The effect of within-pair variation and instructions on the transposition behavior of kindergarten and third grade children

JOURNAL

The

OF EXPERIMENTAL

Effect

CHILD

of Within-Pair

on the Transposition and

14, 379-3~

PSYCHOLOGY

Variation Behavior

Third

Grade

(1972)

and

Instructions

of Kindergarten

Children1

GRETA G. FEIN: Yale

University

The reported studies examined the test choices of kindergarten and third-grade children in the two-stimulus size transposition problem in response to variations in (a) the magnitude of the size difference between two objects (the within-pair difference), (b) the distance between training and test pairs (“near” and “far” tests), and (c) verbal instructions. It was hypothesized that third graders would be sensitive to variations in the degree of the difference between two objects and to instructions which identify specific aspects of the stimulus array. In contrast, kindergarteners were expected to base their choices upon the direction of the difference, and thus transpose regardless of within-pair variations and instructions. Results generally confirmed these expectations, supporting the notion that children at these ages differ in their organization of the stimulus field and in the scale of measurement they apply to objects differing in size.

A critical issue in the attempt to understand children’s performance in discrimination learning tasks is what dimensions of stimulation are related to their learning behaviors. The basic problem is that an experimenter’s definition of the stimulus may not directly reflect t.he manner in which the child organizes the stimulus field. The present studies are based on an analysis of one species of learning and transfer task, the transposition problem, in terms of two ways in which the experimenter’s and the child’s definition may differ. The proposed analysis distinguishes between (1) the manner in which children at different ages organize the units of stimulation on which to base a response, and (2) the scale of measurement they apply to these units. ‘These studies are based on a dissertation submitted to Yale University in partial fulfillment of the requirements of a Ph.D. degree. The author is deeply indebted to Joseph Glick for his advice in the formulation of this research, to William Kessen for his invaluable help in articulating fundamental concepts, to Allan Wagner for many provocative discussions, and to Wendell Garner and Thomas Achenback for their generous assistance. This research was supported under Grant HD 02570 from the National Institute of Child Health and Human Development. ‘Requests for reprints should be sent to Greta G. Fein, Psychology Department, Yale University, New Haven, CT 06510. Copyright All rights

@ 1972 by Academic Press, of reproduction in any form

379 Inc. reserved.

380

GRETA

G. FEIN

Studies of transposition are a proper field to examine these distinctions since major findings suggest that at any particular age level the learning and transfer performance of children may be related to their different conceptions .of the effective stimulus. A prototypic transposition problem consists of training a child to choose one of a pair of objects which differ in size. This pair is selected by the experimenter from an ordered series of sizes (labeled 1,2, . . . n) with a constant area ratio between adjacent sizes. If the training pair is 1-2, the child might be trained to ch.oose 2, the larger object. In a test phase designed to discover the subjective basis of the learning in training, the pair 2-3 or 5-6 might be presented and the child requested to choose either member of the pair. With respect to the ordered series of sizes, pair 2-3 is “closer” to the training pair than pair 5-6 which has given rise to the designation of these tests as “near” and “far” tests, respectively: To illustrate how test choices have been used as the basis for inferences about the dimensions of effective stimulation, consider those studies which report age differences in the choices children make on a far test. Generally, 5- and 6-year-old children transpose (i.e., choose object 6 in the example given) while 3- and 4-year-old children tend not to maintain a uniform pattern of choices (Kuenne, 1946; Alberts & Ehrenfreund, 1951; Potts, 1968). These studies have been interpreted to support the notion that older children classify “relational” features of the objects, whereas younger children presumably classify “absolute” features of the objects (Reese, 1962; White, 1965), or respond inconsistently. These interpretations can be derived either from an analysis of how children organize units of stimulation or from an analysis of the measurement scale they use. An organizational analysis assumes that subjects will respond to the stimulus field in one of two ways: (1) as a succession of pairs containing a small object and a large object, or (2) as an array of particular objects, one of which is the large one in the training pair, the small one in the test pair, the same one throughout, or a middle-sized one in a series composed of training and test objects. According to this analysis, relational might refer to the organization of the stimulus objects as homologous pairs, whereas absolute might refer to the organization of a specific object as a constant element in a changing stimulus array. In contrast, a measurement analysis considers the scale of measurement applied to the stimulus objects. One such scale might use the direction of the difference (the ordinal relationships) between members of a series of objects (i.e., “b” is bigger than “a,” “c” is bigger than (‘b”). Another might consider the degree of difference (the interval relationships) between members of a series (i.e., the difference between “a”

