorr Ah,stmct.s. 1969. 29. 2561-A. Gelman, R. Conservation acquisition: A problem of learning to attend to relevant attributes. J~wr!rtrl of‘E~prrinwnrtrl Child P.s?:c~/rt~/~~y.v. 1969. 7. 167- 187. Kingsley, R. C., & Hall, V. C. Training conservation through the use of learning sets. Child I)e~,c~/o~~,rnr,nt, 1967. 38, 1 I1 I - 1126. Mermelstein, E.. & Meyer. E. Conservation training techniques and their effects on different populations. C/t&f Det~c~/(~~~~wnt. 1969. 40, 47 l-490. Peters. D. L. Verbal mediators and cue discrimination in the training from nonconservation to conservation of number. Child I)~~,r/ol)/nc,,lt. 1970, 41, 707-712. Piaget. J. The child crrld wolilv: Proh/cr~7.\ c!/’ ,qcwtk /I.\w~/w/o~~. New York: Grossman Publishers. 1973. Rosenthal, T. L.. & Zimmerman. B. J. Modeling by exemplification and instruction in training conservation. nr~.c/r)/,nlc,nttr/ f’s~c~/n~/~~~,v, 1972. 6, 392-401. Scott. W. A. ~ 8 Wertheimer, M. /nfrrdrrc./icvr to ~‘,s?‘c./f~jk,,pic,trl r-~.sc~~rrc~h New York: John Wiley & Sons, Inc.. 1962. Siegler. R. S.. & Liebert, R. M. Effects of presenting relevant rules and complete feedback on the conservation of liquid quantity task. l)c~.c,/r,pn~c,n/~l/ P \~c~lrr>/~~,c~. 1977. 7, 133-138. Smith, 1. D. The effects of training procedures upon the acquisition of weight. c‘l~ilcl Dr\~~lopr~w~~r. 1968. 39, 5 15-526. Winer. B. J. Sfoti.sficol [~ritrc,if~ic,.< in (,.i/‘c,rir,,r,~trr/ tiesierr New York: McGraw - Hill Book Company. 1962. RECEIVED:
July
16. 1976: RFVIS~D:
August
31. lY76
OF EXPERIMENTAL
Conservation NANCY
CHILD
PSYCHOLOGY
Training
24, 129- 146 (1977)
in Four-Year-Old
WADSWORTH DENNEY, SEZEN AND S. CLAIRE SELZER Unil,ersity
Children
ZEYTINOGLU.
of‘k’onsas
In Experiment I two training procedures were used to teach four-year-olds to conserve. Verbal rule instruction consisted of providing verbal rules and demonstrations of the operations referred to by the rules. Feedback consisted of providing verbal feedback contingent upon the children’s responses. One week after training on conservation of number and length the children were given a posttest which included tests of conservation of number, length, and mass. Children who were given verbal rule instruction conserved significantly more on the number and length posttest problems than children who were not. However, this learning did not transfer to the mass problems. possibly because mass is not naturally acquired until some time after conservation of number and length. The feedback training procedure had no effect on conservation performance. In Experiment 2, the verbal rule instruction procedure was used to train four-year-olds on conservation of length and mass. One week after training the children were tested on both conservation of number, which is typically acquired before length and mass, and conservation of weight, which is typically acquired after length and mass, as well as on conservation of length and mass. Children who were given training conserved more on all four types of problems than children in the control group.
A number of investigators have attempted to teach nonconserving children to conserve. With some exceptions (e.g., Bucher & Schneider. 1973; Emrick, 1969; Rosenthal & Zimmerman, 19721, the children in most of the successful studies have been close to five years old or older. The purpose of the present research was to teach four-year-old children to conserve. In Experiment 1 the relative efficacy of two training procedures was investigated. One of them, the verbal rule instruction procedure, consisted of providing the children with verbal rules and demonstrations of the operations referred to by the rules. The other, the feedback procedure, involved providing the children with verbal feedback contingent upon their responses to conservation problems. A review of the conservation training literature reveals that, with some exceptions (e.g., Mermelstein & Meyer, 1969), verbal rule instrucExperiment I is based on a Master’s Thesis submitted by Sezen Zeytinoglu to the Department of Psychology at the University of Kansas. Requests for reprints should be sent to Nancy W. Denney. Department of Psychology. University of Kansas. Lawrence, Kan. 66045.
