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Assessing developmental differences in retention
JOURNAL
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
51,
Assessing Developmental ALVIN
Three
studies
dependent
during
incidental studies ologically
recall differed (i.e..
were
displayed
better
ontogenetic of acquisition
to
Differences
in Retention
Y. WANG
determine
In all
of paired with respect trials-to-criterion
grade group was also results across all three measures of absolute were reevaluated that statistically retention largely
designed
childhood.
338-363 (lYY1)
studies
whether 2nd
and
retention 4th
rates
graders
were
agefor
associates following a 48 h retention period. These to how degree of learning was controlled methodor fixed-trials), and in the case of Study 3 a 7th
included. Despite variations in procedure, studies was remarkably consistent. Specifically, and conditionalized recall suggested that
retention
are tested
than
younger
children.
However.
the
pattern traditional older children
when
the
same
of
data
using a technique (Underwood’s successive probability analysis) controls for degree of learning, developmental difference\ in disappeared. This finding suggests that many earlier reports of
changes in retention pcrformancc on
are due measurch
to the persistent and confounding of rccsll. c I’MI .\GNkrnlC rrc\\.
effect\ ,,,c
This paper attempts to clarify the debate concerning the effect of age upon retention rates during childhood. Specifically. do younger or older children perform better on long-term tests of recall? A review of some relevant studies suggeststhat despite the apparent simplicity of this question, there is little agreement regarding its answer. Indeed, a review of some representative studies yields every conceivable developmental outcome when the retention rates of younger and older children arc compared. For instance. some studies have found that rctention ability increases with age (Brainerd, Howe, Kingma. & Brainerd. 1984; Brainerd & Reyna, 1YYO;Chechile, Richman. Topinka. & Ehrensbeck. IYXl; Howe Kr Hunter. lYX6; Longstreth & Zoltan, IY78; Salatas bi Flavcll, lY76). This is compatible with the popular assumption that memory should improve with overall cognitive maturation. However, Portions Psychological assistance anonymous Reprints of Central
of in
the data Association.
wcrc
data collection. reviewer helped may hc obtained Florida. Orlando.
New
presented Orlean>,
at the I%S annual LA. I would like
meeting to thank
The comments of C. J. Braincrd. make this a better paper. from Alvin Y. Wang. Dcpartmcnt FL 31816.
of the Southcastcrn Lori Phillips for D.
W.
Abbott.
of Psychology.
and LJnivcrslty
her an
ASSESSING
RETENTION
IN CHILDREN
349
other investigations have reported the reverse finding; that is, superior long-term recall for younger compared to older children (Dempster, 1984; Walen, 1970). There are even a few studies suggesting that no ontogenetic changes in retention occur during childhood (Fajnsztejn-Pollack, 1973; Foos, Sabol, Corral, & Mobley, 1987). Is there any way by which these disparate findings may be reconciled? One possiblity is that this lack of consensus reflects the use of inadequate controls for equating learner differences during acquisition. Because measures of learning and retention tend to be correlated, uncontaminated measures of retention must somehow equate the amount learned by fast versus slow learners by the end of acquisiton (Underwood, 1954). Typically, older children learn faster than younger children; this was the case in all of the aforementioned developmental studies. Consequently, if the degree of original learning for younger and older children is not equated, measures of retention will necessarily be confounded with acquisition performance (Brainerd & Reyna. 1990; Dempster, lYX4). Two established procedures for equating learner differences hdve been used: the trials-to-criterion and the fixed-trials techniques. However, it may be that these traditional controls do not successfully equate learner differences as intended (Underwood, 1954). In the fixed-trials procedure, fast learners have a greater opportunity than slow learners to overlearn easy items. On the other hand. when a lenient trials-to-criterion technique is used, slow learners are more likely to overlearn easy items. However, a stringent acquisition criterion (e.g., two or more errorless trials) may provide greater opportunities for fast learners to develop effective learning strategies or encodings compared to slow learners (Wang, lY83). Thus. inconsistencies found across earlier studies may be due to the ineffcctiveness of traditional techniques for controlling degree of original learning. The Successive Probability Analysis The Successive Probability Analysis (SPA) was developed by Underwood (1954, 1964) for two reasons. First, it was designed to avoid the item-difficulty confound associated with traditional methods of control. Second, there is the cost-effective savings of needing to collect only delayed recall scores. Because the long-term retention of individual subjects is assessed against their degree of original learning (described below), subjects provide their own “baseline” data. Consequently, only one-half of the subjects are needed for the SPA compared to traditional procedures that require both immediate and delayed recall groups. The SPA requires an item-by-item assessment of associative strength (H) for each learning condition or age group. Measures of H are initially derived from the probability that an item was correctly learned at each trial of acquisition. After a constant number of trials, low H values rep-