MEASUREMENT

SCALES

IN

TRANSPOSITION

381

and “b” is equal or unequal to the difference between ‘(c” and “b”). According to this analysis, the use of an interval scale might be indexed by the sensitivity of subjects to variations in the magnitude of the difference between the objects of a pair. In the example given, a variation of the within-pair difference occurs when the training pair is l-2 and the test pair is 2-6, rather than 2-3. Thus the terms relational and absolute might refer to the use of ordinal scales and metric scales, respectively. Studies of transposition have not attempted to distinguish the way children organize stimulation from the type of measurement scale they use. Moreover, the designations of relat,ional and absolute responding to describe choice behavior, by ignoring these alternative modes of stimulus classifica’tion, may offer a restricted view of the type of classifications children use. The present studies examined alternative ways of interpreting the choice behavior of 5- and g-year-old children. Experiments I and II considered the question of measurement scale. It was assumed that by 9 years of age, children are sensitive to the interval properties of a size series whereas at the younger age level they are not sensitive to these properties. In Expts. III and IV, it was assumed that age differences in the way children organize the stimulus field would be reflected in the way test instructions influence choice behavior. For example, the older children were expected to respond to the instruction, “choose the same one” by selecting the specific size which was correct during training, whereas the younger children were expected to choose the same pair value (i.e., small or large) which was correct during training. EXPERIMENT

I: THE EFFECT OF AGE AND WITHIN-PAIR TEST DIFFERENCE

Experiment I examined the notion that kindergarten children (5-6 years of age) use an ordinal scale to classify the difference between two objects, and that third-grade children (8-10 years of age) take into account the interval properties of the difference. These considerations led to the expectation that, on a near test, third- and fourth-grade children would transpose less as the magnitude of t’he within-pair test ratio increased and less than kindergarten children when within-pair test ratios were relatively extreme. Method Design. A 2 X 3 X 2 factorial design contained two grade levels (kindergarten and third grade), three within-pair test area ratios (1: 1.4, Group S-Small; 1: 1.96, Group M-Medium; and 1:3.8, Group L-Large),

382

GRETA

G. FEIN

and two training directions (Up-Down). The training ratio was 1:1.4 for all subjects. Test conditions are presented in Fig. 1. Subjects. Seventy-nine children were selected from a summer day camp. Forty-one who had completed kindergarten and ranged in age from 5.5 to 6.5 years and 28 who had completed third grade and ranged in age from 8.5 to 9.5 years were randomly assigned to experimental groups until there were eight Ss in each cell who met the training criterion. Nine kindergarteners and six third graders failed to reach criterion. Apparatus and stimuli. The apparatus was a modified version of the Wisconsin Testing Apparatus with two reward wells. The stimuli were selected from a series of 11 white %-in. thick masonite squares differing from each other by area ratios of 1: 1.4 and ranging in size from 1 to 28.9 in. Half the Ss in each condition were trained and tested with squares selected from the relatively large end of the continuum. For these Ss the training squares were 10-9, and 9 was positive (down direction). The other half were trained and tested with squares from the relatively small end of the continuum. Here the training squares were 2-3, and the positive square was 3 (up direction). Procedure. Two experimenters were employed. One experimenter (El), who sat behind the testing apparatus, arranged the stimuli and rewards UP TRAINING

DIRECTION

DOWN

DIRECTION

RATIO

I : 1.4

TEST

RATIO: +

Group

S -

1~1.4

q

il

Group

M -

I: 1.96

q+

h

Group

L -

I: 3.6

0 9

FIQURE

1

+ 0

5

MEASUREMENT

SCALES

IK

TRANSPOSITION

383

(golden raisins). The stimuli were alternated from left t,o right in a predetermined order (Gellerman, 1933). The other experimenter (E2), who sat slightly to the side and behind the subject, explained the experimental procedure, introduced each trial, and provided verbal information after each response. Instructions to the S were as follows: “Here are a raisin under the correct block. If you pick the correct the raisin. In this game you can win a raisin on every pick the correct block every time. Take a turn now correct block.” On every trial, before the stimuli appeared, the S other turn. Remember, pick the correct block.” All criterion of eight successive correct choices. The Ss terion in 60 trials were dropped from the experiment.

two blocks. (El) put block, you can keep turn. The idea is to and try to pick the was told, “Here’s nnthe Ss were run to a not reaching this cri-

The ten test trials began without a break in the procedure. The S received material reinforcement .on all test trials and verbal reinforcement was discontinued. All tests were near tests, i.e., the positive stimulus appeared in the test pair. Test stimuli for each condit.ion are shown in Fig. 1. Results rind D&cu.&on Trnining phase. The number of trials required to reach criterion was used to assess performance on the initial discrimination problem. The overall median was determined, and the proportion of Ss in each condition whose criterion score was less than the overall median of 6.5 was computed. An arcsin transformation was applied to these proportions. An analysis of variance performed on the transformed proportions failed to yield significant differences among groups.3 Test phase. Ninety-three percent of the Xs made the same choice on Test Trial 1 that they made on the remaining test trials. Therefore, only Trial 1 choices were considered in the following analyses. The proportion of subjects transposing in each condition is shown in Table 1. A preliminary analysis indicated that up-down differences were not significant. In subsequent analyses, these groups were collapsed. ‘With proportions, homogeneity of variance cannot be assumed because O’p varies with the values of P and N. When proportions are transformed to arcsins (+), the resultant distribution of + is approximately normal with unit variance: 0’ = l/N (Mosteller & Bush, 1954). Thus homogeneity of variance is assured. When proportions are negatively correlated, which is the case for proportions based on a median split, a correction factor must be applied to the base-line variance. In the present case, the base-line variance for the analysis of trials to criterion was increased by a factor 1 -7 where? was the average item intercorrelation (Gilson & Abelson, 1965).