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tion training procedures usually have led to improved conservation behavior in children who are within the age range of five to seven (e.g., Beilin, 1971: Peters, 1970; Rosenthal & Zimmerman, 1972: Siegler & Liebert, 1972; Smith, 1968). Feedback procedures have also been widely employed in attempts to teach nonconservers to conserve. Some of these attempts have been successful in leading to improved conservation behavior(e.g.. Brainerd, 1974: Bucher& Schneider, 1973; Emrick, 1969: Gelman, 1969: Kinsley & Hall, 1967: Siegler & Liebert, 1972) while others have not (e.g.. Beilin. 1965: Christie & Smothergill. 1970: Smith. 1968). The rules for the verbal rule instruction condition were adapted from Beilin (1965). In Beilin’s procedure, although the rules referred to reversibility and addition/subtraction operations, only reversibility was actually demonstrated to the children. However. in the present research both addition/subtraction problems and standard conservation problems were presented along with the relevant rules. The feedback procedure employed in Experiment 1 was patterned after Gelman’s (1969) requirements of (a) systematically varying the irrelevant stimuli, and (b) feedback to inform the subjects of the conservation-relevant dimensions. Gelman claims that young children’s failure to conserve on classical conservation tasks is due to their attending to the irrelevant and ignoring the relevant attributes of the stimulus display. If this is the case, then giving feedback on conservation problems in which the irrelevant dimensions are varied on successive problems should force the subjects to attend to the relevant dimensions and thereby conserve. In Experiment 1, number and length problems were alternated to inform the subjects what quantity dimension was relevant to the particular conservation task. Furthermore, it was assumed that the alternated presentation of addition/subtraction problems and standard conservation problems would inform the children of the types of transformations that do and do not affect the relevant quantity dimension. EXPERIMENT
1
Method
The participants were 20 male and 20 female white. middle-class children between the ages of 4 years, 0 months and 4 years, 10 months. The children ranged in age from 4 years, 0 months to 4 years, 11 months. The mean age of the total sample was 4 years, 6 months. The children were selected from nursery schools and day-care centers in Lawrence, Olathe, and Kansas City, Kansas. The children were tested and trained individually by a 23-year-old, white female.
CONSERVATION
TRAINING
131
Procedure
The study consisted of three phases: (a) a pretest for conservation of number, length, and mass, (b) a training session involving conservation of number and length, and (c) a posttest for conservation of number, length, and mass. Pretest. The pretest consisted of three subtests: one for conservation of number, one for conservation of length, and one for conservation of mass, in that order. Each subtest included two conservation problems. The materials used were two rows of five checkers (for the number conservation problems), two 12-in. strips of cardboard (for the length conservation problems), and two round balls of Plasticine (for the mass conservation problems). Each child was seated at a table directly opposite the experimenter and was told that he was going to play a number of games with the experimenter. At the start of each problem, the two stimuli were presented so that they were both perceptually and quantitatively equal. That is, the two rows of checkers were placed in one-to-one correspondence, the two strips of cardboard were placed side-by-side on a vertical plane with their ends matching, and the clay was shaped into two equal round balls. Then the child was asked if the two stimuli had the same or a different amount of the relevant attribute (number, length, or mass). Stimuli were changed until the child agreed that they were equal. Then the experimenter rearranged or altered the form of one of the two objects. The rearrangement only disturbed the perceptual equality, not the quantitative equality. For example, in a number conservation problem one of the rows was spread to look longer than the other row: in a length conservation problem one cardboard was placed perpendicular to the other one; and in a mass conservation problem one of the balls was made into a sausage shape while the other remained in a ball shape. The experimenter then questioned the child regarding the equivalence of the two stimuli. For the number conservation problems, the child was asked, “Do these two rows have the same number of checkers or does one row have more?” For the length conservation problems, the child was asked, “Do these two papers have the same length or is one of them longer?” For the mass conservation problems, the child was asked, “Do these two objects have the same or a different amount of play dough?” If the child answered that the two stimuli were not the same the experimenter asked him or her which had more (or was longer) and why. If the child answered that the stimuli were the same the experimenter asked, “Why do you think so?” The following were the actual stimulus rearrangements used for the
132
DENNEY.
pretest problems. following order:
These problems
Conservation subtest Numbet-
Length
Mass
ZEYTINOGLU
AND
were
SELZER
presented
to each child in the
Problem I
One row was spread in both directions longer than the other row.
2
One row was placed other row.
I
One cardboard on the vertical plane was moved toward the subject so the ends of the two strips of cardboard were no longer in correspondence.
?
One cardboard perpendicular
I
One ball was made into a sausage shape while the other remained unchanged.
2
One ball was made into a pancake the other remained unchanged.
perpendicular
to look
to the
was placed at the center to the other cardboard.