350
ALVIN
Y. WANG
resent slow learning whereas high H values indicate more rapid acquisition rates. The H for each item is calculated by observing whether an item was correctly learned by a given trial as a function of the number of times it was correctly learned on the previous acquisition trial. For illustrative purposes, consider a study involving only three study-test trials during acquisition. The SPA would record whether an item was learned on trial 2 and also tally whether that item was correctly given on the first trial of acquisition. The SPA then continues to the next trial so that an item correctly learned on trial 3 is tabulated as a function of its learning history on trial 2. Thus, H values represent the probability that an item will be correctly learned on trial N + 1 given that it was learned a particular number of times on previous N trials. With sufficient sample size the average H values typically result in smooth “associative growth” curves for younger versus older children. The curves for each group are then fitted with exponential functions using a natural log (e) formula as seen below: H = 100 - Xr
“!’
In this generalized formula, the H for each item is a function of X (asymptotic value of the curve), b (exponent representing slope), and N (number correct during learning). The value 100 occurs because this is the theoretical limit (100% correct) of each learning curve. The significance of these formulas is that a common dimension of associative strength (i.e., item-difficulty) is now available for comparing the retention rates between groups. After obtaining the respective curve-fitting formulas for each age group, values of N can be substituted in the equation to solve for their respective Hs. If there are six study-test trials during acquisition, then N can take on the values from zero to six correct. This is the basis for the multiple abscissas seen in Figs. 2, 4, and 6. Once the abscissas have been established, the actual probability of recall (y-axis) is plotted as a function of the number of times an item was correctly learned (x-axis). Now it is possible to determine which values of N would produce equivalent measures of H for different age groups. For instance, compare the logarithmic abscissas of 2nd and 4th graders in Fig. 2. Older children required four correct learning trials for an item whereas younger children needed about six correct trials to reach comparable levels of associative strength. Thus, controlling learning rate in terms of H (rather than methodologically) is the basis whereby the SPA statistically equates for learner differences. Despite wide variations in learning speed, there are no differences in the retention rates of fast versus slow adult learners when the SPA is employed (Underwood, 1954, 1064). In fact. it has been suggested that material equated for H will have the same probability of being recalled
ASSESSING
RETENTION
IN CHILDREN
351
regardless of who is recalling the material (Underwood, 1972). Consequently, it is plausible that earlier reports of developmental differences in retention may be due to persistent item-difficulty confounds (termed “memorability gradients” by Brainerd & Reyna, 1990) rather than to ontogenetic changes in retention per se. The Present Studies
The three studies reported here used a modified version of the SPA’ for evaluating the retention rates of younger and older children. Moreover, the SPA was applied to learning and retention data that had been obtained in the traditional manner-the criterion and fixed-trials techniques. This was done so that an omnibus comparison across all of these control techniques could be undertaken. The present studies compared 2nd and 4th graders who were given an incidental test of cued recall for paired associates following a 48 h retention period. These studies differed in that one or the other traditional method of control was used, and in the case of Study 3, a 7th grade group was also included. Two related hypotheses guided the design of these three studies. The first hypothesis was that developmental differences in retention would be found using traditional techniques for evaluating recall. Because traditional procedures (and their associated measures of absolute or conditionalized recall) do not adequately equate for differences in learning speed across groups, any group differences that emerge in acquisition might still exist during recall. The second hypothesis was that by applying the SPA to the same data, any retention differences that were previously indicated by traditional analyses would now decrease or disappear. This seemed a reasonable outcome since the SPA would factor out any itemdifficulty effects not adequately controlled by either the criteria1 or fixedtrials method. STUDY
1
Method Subjects. The subjects were 30 2nd-grade (M = 86.3 months) and 30 4th-grade (M = 123.2 months) students attending two public elementary schools in Central Florida. They were randomly selected from a pool of potential subjects that returned signed informed consent forms from their parents. None had previously participated in a psychological study. Materials. Two different lists comprising 14 noun pairs each were devised with the restriction that pair members possess no discernable re’ A modified version of Underwood’s SPA was used here since no attempt WAS made to project associative growth curves to a seventh hypothetical acquisition trial. Therefore, all of the best-fit functions (see Appendix A) are based upon actual acquisition data without using any extrapolated data.