384

GRETA

EXPERIMENT

I: PROPORTION

G.

FEIN

TABLE

1

OF SUBJECTS

TRANSPOSING

Test conditions within-pair Grade

S (1:1.4) 1.00 1.00

K 3

M (1:1.96) 1.00 .88

ON TEST

TRIAL

1

test area ratio L (1:3.8) .88 .50

Analysis of variance performed on arcsin-transformed proportions failed to reveal a significant age effect, nor any other main effects or interactions. As can be seen from Table 1, kindergarten children uniformly transposed regardless of conditions of test; third graders, on the other hand, transposed somewhat less as the within-pair difference increased. In order to assess the prediction that third- and fourth-grade children would transpose less than kindergarten children as the magnitude of the within-pair test ratio increased, analyses of variance were performed separately at each age level. These analyses indicated a marginal effect of within-pair difference for third graders [F(2,21) = 3.13, p < .lO], but not for kindergarteners (p < 1). Although the differences between age groups when test ratios were extreme were in the expected direction, these differences were not significant. Experiment I provides some support for the notion that the choice behavior of third graders would vary as a function of changes in the magnitude of the within-pair ratio. At the same time, the data suggest that in the absence of extreme variations in the test objects there is a strong tendency to transpose in both age groups. EXPERIMENT AND

II: THE EFFECT TEST DISTANCE

OF AGE, TEST DIFFERENCE, ON TRANSPOSITION

Experiment II was designed to replicate and extend the finding of Expt. I. Since the experimental variation presented in Expt. I might be equivalent to the variation presented in the usual dimension of near and far distance, attention was directed to separating the effect of withinpair change from the possible effect of change in general. Moreover, Zeiler (1966) reported a decline in transposition on a far test for 4- and &year-old children when the within-pair difference was relatively small and constant (area ratios of 1: 1.4). Experiment II, therefore, added the factor of between-pair distance to the factor of within-pair difference. A major difficulty in the interpretation of transfer effects stems from the limited amount .of information contained in the choice response. In order to permit a more detailed analysis of choice behavior, a choice-

MEASUREMENT

SCALES

IN

385

TRANSPOSITION

time measure was used in Expt. II. Generally, one would expect choice time to reflect the degree to which a child examines choice alternatives. In Expt. I, the uniform tendency of kindergarteners to transpose a.fter Test Trial 1 might have been supported by the occurrence of reinforcement on all test trials. In order to examine whether nonreinforcement of the choice made on the first test trial would lead kindergarteners to depart from uniform transposition and lead third graders to shift from one basis of choice to another, Expt. II eliminat,ed reinforcement during test trials. Method

Design. Two levels of within-pair difference (Small-Large), two levels of between-pair distance (Near-Far), and two directions (Up-Down) constituted the test variations presented to two age groups (kindergarten and third grade) and two sex groups. Training ratios for all subject.s were 1:1.4. Table 2 indicated the test conditions and the specific squares used. Subjects. The Ss were 62 kindergarteners and 48 third graders from a public school in a middle-class community. At each age level, the Ss were randomly assigned to each of four test conditions until there were 12 subjects in each condition who met the learning criterion. Fourteen kindergarteners failed to reach criterion and were excluded from further testing. The mean age of the kindergarteners was 5.6 years (range, 5.26.2 years). The mean age of the third graders was 8.8 years (range, 8.09.5 years). Apparatus and stimuli. The apparatus described in Expt. I was modi-

TEST

Group K ear-small

CONDITIONS

TABLE 2 AND STIMULI FOR EXPERIMENT

Experimental

conditions

Steps

WPTR

1

1:1.4

Near-large

1

1:3.8

Far-small

4

1:1.4

Far-large

4

1:3.8

Stimlh Training

numbers Test. pair

2.3

3-4

IO-9

9-x

2-3 10-Y 2-3 1 o-9

3-7 9-5 6-7 6-6

2-3

6-10

10-9

a 3 is positive b 9 is positive.

pair

II

6-2

386

GRETA

G.