and
shape while
Two measures of conservation were obtained. Judgment scores were based upon the child’s judgments regarding the equality of the two objects after the transformation. A correct judgment was given a score of 1, while an incorrect judgment was given a score of 0. Since the pretest consisted of six conservation problems, each child received a pretest judgment score between 0 and 6. Explanation scores were based upon the experimenter’s rating of the child’s answers to “Why do you think so?” questions. A correct explanation was given a score of 1, while an incorrect explanation was given a score of 0. Again, each child received a pretest explanation score between 0 and 6. An explanation was rated correct if it referred to either the former equality of the stimuli, compensation, addition/subtraction, reversibility. or the irrelevancy of the transformation. Children who gave both correct judgments and correct explanations on both of the number and both of the length conservation problems were classified as conservers and were eliminated from the study. There was only one child who met this criterion and was thus eliminated from the study. Of the 40 children who remained in the study, one gave correct judgments on both of the number problems and on one of the mass problems, 11 gave correct judgments on only the two number problems. four gave a correct judgment on only one of the number problems, and one gave a correct judgment on only one of the length problems. Twutment condirions. Upon completion of the pretest the children were randomly assigned to one of the five treatment conditions, with the restriction that the same proportion of nonconservers (children who made no conservation judgments or conservation explanations on the pretest)
CONSERVATION
TRAINING
133
and partial conservers (children who made one or more conservation judgments or explanations on the pretest) were included in each condition. Half of the children in each condition were male and half were female. The treatment conditions were the four cells of a 2 (presence or absence of verbal rule instruction during training) x 2 (presence of absence of feedback during training) factorial design and an additional no-training-trials control group. Children in every treatment condition except the no-training-trials control group received six number conservation problems and six length conservation problems. Three of the six problems involved changing the spatial arrangements of the stimuli and thus disturbing their perceptual equality but not their quantitative equality. One problem involved the addition of some stimulus substance to one of the stimuli but not to the other. Another problem involved the subtraction of some stimulus substance from one of the stimuli but not from the other. Still another involved the addition of the same amount of the stimulus substance to both of the stimuli. The six number conservation problems were presented to every child in the following order: 1. One row spread in both directions to look longer than the other row. 2. A checker added to one row but not to the other. 3. One row made into a ring shape while the other row remained unchanged. 4. A checker taken away from one row but not from the other. 5. One row placed perpendicular to the other row. 6. A checker added to the end of both of the rows. The six length conservation the following order:
problems
were presented to each child in
1. One cardboard on the vertical plane moved toward the child so the ends of the two strips of cardboard were no longer in correspondence. 2. A small strip of cardboard added to the end of one of the cardboards but not to the other. 3. One cardboard placed at the center and perpendicular to the other cardboard. 4. A small strip of cardboard cut from the end of one of the cardboards but not from the other. 5. One cardboard placed at the top and perpendicular to the other cardboard in an L shape. 6. Two equal strips of cardboard added to the ends of both of the stimulus cardboards. These six different problems were each presented different sets of stimuli. For conservation of number.
four times with the four sets of
134
DENNEY.ZEYTINOGLU
ANDSELZER
stimuli were determined by the four possible combinations of color of the checkers (red or blue) and number of the checkers (two rows of five checkers or two rows of six checkers). For length conservation, the four sets of stimuli were determined by the four possible combinations of color of the cardboard (red or blue) and length of the cardboard (9-in. strips or 12-in. strips). All six of the number conservation problems were presented with one of the four sets of number stimuli, then all six of the length conservation problems were presented with one of the four sets of length stimuli, then all six of the number conservation problems were presented with a second set of number stimuli, and so forth until all six of the number and length problems had been presented with each of the four sets of stimuli. The order of presentation of the sets of stimuli was randomly determined with the restriction that number and length stimulus sets were alternated. The conservation problems were presented with the various stimulus sets in the following order: 1. 2. 3. 4. 5. 6. 7. 8.
Two Two Two Two Two Two Two Two
rows of five blue checkers 12-in., red strips of cardboard rows of six red checkers 9-in., blue strips of cardboard rows of six blue checkers 9-in.. red strips of cardboard rows of five red checkers 12-in., blue strips of cardboard
At the beginning of each problem the two stimuli were equalized and the child was asked if they had the same amount of the relevant attribute (i.e., “Do these two rows have the same number of checkers or does one row have more’?” or “Do these two papers have the same length or is one of them longer’?“). If necessary, stimuli were adjusted until the child agreed that they were equal. Then the experimenter made the appropriate rearrangement of the stimuli. What happened subsequent to the stimulus rearrangement varied with the treatment condition. In the feedback and verbal rule instruction condition the experimenter then asked the child. “Now do these two rows have the same number of checkers or does one row have more?” (for the number conservation problems) or “Now do these two papers have the same length or is one of them longer?” (for the length conservation problems). If the child responded correctly. the experimenter said, “That’s the right answer.” and provided the child with the relevant conservation rule depending on the particular trial. If the child’s response was not correct the experimenter said, “That’s not the right answer,” and again provided him or her with the relevant rule. The following rules were given for the standard conservation of num-
CONSERVATION
TRAINING
135
ber, the unequal addition of number, the unequal subtraction of number. and the equal addition of number problems, respectively, while the operations referred to by the rules were demonstrated: 1. “Whenever we start with two rows of the same number of checkers, and we don’t add any checkers or take away any checkers, but only move them, they will still have the same number even if they now look different. See, I can put them back the way they were, so you see. they still have the same number.” 3-. “Whenever we start with two rows of the same number of checkers and we add a checker only to this row (pointing) and not to the other, there will be more checkers in this row. They don’t have the same number anymore, because I added a checker only to this row.” 3. “Whenever we start with two rows of the same number of checkers, and take away a checker only from this row (pointing), and not from the other, there will be fewer checkers in this row. They don’t have the same number anymore. because I took away a checker only from this row.” 4. “Whenever we start with two rows of the same number of checkers and we add the same number of checkers to both of the rows (pointing), the rows still have the same number of checkers.” Similar rules were given for the standard conservation of length, the unequal addition of length, the unequal subtraction of length, and the equal addition of length problems. In the verbal rule instruction condition, the children were HOG asked if the two stimuli were “same” or “different” after the rearrangement. Instead. the experimenter immediately provided the child with the relevant conservation rules and demonstration depending on the particular trial. The rules were the same ones provided to children in the feedback and verbal rule instruction condition. The children in this condition were not asked to make a judgment concerning the equality of the two stimuli because the provision of a rule following a child’s judgment would provide him or her with feedback. In the feedback condition, after the experimenter made the appropriate stimulus rearrangement, she then asked the child if the two stimuli were the “same” or “different” in number (for number conservation problems) or in length (for length conservation problems). If the child responded correctly. the experimenter said, “That’s the right answer.” If the child’s response was not correct, the experimenter said, “That’s not the right answer.” The conservation rules were not given to the children. In the no feedback and no verbal rule instruction condition the experimenter asked the child if the two stimuli were the “same” or “different” in number (for number conservation problems) or in length (for
136
DENNEY.
ZEYTINOGLL
AND
SELZER
length conservation problems) after the rearrangement. Neither the feedback nor the rules were given to the children. The experimenter proceeded to the next problem regardless of the child’s response. All of the children in the above four training conditions received the training in the same day on which they were pretested. The children in the no-training-trials control group received only the pre- and posttests. They were not presented with the training problems at all. This group was added in order to control for possible repeated testing effects. Posttesr. The posttest was administered one week after the pretest. The procedure, the problems, the order of presentation of the problems, and the scoring of the children’s responses were identical to those employed in the pretest. Results The explanations given by the children in the pre- and posttests were recorded on tape and transcribed. A random selection of 240 explanations were scored independently by two raters as either conserving or nonconserving. The interrater reliability, calculated from the Index of InterCoder Agreement for Nominal Scale Judgements (Scott & Wertheimer, 1962, p. 194) was .95. Because of the lack of variability in both judgment and explanation scores in the no feedback, no verbal rule instruction, and no training trials control groups, a nonparametric test had to be used to compare the pre- and posttest scores for these two groups. The children’s responses were divided into those in which there was improvement from pre- to posttest and those in which there was no improvement from pre- to posttest. A child’s response was classified as exhibiting improvement if it changed either from zero to one or two, or from one to two conservation responses from pre- to posttest. None of the children in these two groups gave more than two correct conservation judgments on either the pre- or posttest. A 2 (no feedback and no verbal rule instruction vs. no training trials control group) X 2 (improvement vs. no improvement) Fisher’s Exact Test was then performed. The differences were nonsignificant for both the judgment and the explanation scores. Therefore, neither the additional experience with the stimuli and the experimenter nor the questioning that took place during training had any effect. Consequently, the no training trials control group was excluded from further analyses. The means of the judgment and explanation scores for the four remaining experimental groups are presented in Table 1. Since these experimental groups were equated for pretest performance before training, only the posttest scores were analyzed. A 3 (verbal rule instruction vs. no
CONSERVATION TABLE MEANS
OF BOTH
JGDGMENT
AND
137
TRAINING 1
EXPLANATION
SCORES
Type Training
conditions Judgment
Feedback and verbal rule instruction Verbal rule instruction Feedback No feedback and no verbal rule instruction
EXPERIMENT
1
of conservation
Number
Length
Mass
2.00 2.00 2.00 1.00
2.00 1.25 .X8 .25
.LO .50 .25 .oo
2.00 1.88 1.25 .88
I .88 1.00 .25 .oo
.75 .SO .25 .oo
scores
Feedback and verbaf rule instruction Verbal rule instruction Feedback No feedback and no verbal rule instruction Explanation
FOR
scores
-
verbal rule instruction) x 2 (feedback vs. no feedback) x 3 (number vs. length vs. mass) x 2 (judgment vs. explanation) analysis of variance was performed on the posttest scores. Verbal rule instruction and feedback were between-subjects variables, while concept and type of response were within-subject variables. A significant effect was obtained for verbal rule instruction, F(1,28) = 22.72, p < .Ol, indicating that children who were given the rules conserved more after training than children who were not given the rules. Type response was a significant source of variance, F( 1,28) = 7.61,~ < .05: judgments were more often correct than explanations. Concept was also a significant source of variance. A Tukey B test yielded significant differences, p < .Ol, between all three concepts. with mass, length, and number the order of decreasing difficulty. Both the interaction between verbal rule instruction and concept, F(2,56) = 4.50,~ < .05. and the interaction between concept and type of response, F(2,56) = 3.71,~ < .05, were significant. A simple main effects test indicated that the interaction between verbal rule instruction and concept was obtained because while performance on both length, F( 1,56) = 17.86, p < .Ol, and number, F(1,56) = 36.46, p < .Ol, problems was better in the verbal rule instruction condition, performance on the mass problems did not differ as a function of verbal rule instruction. A simple main effects test also indicated that the interaction between concept and type of response occurred because, although there were no differences in the number of correct judgments and number of correct explanations given on either number or mass problems, more correct judgments than correct explanations were given on length problems, F( 1.56) = 14.29, p < .Ol .