FEIN

fied by fitting a blotter over the stimulus tray. Training and test objects were selected from the series described in Expt. I. For each direction (Up-Down), the square that would count as a transposition choice in the Near-Large condition was identical to the square that would count as a transposition choice in the Far-Small condition (i.e., block number 5 or 7, see Table 2). Procedure. The training procedure used in Expt. II differed from Expt. I in the following respects: (a) “Good player awards” were promised for being “good at figuring out things” and only verbal reinforcement (as described in Expt. I) was given for correct choices, and (b) during the initial instructions the stimulus objects were placed % in. apart and returned to their original 7-in. separation before the first training trial. Since the Near-Small and Near-Large tests were identical in Expts. I and II, it was possible to note the effect of these procedural changes on test behavior. In all other respects, training procedures were identical to those described in Expt. I. On Criterion Trial 6 of training, El recorded the S’s choice time. This criterion trial was close enough to Test Trial 1 to provide a baseline for evaluating change on Test Trial 1 without interfering with El’s handling of test objects on that trial. El recorded choice time on Test Trials 1, 2, 5, and 6. The ten test trials began without a break in the procedure. However, the Ss received no reinforcement on the first test trial or thereafter. Results

and Discussion

Training phase. The number of trials required to reach criterion was used to assess performance on the initial discrimination problem. Analyses were performed on the transformed proportion of subjects in each condition whose criterion score was less than the approximate overall median of 2.5. Approximately 65% of the third graders and 38% of the kindergarteners solved the problem in fewer than the median number of trials [P(1,88) = 6.3, p < .025]. Analyses failed to reveal any other overall effects or any differences within each age level among the four experimental groups. Whereas modifications in training procedures apparently produced faster learning in Expt. II than in I, it was the third graders who benefited the most from these changes. Test phase. Two measures of transposition, one for Test Trial 1 and another for Test Trials 2-10, were employed. The data for transposition and choice-time measures are presented in Tables 3 and 4, respectively. Since preliminary analyses performed on arcsin-transformed proportions failed to reveal effects related to direction or sex, these groups were collapsed in subsequent analyses.

3IEASUREMENT

SCALES

IN

TABLE EXPERIMENT

MORE

II-PROPORTION THAN THE MEDIAN

387

TRANSPOSITION

3

TRlNSPOSING ON TEST NUMBER OF TRIALS FOR TI~;w OF 8s

Text

TEIAL 1 AND TRIALS 2-10

conditions Far

Near .Measure Test, Trial Test Trials

1 2-10

ON

Grade

Small

Large

K 3 K 3

1.00 .Y2 1.00 .s3

1.00 ,50 1 .oo .30

--Small

Large

1 00 .s3 (83 .83

.83 .G7 .83 .50

Experiment I, as well as the theoretical orientation of these studies, suggested that, whereas kindergarteners would maintain a uniformly high level of transposition, third graders would range from high t,o low levels depending on the relative ambiguity of the task. However, a significant interaction was not expected since little change in the choices of the younger children was expected. On the other hand, a priori expectations regarding relationships among cells could be formulated and evaluated. Contrasts were applied to the results of t’his experiment and to those which follow it in order to provide a more sensitive test of these expectations. Transposition-test trial 1. As expected, kindergarteners transposed more t’han third graders [F(1,88) = 9.34, p < .OOS]. Transposit,ion occurred more often when within-pair differences were small than when they were large [F(1,88) = 5.61, p < .025]. No other main effects or interactions were significant. Analyses performed separately at each age level on arcsin-transformed cell proportions indicated a significant withinpair main effect for third graders [F(1,44) = 5.64, p < .025]. Neither the distance main effects nor any of the interactions reached convenTABLE

EIPEEXMENT II-PROPOWION OF Ss TRIAL 1 WBS LESS TH.IN

4

WHOSE THE

CHOICE MEDIAN

Test

TIME (ME:D

INCRE.~SE =

conditions

Near

Far .__

Measure Test Trial

Grade

1

K 3

TICST

ON

.75)

---~_

Small

Large

Small

Large

75

.s3

.42

.33

.75

.2 5

.50

2s

388

GRETA

G.