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AND
SELZER
Ten children provided correct judgments on both of the pretest number conservation problems, while nine children provided correct explanations on both of the pretest number conservation problems. None of the children made correct judgments or correct explanations on both of the length or both of the mass pretest problems. The possible effects of conserving number on the pretest upon the overall posttest scores were investigated. Six separate point-biserial correlations were computed-one on the judgment scores of the total sample, one on the explanation scores of the total sample, one on the judgment scores of the verbal rule instruction groups. one on the explanation scores of the verbal rule instruction groups. one on the judgment scores of the no verbal rule instruction groups. and one on the explanation scores of the no verbal rule instruction groups. The continuous variable of the point-biserial correlations was the total posttest score, while the dichotomous variable was the pretest number conservation score. More specifically, any child who gave one or more correct pretest number conservation judgments was assigned a score of 1, while any child who did not give at least one correct pretest number conservation judgment was assigned a score of 0. Explanation responses were scored in the same fashion. To test the significance of each of these correlations, separate t tests were performed. The only significant correlation on the explanation scores was in the no verbal rule instruction groups, t( 14) = 2.91.1, < .O:! (rpb = + .61). None of the correlations on the judgment scores was significant. However, the correlation on the judgment scores of the no verbal rule instruction group approached significance. t( 14) 1.86. p < .lO (rpb = +.45). Therefore, conserving number on the pretest influenced the overall posttest conservation scores only in the no verbal instruction groups, the influence being stronger on the explanation scores than on the judgment scores. Therefore, the superior posttest conservation performance of the verbal rule instruction groups over that of the no verbal rule instruction groups appeared to be primarily due to the effects of the training rather than being due to the initial conservation levels of the subjects. In order to test for nonspecific transfer, the responses to the mass conservation problems were analyzed separately. In the verbal rule instruction groups, four children provided correct judgments and five children provided correct explanations on both of the posttest mass conservation problems. None of these children could provide correct judgments or correct explanations on any of the pretest mass conservation problems. On the other hand, only one child in the no verbal rule instruction groups could correctly judge and explain the conservation of mass on the two posttest mass conservation problems. It is interesting to note that this child was already able to correctly judge and explain one of the two mass conservation problems on the pretest. A 2 (verbal
CONSERVATION
TRAINING
139
rule instruction vs. no verbal rule instruction) x 2 (conservation on posttest mass problems vs. no conservation on posttest mass problems) ChiSquare test performed on the judgment scores did not reveal a significant difference, x2(1) = 2.13. A 2 (verbal rule instruction vs. no verbal rule instruction) x 2 (conservation on posttest mass problems vs. no conservation on posttest mass problems) Chi-Square test performed on the explanation scores approached significance, x’(1) = 3.28. p < .lO. Discussion
The results of the present study demonstrate the effectiveness of the verbal rule instruction procedure in teaching four-year-old children to conserve. Subjects who received the verbal rules obtained better posttest scores a week after training than the subjects who did not receive the verbal rules. Although no subject in the verbal rule instruction conditions recited verbatim the rules provided by the experimenter, many subjects referred to reversibility (“because you can put it back here”) or to the lack of either addition or subtraction operations (“because you did not add anything’* or “because you did not take away anything”) in explaining their judgments. From the explanations. it appears that many subjects learned to focus on the transformations and were able to discriminate the types of transformations that do and do not affect the quantitative equality of the objects. The feedback procedure employed in the present study was not effective in training four-year-olds to conserve. The disparity of the present results with those in which feedback was successful may be a result of procedural differences. In the present study the subjects were simply given verbal feedback contingent on their judgments of conservation problems, while in both Kingsley and Hall’s (1967) and Bucher and Schneider’s (1973) studies the subjects were trained on a graded series of subtasks related to conservation with the use of several different types of feedback. If the subjects of the present study had been trained in the attainment of a hierarchy of subtasks related to conservation of number and length with the employment of the various types of feedback, especially those employed by Kingsley and Hall, the feedback procedure may have been more effective. Gelman’s requirements of systematically varying the irrelevant dimensions together with feedback were met in the present feedback procedure. If, as Gelman claims, nonconserving responses were due to the lack of feedback and chances to try alternative cues in conservation problems, then it would be expected that with the present feedback procedure subjects would learn to attend to the relevant and ignore the irrelevant dimensions, and thereby conserve. However. the results did not support this prediction. The most probable reason for the disparity may be the employment of fewer training trials in the present study in com-
140
DENNEY,
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parison with Gelman’s (1969). Another reason may be that the subjects in the present study were younger than those used in Gelman’s study. However, Emrick (1969) reported successful learning of conservation in four-year-olds using a similar procedure. A third reason for the disparity may be that the feedback procedure of the present study differed from both Gelman’s and Emrick’s in the employment of conservation rather than three-element oddity problems during training. Oddity problems may be more conducive to the discrimination of the relevant dimension than conservation problems. In each oddity problem, the subject is asked to respond with reference to a dimension such as “length.” Positive feedback confirms the subject’s prediction of the relevant dimension while negative feedback eliminates one of the dimensions. However, with conservation problems, the situation demands the subjects’s awareness of the relevant dimension ~1~s his judgment of what transformations do and do not affect that dimension. Consequently, while positive feedback confirms both of his predictions. negative feedback does not tell the subject precisely where he has gone wrong. Brainerd’s (1974) training procedure was very similar to that employed in the present study; training was given only on standard conservation problems and only verbal feedback was given. However, since “they are the same” was the correct answer on all of his pretest, training, and posttest trials, it could be that his subjects simply learned to say “the same” regardless of the question asked. Thus, we cannot conclude that his subjects actually learned anything about conservation. Although the subjects in the verbal rule instruction groups gave significantly more conservation responses to the length and number problems than the subjects in the no verbal rule instruction groups, they did not give more conservation responses on the mass problems. Thus, training children on number and length did not foster nonspecific transfer to mass conservation problems. This is not too surprising since children naturally acquire conservation of both number and length prior to conservation of mass. Generalization to types of conservation which are acquired prior to those on which training is given would be more likely to be obtained. Experiment 2 was designed to test this hypothesis. EXPERIMENT
2
In Experiment 2 four-year-olds who were trained on both length and mass conservation were tested for generalization on both number, which is naturally acquired before length and mass, and weight, which is naturally acquired after length and mass. Only the verbal rule instruction training method was used since the feedback training method used in Experiment 1 was not found to be effective.
CONSERVATION
141
TRAINING
Method
Participants were 32 white, middle-class, four-year-old children who attended day-care centers or nursery schools in Lawrence, Kansas. Half of the participants were male and half were female. Each child was tested and trained by one of two undergraduate male experimenters.
The study consisted of three phases: (a) a pretest for conservation of number. length, mass, and weight, (b) a training session which included conservation of length and mass tasks, and tc) a posttest identical to the pretest. Prefest. The pretest consisted of four subtests: one for conservation of number, one for conservation of length, one for conservation of mass, and one for conservation of weight. Each subtest was composed of two actual conservation problems and one addition/subtraction problem. The materials used were two rows of eight checkers each for number conservation tasks, two 12-in. strips of cardboard for length conservation tasks, two ball-shaped portions of red cfay for mass conservation tasks. and two round balls of clay and a balance for weight conservation tasks. Each child was seated directly opposite the experimenter at a table and was tested in the same manner as in Experiment 1 (i.e., equality of the stimuli was established in the same manner, and the format of the questions was the same). The exact stimulus rearrangements were as follows: Conservation subtest
Problem
Number
1
One
row
longer 2
One
One
I
the
was
placed
in both other
was
other
row
One cardboard toward the
perpendicular
removed
to look
to the
were
A small strip of cardboard the end of one of the
3
One
the
perpendicular
one
rev+
while
unchanged.
on the vertical plane child so that the end
2
cardboard
from
remained
strips of cardboard spondence.
from
directions
row.
row.
checker
the Length
spread
row
other 3
was than
was moved of the two
no longer
was cut cardboards
in correoff from but not
other. was
placed
to the
other
at the
center
cardboard.
and
142
DENNEY.
ZEYTINOGLU
AND
I
One ball uai; formed the other remained
2
A small amount hall while the
3
One
ball
the Weight
SELZER
wax
other
for-med
2
One
3
A small while
into
remained
One hall wa\ formed the other remained ball
wa\
fol-med
remained amount the
other
while
of clay wa5 added to one other remained unchanged.
I
other
into a su~sage unchanged.
a pancake
while
unchanged. into a snake unchanged. into
;L cube
while
while
the
unchanged. of clay remained
was
added
to one
ball
unchanged.
The experimenter obtained both a judgment measure and an explanation measure in the same manner as in Experiment I. A child who gave both a correct judgment and a correct explanation on any one of the nine actual conservation problems, i.e., those not dealing with addition or subtraction, was classified as a conserver and eliminated from the study. Treatment ~orzu’ifions. At the completion of the pretest the children were randomly assigned to one of the two treatment conditions-the verbal rule instruction condition or the control condition. An equal number of males and females were assigned to each condition. The children then were presented with six length conservation problems and six mass conservation problems. Three of the six problems involved changing the spatial arrangements of the stimuli and thus disturbing their perceptual equality, one problem involved the addition of some of the stimulus material to one of the stimuli but not to the other, one problem involved the subtraction of some of the stimulus material from one of the stimuli and not from the other, and one problem involved the addition of the same amount of stimulus material to both of the stimuli. The six length conservation problems were presented to each child in the following order: 1. One cardboard on the vertical plane was moved toward the child so that the two strips of cardboard were no longer in correspondence. 2. A small strip of cardboard was added to the end of one of the cardboards but not to the other. 3. One cardboard was placed at the center and perpendicular to the other cardboard. 4. A small strip of cardboard was cut from the end of one of the cardboards but not from the other. 5. One cardboard was placed at the top and perpendicular to the other cardboard in an L shape.