FEIN

tional levels of significance. Analyses of kindergarten data failed to reveal significant main effects or interactions among the four experimental groups. The decrease in transposition on a far test reported by Zeiler (1966) did not appear in the present study. A contrast was performed on proportions obtained by collapsing NearFar cells. The weights +l, fl, +l, and -3 were applied to KS (N + F), KL (N + F), 3s (N + F), and 3L (N + F). As expected, third graders in the Large Within-Pair Difference conditions transposed less than third graders in the Small Within-Pair Difference conditions, and less than kindergarteners in all conditions [F(1,92) = 13.73, p < .OOl]. Contrasts comparing Near-Far conditions failed to reveal significant differences. The notion that a reduction in transposition would depend on the large change in the physical size of the stimulus representing a transposition choice (in contrast to a change in the ratio) were not supported. In addition, the presence of the positive stimulus in the test pair did not have a significant influence on transposition. Although thirdgrade Ss in the Near-Large condition transposed somewhat less than Ss in the Far-Large condition, these differences were not significant. Transposition.-test trials 2-10. Only 10% of the kindergarteners and 22% of the third graders showed a shift in choice after nonreinforcement on Test Trial 1. None of these kindergarteners was in the Near-Large condition. Otherwise, there were no differences among experimental conditions. The measure used to assess transposition over Test Trials 2-10 was based on the proportion of subjects in each group who transposed on more than the median number of trials (median = 4.5). In other respects, analyses were identical to those reported for Test Trial 1. Kindergarteners transposed more than third graders [F( 1,88) = 9.9, p < .005], and the effect of within-pair differences reached a marginal level of significance. Analyses performed separately at each age level revealed that third graders transposed less when within-pair differences were large than when they were small [F(1,44) = 6.2, p < .025]. No other main effect or interaction was significant. Analyses of the kindergarten data failed to reveal significant main effects or interactions. The Grade X Within-Pair contrast indicated that third graders transposed less when differences were large than when they were small, and less than kindergarteners in all conditions [F(1,92) = 14.8, p < .OOl]. Thus, the pattern of results is similar for both transposition measures, suggesting that nonreinforcement of Test Trial 1 failed to modify choices made on that trial. Choice time. A difference measure was used to assess choice-time effects. For each S, choice time on Criterion Trial 6 during training was

MEASUREMENT

SCALES

IN

TRANSPOSITION

389

taken as a baseline, and the difference between baseline and choice time on Test Trial 1 was computed. A similar procedure was used to obtain difference scores for Test Trials 2, 5, and 6. The proportion of Ss in each cell whose difference scores on Test Trial 1 were less than the overall median are shown in Table 4. A high proportion indicates that many Ss failed to show substantial increases in choice time on the first test trial. In the overall analysis age differences were not significant, although far tests produced longer choice times than near tests [F(1,88) = 7.75, p < .Oll. Third grade choice-time effects paralleled those found on transposition measures. Longer choice times tended to be associated with large within-pair test differences. The within-pair main effect was significant [F(1,44) = 7.42, p < .Ol]. For those third graders who were tested with small within-pair differences, the negative correlation between choice time and Test Trial 1 choices was significant [@ = - .54, p < .005], whereas for those tested with large ratios the correlation (a = .13) was not significant. In addition, third-grade Ss in the Large condition who transposed on Test Trial 1 took longer to respond than Ss who transposed in the Small condition [x2 = 4.99, p < .05]. Thus, both transposition and non-transposition choices contributed to the increase in choice time when within-pair differences were large, indicating that large variations in the within-pair difference exerted a general influence on third graders regardless of their actual choice response. For kindergarteners, longer choice times appeared on far tests than on near tests [F(1,44) = 9.24, p < .OO5]. No other main effects or interactions were significant. A “distance” effect thus appeared on the choicetime measure, but not on transposition measures. Choice-time differences failed to appear on Test Trials 2, 5, and 6. The mean difference score on these trials was not significantly greater than zero, which indicates that choice time returned to baseline values on these trials. To summarize, the pattern of test choices of kindergarten and thirdgrade children found in Expt. I was replicated in Expt. II. The findings from choice-time and transposition measures suggest that the critical test event occurred on Test Trial 1, that this test event was related to within-pair variation for third graders, and that the influence of stimulus variation was not substantially modified by nonreinforcement. Within the range of conditions sampled, kindergarteners were persistent transposers, although a dist.ance effect appeared on the choice-time measure. On all measures, third graders exhibited variability related to variations in the degree of difference within pairs, but not to variations

390

GRETA

G. FEIN

in the distance between training and test pairs. Thus, children at each age level appeared to classify size differences within the pair of objects. However, the behavior of the kindergarten children was consistent with the view that they classify objects according to a dichotomized ordinal scale which is insensitive to metric variations. The behavior of older children, on the other hand, suggests that these children classify interval properties of the within-pair difference. EXPERIMENT

III:

CHOICE

AS A FUNCTION

OF

INSTRUCTIONS

The transposition task is often used to study the way in which children classify features of the environment. In order to serve this purpose a task must present subjects with a problem which, from the viewpoint of the experimenter, permits two or more solutions. We are proposing that children come to appreciate the experimenter’s classification scheme; that when they do so, they are faced with choice alternatives that instructions will influence according to the word meanings already established by the children. To examine this notion, instructions to choose the same block, the middle-size block and the correct block were given immediately prior to the first test trial. Within-pair test variations were introduced to examine the relation between the response to instructions and variations in the magnitude of the withinpair difference. Method Design, A 2 X 2 X 3 X 2 factorial design contained two grade levels (kindergarten and third grade), two within-pair test area ratios (Small, 1: 1.96; Large, 1:3.8), three test instructions (Correct, Same, and Middle-size), and two directions (Up-Down). The within-pair area ratio was 1: 1.96 for all Ss during training. All tests were near tests. Withinpair ratio variations are shown in Table 5.