CONSERVATION
6. Two the stimulus
equal strips cardboards.
of cardboard
The six mass conservation the following order:
problems
143
TRAINING
were added to the ends of both of were
presented
to each child in
1. One ball was formed into a snake while the other remained unchanged. 3. A small, equal amount of clay was added to each ball. 3. One ball was formed into a ring while the other remained unchanged. 4. A small amount of clay was added to one ball while the other remained unchanged. 5. One ball was formed into a triangle while the other remained unchanged. 6. A small amount of clay was taken away from one ball while the other remained unchanged. These six different problems were each presented twice with different sets of stimuli. The conservation training problems were presented with the indicated stimulus sets in the following order: 1. 2. 3. 4.
Two 9-in. blue strips of cardboard (length conservation). Two equal balls of clay (mass conservation). Two 12-in. red strips of cardboard (length conservation). Two equal logs of clay (mass conservation).
At the beginning of each problem each child was asked if the two stimuli had the same amount of the relevant attribute. Equality of the two stimuli was estabiished in the same manner as in the pretest. Then the experimenter made the appropriate rearrangement ofthe stimuli. What happened subsequent to the stimulus transformation varied with the treatment condition. In the verbal rule instruction condition, the child was asked if the two stimuli were the “same” or “different” after the rearrangement. Following this the experimenter indicated the correct answer, then immediately provided the child with the appropriate conservation rule and demonstration in the same manner as in Experiment 1. In the control condition, the experimenter asked the child if the two stimuli were the “same” or “different” after each transformation. The experimenter did not give the child any feedback about the correctness of his or her answer or provide the child with any of the conservation rules, but instead proceeded directly to the next problem. Posttrst. A posttest was administered to each child approximately one week after the pretest. The procedure, the problems, the order of
144
DENNEY.
ZEYTINOGLU
AND
SELZER
presentation of the problems, and the scoring of the children’s were identical to those employed in the pretest.
responses
Results
The means of the judgment and explanation scores are presented in Table 2. Because performance on the pretest was equated by eliminating from the study all participants who gave a correct judgment and a correct explanation on any of the conservation questions, only the posttest results were analyzed. A 2 (training vs. no training) x 2 (male vs. female) x 2 (judgment vs. explanation scores) x 4 (number, length, mass, and weight conservation subtests) mixed analysis of variance was computed on the posttest scores. Training and sex were between-subjects variables: type of response and type of conservation were within-subject variables. This analysis revealed a highly significant main effect for training, F( 1.28) = 33.78,~ < .OOl. The children who received training had significantly higher posttest judgment and explanation scores than the children who did not receive training. The main effect for type of response was also significant, F( 1,28) = 8.18, /j < .Ol, indicating that participants made more correct judgment responses than explanation responses. The main effect for type of conservation was significant, F(3,84) = 5.95, /I < ,001, indicating that the children’s posttest scores differed significantly among the four subtests. A Tukey B comparison of the means of the four conservation subtests revealed that the children conserved more frequently on the length than on the mass or weight subtests. No other differences between subtests were significant. The interaction between training and type of conservation was significant. F-(3,84) = 2.89, (7 < .05, suggesting that the training differentially influenced posttest performance on the four subtests. The simple main TABLE MEANS
ot
Bo-FH JUDGMENT
2
4~11 EXPLANATION Type
Training
Verbal Control
Verbal Control
conditions
Number
Length
Judgment
score\
Explanation
xores
SCORES toR EXPNUMENI
7
of conservation Substance
Weight
rule instruction
rule instruction
I.75 .50
2.00 .x1
I .50 .?
I.31 .3x
CONSERVATION
TRAINING
14.5
effects procedure (Wirier, 1962) was used to further investigate this interaction. This analysis indicated that children who received training conserved more frequently on the number, length, mass, and weight subtests than did children who did not receive training, F(1,90) = 18.72, 30.10, 22.54, and 12.87, respectively, p < .OOl. Since training produced significant increases in performance on all four subtests, the interaction between training and type of conservation was not investigated further. It clearly was obtained only because the training effects were stronger for some subtests than for others. Discussion
The results of Experiment 2 clearly demonstrate significant nonspecific transfer both to a type of conservation which is typically acquired prior to those on which training was given (i.e., number) and to a type of conservation which is typically acquired after those on which training was given (i.e., weight). Although significant nonspecific transfer was not obtained in Experiment 1, the results of Experiment 2 are not too surprising since the transfer effects in Experiment 1 approached significance, x’( 1) = 2.13, p < .20 and x2(1) = 3.28, p < .lO for judgments and explanations, respectively. Thus, the results indicate that the verbal rule instruction procedure employed in the present research is an effective method for increasing conservation performance among four-year-olds on tests of both specific and nonspecific transfer up to one week after training. From a Piagetian perspective, one would not expect successful conservation learning with a procedure based exclusively upon the verbal provision of the conservation principle. With respect to the role of verbal transmission upon concept acquisition, Piaget (1973) stated that: Adequate verbal transmission of information relative to the operatory structures is assimilated only on the levels where the operations are elaborated on the basis of actions themselves or operations as interiorized actions, and if language favors this interiorization, it neither creates nor transmits ready-made structures by an exclusively linguistic means. (p. 1191.
In other words, according to Piaget, the child must possess the relevant cognitive structures before he will be able to assimilate verbally transmitted information. However, the present research demonstrated that children who have not yet acquired conservation concepts, and who are too young to possess the relevant cognitive structures, nevertheless benefit from the verbal rule instruction procedure in conservation acquisition. The superior posttest performance of the subjects in the verbal rule instruction conditions indicated that they effectively learned the information conveyed by the verbal rules, and were able to apply this learning to conservation problems presented to them a week after the training. The success of the verbal rule instruction procedure with fouryear-old children can be interpreted as resulting from the joint function
146
DENNEY.
ZEYTINOGLU
AND
SELZER
of the verbal rules and the demonstrations of the operations referred to by the verbal rules. The demonstrations of reversibility and addition/ subtraction operations performed on the objects during training may have served to make the verbal rules, which might otherwise be abstract, concrete and thus meaningful for the four-year-olds. Consequently, the understanding of the verbal rules as they apply to manipulable objects effectively served for the transfer of the information they conveyed to posttest conservation tasks. However, with the present experimental design the effects of the rule presentation and the demonstrations cannot be separated. In future research, verbal rule presentation and the demonstration of conservation-relevant information should be varied independently to assess the contribution of each upon conservation learning. REFERENCES
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operational convergence in logical thought development. J~III.II(I/ c~f‘ErprprrifF7cv7rtrl Ciiild /?YKh,/0~~. 1965. 2, 653-660. Beilin. H. The training and acquisition of logical operations. In M. F. Rosskopf. L. P. Steffe. & S. Taback t Eds. t. Piqytiw7 c.o~:r2ili1.e-d~~,~/~)~~~~1~~~f cd rntrrhrn2trric.cll cdrrc-crtiort Washington: National Council of Teachers of Mathematics. 1971. Brainerd, C. J. Training and transfer of transitivity, conservation, and class inclusion of length. Clrild fIer~a/<~~nrerrt. 1974. 35, 324-334. Bucher. B.. & Schneider. R. E. Acquisition and generalization of conservation by preschoolers. using operant training. J~wrr~crl o~‘Er/~c,rimr,2/trl Cllild Pc,rc.lr~~/og\, 1973. 16, 187-204. Christie, J. F.. & Smothergill. D. W. Discrimination and conservation of length. ~.~~c~/roflOF77iC Scicn~~e. 1970. 21, 3366337. Emrick. J. A. The acquisition and transfer of conservation skills by four-year-old children. Dksrrtutiorr Ah,stmct.s. 1969. 29. 2561-A. Gelman, R. Conservation acquisition: A problem of learning to attend to relevant attributes. J~wr!rtrl of‘E~prrinwnrtrl Child P.s?:c~/rt~/~~y.v. 1969. 7. 167- 187. Kingsley, R. C., & Hall, V. C. Training conservation through the use of learning sets. Child I)e~,c~/o~~,rnr,nt, 1967. 38, 1 I1 I - 1126. Mermelstein, E.. & Meyer. E. Conservation training techniques and their effects on different populations. C/t&f Det~c~/(~~~~wnt. 1969. 40, 47 l-490. Peters. D. L. Verbal mediators and cue discrimination in the training from nonconservation to conservation of number. Child I)~~,r/ol)/nc,,lt. 1970, 41, 707-712. Piaget. J. The child crrld wolilv: Proh/cr~7.\ c!/’ ,qcwtk /I.\w~/w/o~~. New York: Grossman Publishers. 1973. Rosenthal, T. L.. & Zimmerman. B. J. Modeling by exemplification and instruction in training conservation. nr~.c/r)/,nlc,nttr/ f’s~c~/n~/~~~,v, 1972. 6, 392-401. Scott. W. A. ~ 8 Wertheimer, M. /nfrrdrrc./icvr to ~‘,s?‘c./f~jk,,pic,trl r-~.sc~~rrc~h New York: John Wiley & Sons, Inc.. 1962. Siegler. R. S.. & Liebert, R. M. Effects of presenting relevant rules and complete feedback on the conservation of liquid quantity task. l)c~.c,/r,pn~c,n/~l/ P \~c~lrr>/~~,c~. 1977. 7, 133-138. Smith, 1. D. The effects of training procedures upon the acquisition of weight. c‘l~ilcl Dr\~~lopr~w~~r. 1968. 39, 5 15-526. Winer. B. J. Sfoti.sficol [~ritrc,if~ic,.< in (,.i/‘c,rir,,r,~trr/ tiesierr New York: McGraw - Hill Book Company. 1962. RECEIVED:
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31. lY76