TEST

CONDITIONS

Experimental Group

Steps

Near-small

1

Near-large

1

0 4 is positive. * 9 is positive.

TABLE 5 AND STIMULI FOR EXPERIMENT conditions WPTR

Stimulus Training 2-45 11-96 2-4a ll-9b

pair

III numbers Test 4-6 9-7 4-8 9-5

MEASUREMENT

SCALES

IN

TRANSPOSITION

391

Subjects. The Ss were 146 kindergarten and third-grade children selected from two schools in middle-class neighborhoods. They were randomly assigned to experimental conditions until twelve Ss in each cell had met training criterion. One kindergartener and one third grader failed to reach criterion. Approximately half the Ss in each group were boys and half were girls. The mean age of the kindergarteners was 5.9 years (range 5.5-6.4 years). The mean age of the third graders was 9.1 (range, 8.7-10.0 years). Procedure. Upon entering the experimental room the Ss were shown two prizes (a good player ticket and a chocolate bar) and told that children who were very good at figuring out things could pick one of the prizes when the games were over. As soon as the S was seated at the apparatus, he was instructed in the manner described in Expt. II. After the last criterion trial and before the first test trial, Ss were instructed to choose either the correct, the same, or the middle-size block. In the correct condition, subjects were told, “Here’s another turn. Remember, touch the correct block.” In the other instruction conditions, the word same or middle-size was substituted for the word correct. Subjects were told “good” on all test trials regardless of the test object selected. Postexperineental interview. All Ss were asked to enumerate, to describe, and then to draw “all the different blocks in the game.” The stimulus objects were not present at this time. Results

and Discussion

Training phase. The number of trials required to reach criterion was used to assess performance on the initial discrimination problem. An analysis of variance was performed on the arcsin-transformed proportion of Ss in each condition whose criterion score was less than the approximate overall median of 1.5. More kindergarteners (64%) than third graders (23%) solved the problem in fewer than the median number of precriterion trials [F( 1,142) = 25.08, p < .OOl] . In comparison with Expt. II, the larger training ratio of Expt. III substantially reduced t.he proportion of Ss who failed to reach criterion. It also may have influenced the differential difficulty of the task for those Ss who reached criterion at each age level. No other main effect or interaction was significant. Test phase. (a) Transposition-test trial 1. Differences between grades in the effect of the instructions Same and Middle-size (see Table 6) were reflected in the significant Grade X Instruction interaction [F(2,142) = 3.26, p < .05] which appeared in the overall analysis of transformed cell proportions. Kindergarten subjects transposed more than third-grade subjects [F(1,142) = 34.24, p < .OOl]. The Instruction main effect was also

392

GRETA

EXPERIMENT III-PROPORTION

G. FEIN

TABLE 6 OF Ss TRANSPOSING ON TEST TRIAL I Test conditions

Correct

Same

Middle-sized

Grade

Small

Large

Small

Large

Small

Large

K 3

.83 .83

.83 .42

.92 .17

.83 .25

.50 .08

.50 .08

significant [P(1,142) = 12.22, p < .OOl]. No other main effect or interaction was significant, although the pattern of effects for within-pair differences conformed to those found in previous studies. Orthogonal contrasts applied separately to third grade and kindergarten data revealed a significant difference between the Correct condition and all others for third graders [F(1,142) = 19.09, p’< .OOl], and failed to reveal a significant difference between Same and Middlelsize conditions. For kindergarten Ss, contrasts revealed a significant difference between Same and Middle-size conditions [F(1,142) = 8.91, p < .OOl], and not between Correct and all others. Thus for kindergarten subjects, it was the Middle-size instruction which reduced transposition, whereas for third-grade subjects both Same and Middle-size instructions produced this effect. (b) Post-experimental interview. In the postexperimental interview, 8s were asked to report the number of different blocks used during the experimental session. The Xs were given the opportunity to respond first verbally and then nonverbally to this question. In the verbal phase, S was credited with a correct response if he clearly designated three objects. Kindergarteners tended to use labels such as big, small, and middlesize, and only 33% gave a number in answer to the question, “How many blocks were in the game?” The third graders, on the other hand, exhibited considerable variety in their verbal descriptions. Some children outlined three sizes with their fingers or hand (“one this size, and another this size”), and a few attempted to estimate size (“the 2-inch ,one”), or size difference (“one was much bigger, about two times as big as the other one?). Approximately 97% of the third graders gave a number in answer to the “How many” question. Although generally the kindergarten children produced more correct reports when the within-pair difference was large than when small, these differences were not significant. In the second phase of the interview, Xs were asked to draw a picture of all the different blocks in the game. The proportion of correct judgeme&s is shown in Table 7. It is clear from the data that, when the

MEASUREMENT

SCALES

TABLE POSTEXP~;RIMGNTAL

Correct

Ii 3

393

TRANSPOSITION

7

INTERVIEW-PROPORTION OF Ss DRAWING NUMBER OF BLOCKS-EXPERIMENT III Test

Grade

IN

THE CORRECT

conditions Same

Middle-size

Small

Large

Small

Large

Small

Large

.50 ,543

.83 .83

.33 .s3

.93 .92

.50 58

.67 .75

within-pair difference is large, kindergarteners are as accurate as third graders. Surprisingly, performance in the Middle-size condition was less accurate than performance in other conditions. The failure of large ratios to reduce the transposition choices of kindergarten children even though three objects are discriminated, suggests that the extreme object might be treated as the second instance of a dichotomous category. A correct assessment could occur if, when the positive training object appears in the test pair, it is identified through its dichotomous value as the negative object of the training pair. For example, if the training pair is 1-2, and the test pair is 2-6, the child might first analyze the test pair into big and small, and then equate the training small with the test small. If test stimulus 6 is classified as an instance of large, although different from the training large, the child could arrive at a correct judgement by adding two large ones and one small one. Although kindergarteners seem able to discriminate size differences when one of the objects to be discriminated is represented in memory, these children appear to view the change between training and test as a substitution of objects within the category large rather than as a displacement of sizes along a continuum. The results for each type of test choice in the Middle-size condition suggest that the kindergarten child’s substitution hypothesis can be overcome. Of the Xs who transposed, 25% judged correctly, while of the Ss who chose the positive training object, 83% judged correctly. Thus for some children the instruction to choose the middle-size block might have disrupted the dichotomous categorizing of the test pair sufficiently to permit them to view the training-test shift as a displacement along an ordered continuum and to choose the appropriate block. Those children who transposed and drew only two blocks appeared to t,reat the label middle-size as another term for big or small. In sum, the present study indicated that, in the context of the twoobject transposition task, the referent of the terms correct, same, and

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middle-size will depend on the age of the child. In general, children between the ages of 8 and 10 years understand correct to refer to the withinpair component, and the terms same and middle-size to refer to specific properties of objects. Verbal instructions in the test phase, therefore, can influence the task component that a child of this age will apply to the test pair, a finding which supports the notion that multiple components of the situation are classified. Quite a different kind of understanding was demonstrated by children between the ages of 5 and 6 years. The finding that children at these ages apply the term same t,o the within-pair component is consistent with the notion that they organize a single component of the stimulus array which is maintained during training and test phases of the task. However, at some level, these children do seem to perceive specific properties of the objects-they were able to assess correctly the number of blocks used in the task, although this ability was expressed in choice behavior only when instructed to choose the middle-size block. Those children who chose the middle-sized object and drew a threeobject series were demonstrating their semantic comprehension of the term, their recognition of specific properties of objects, and their ability to construct an ordinal scale. In contrast, the children who transposed in this condition seemed to work with a binary classification scheme; the instructional ,label was either assimilated to this scheme or ignored. Thus, for some children verbal instructions may induce a more advanced level of analysis and choice. EXPERIMENT

IV:

THE

EFFECT

OF “NAMING”

ON TEST

CHOICE

Short of introducing additional stimulus dimensions, “naming” the positive training block would be another way of emphasizing the uniqueness of that block, If subjects were trained, for example, to choose the Susan block, the test instruction, “touch the Susan block” should indicate that choice on the basis of specific features was desired. Method Subjects. The subjects were 12 kindergarteners

and 12 third graders selected from the subject population described in Expt. III. Training and test. After being seated at the apparatus, the S was told, “Here are two blocks. We are going to pretend that one of them is the (child’s name) block.” The child’s own name thus replaced the word “correct” used in Expt. III. In all other respects, training procedures were identical to those used in that study. Instructions used during training were continued during the test phase. Within-pair area ratios were con-

MEASUREMENT

stant

(1: 1.96) during

training

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and test phases, and all tests were near

tests. Results

and Discussion

The overall median trial to criterion was approximat.ely 0.5, and differences in the number of trials required to reach criterion were not significant. The proportion of kindergarteners and third graders transposing on Test Trial 1 was 83% and 42Pr,, respectively. An F test performed on arcsin transformations of these proportions indicated that this difference was statistically significant [F(1,22) = 4.68, p < .051. Thus, naming the positive training object did not lead kindergarteners to use a specific criterion, but did influence the choices of third graders. Perhaps the best account of why this instruction failed to induce kindergarteners to choose on the basis of specific features was supplied by the child who commented, “Yeh, the big one is my brother and the lit’tle one is me.” SUMMARY

AND DISCUSSION

Over the range of conditions explored in these studies, kindergarteners transposed either more than, or as much as, third graders. With one exception, kindergarteners were persistent transposers. The instruction to choose t.he middle-size block in Expt. III produced the only decline in transposition at this age level. The first two studies reported here lend support to the view that there are differences in the kind of measurement scale used by kindergarten and third-grade children when they classify objects that differ according to size. Kindergarten children seem to use an ordinal scale which requires only that the direction of the difference (big-small) be considered. In contrast, third graders seem to add restrictions to the classification scheme which take into account the degree of the difference within a stimulus pair. The choice behavior of these older children thus appears to reflect the capacity to generate a series of sizes from the two presented during training such that the magnitude of the difference between adjacent members of the series (the unit interval) is determined by the area ratio of the training pair. As traditionally formulated, the transposition problem has been relatively insensitive to developmental changes such as these. If level of transposition were to be the only criterion of developmental status regardless of test circumstances, the third graders of the present study would be difficult to distinguish from the 3- and 4-year olds of other studies (Alberts & Ehrenfreund, 1951; Kuenne, 1946; Potts, 1968). The important developmental issue, however, is the relationship between the level of transposition displayed and the experimental conditions under

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which transposition and other aspects of choice behavior ‘are modified. Specifically, third graders entertain choice alternatives under conditions that fail to modify the choices of younger children. It may be the case that test variations in the within-pair ratio contradict the expectations developed by third graders during training about the nature of the series from which the objects have been selected. They may then reexamine the test objects and reassess the relationship between these and the training objects. It is at this point that they might discover plausible alternatives. Kindergarteners indicated a capacity for reexamination insofar as increased choice time on a far test might be taken to reflect such a capacity. Nonetheless, within-pair variations failed to produce a similar effect. Thus, it would appear that kindergarteners do not entertain expectations about the interval properties of the stimulus series. Although under some circumstances, kindergarteners detected as complete a set of events as third graders (in Expt. III they were able to estimate accurately the number of blocks when the within-pair test ratio was large), their overt choices depended on a single scheme, i.e., an ordinal classification of the within-pair component. Indeed, the ordinal label “middle-size” produced the only shift in kindergarten choices. At least some kindergarteners were able to apply the label appropriately by constructing a three-object series from two overlapping pairs, while others assimilated the middle-size label to a two-value binary system. These findings bear upon the nature of the relationship between language and thought in that they suggest that under certain conditions language may precipitate a reorganization of the stimulus field. Although third graders seemed to prefer a within-pair scheme, violations of interval restrictions, instructions such as “same,” and “naming” of the positive block were sufficient to indicate to these children that the specific object might be the appropriate choice. Other conditions that might influence the behavior at these age levels require further investigation. In summary, these studies provide data for inferences about the way children understand words and structure events to accommodate the response restrictions imposed by a task. In general, it would appear as though the potential for finding ambiguities in problems and in language increases with age. At least the number of alternative ways of defining the identity of objects and of establishing the reference of words seems to increase as children become able to code more dimensions of variability. Understanding the child’s system of meaning and reference has significance for the researcher who wishes to examine a particular aspect of development. Clearly, an experimental situation or a set of instructions

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that conveys one message to children at one age might convey a different message to children at another age. The outcome of an investigation might thus depend more on situational and instructional factors than on the factors presumably under investigation. Similar uncert.ainties face teachers, parents, and others concerned with the problem solving and language competence of children REFERENCES E., & EHRENFREUND, D. Transposition in children as a function of age. Journal of Experimental Psychology, 1951, 41, 3938. GELLERMANN, L. W. Chance orders of alternating stimuli in visual discrimination experiments. Journal of Genetic Psychology, 1933, 42, 296-208. GILSON, C., & ABELSON, R. P. The subjective use of inductive evidence. Journal of Personality and Social Psychology, 1965, 2, 301-310. KUENNF,, M. R. Experimental investigation of the relation of language to transposition behavior in young children. Journal of Experimental Psychology, 1946, 36, 471-490. MOSTELLER, F., & BUSH, R. R. Selected quantitative techniques. In G. Lindzey (Ed.), Handbook of social psychology, Vol. 1. Theory and method. Cambridge, MA: Addison-Wesley, 1954. POTTS, M. The effects of a morphological cue and of distinctive verbal labels on the transposition responses of 3, 4, and 5 year olds. Journal of Experimental Child Psychology, 1968, 6, 75-85. REESE, H. W. Verbal mediation as a function of age level. Psychological &&tin, 1962, 59, 502509. WHITE, S. H. Evidence for a hierarchical arrangement of learning processes.In I,. p. Lipsitt and C. C. Spiker (Eds.), Advances in child development and behavior. New York: Academic Press, 1965. ZEILER, M. D. Solution of the two-stimulus transposition problem by 4 and 5 year old children. Journal of Experimental Psychology, 1966, 71, 576579. ALBERTS,