352
ALVIN
Y. WANG
12 IO 8
Mean Number Correct
6 4 2 0 0
1
2
3
4
5
6
Learning Trial FIG.
I.
The
mean
number
of pairs
learned
throughout
acquisition
hy 2nd
and
4th
gr;lde
children.
lationship to one another. Both lists contained simple, concrete nouns used previously by Wang & RiCharde (1987). In order to control for item effects, each list was learned by one-half of the children from each grade, Furthermore, different presentation orders for both acquisition and recall trials were generated for each child so that serial learning would be minimized. Procedure. Children were tested individually in sessions lasting approximately 30 min. During acquisition, all subjects learned a list of 14 noun pairs across 6 study-test trials. Both members of a paired associate were presented simultaneously on study trials whereas only the stimulus words followed by blank lines were shown on test trials. On test trials subjects were instructed to say aloud the response word they thought was presented with each stimulus word. Items on both study and test trials were presented at a 4 s rate using 4 x 6 inch index cards. The unannounced test of cued recall occurred 4X h after acquisition. A list of the original 14 stimulus words was shown with instructions to write down the correct response word next to the appropriate stimulus word. Children were encouraged to guess during the 5 min period of cued recall. Results und Discussim Acquisition. Figure 1 shows the mean number of correct pairs learned for each grade across the 6 study-test trials of acquisition. A 2 (Grade) x 6 (Trial) Analysis of Variance (ANOVA) revealed a main effect for Trial. F(5, 290) = 322.99, 19 < .OOl, and a highly significant Grade x Trial interaction, F(5, 290) = 594.01. p < ,001. The main effect of Grade was marginally significant. F (I, 58) = 2.60, p < .lO. This overall pattern of results suggests that while initial learning scores were comparable for
ASSESSING
Percent Recall
RETENTION
353
IN CHILDREN
40 -
.-.
2nd
t-t
4th
2nd 0
1
2
3
4
56 4th
0
Number Corrkt C&g Lear%& FIG. 2. The mean percentage recall for 2nd and 4th grade children as a function of the number of times an item was correctly learned (note the different logarithmic baselines due to different Hs).
all subjects, older children learned at increasingly faster rates as acquisition progressed. Recall. Long-term retention was evaluated using two traditional scoring methods in addition to the SPA. The traditional methods analyzed either absolute recall scores (max. = 14 pairs) or the percentage recalled conditionalized against the number correct on the last learning trial. A one-way ANOVA using absolute recall scores indicated that 4th graders (M = 12.0 pairs) retained significantly more pairs than 2nd graders (M = 7.7 pairs), F(I, 58) = 33.49, p < .OOl. Evaluating the conditionalized recall scores by the same ANOVA also suggested superior retention for older (M = 84.5%) compared to younger children (M = 74.8%). F(1, 58) = 5.72, p < .05. However, as noted earlier, interpretation of traditional recall measures is problematic given that they do not attempt to equate learner differences in associative strength (H). Consequently, preliminary conclusions are unwise despite the direction of the two reported ANOVAs. Therefore, the SPA was applied to the data of Study 1 to determine whether consideration of H would produce a different outcome. Figure 2 shows the cued recall performance of 2nd and 4th graders when recall is reevaluated using the SPA (see Appendix A). Notice that there are different logarithmic scales along the abscissa associated with each grade (faster accelerating H values are associated with older children throughout all the present studies). In comparison to their acquisition curves, there is no discernable difference in the overall recall ability of younger versus older children. This also stands in marked contrast to the two traditional. albeit imperfect measures of retention reported earlier. Nevertheless, it may be argued that a visual comparison of SPA curves may not wholly justify any conclusions that differ markedly from that which was obtained using traditional analyses. To counter this argument,
354
ALVIN
Y. WANG
a statistical technique which uses SPA data to derive loss scores was used.’ In this technique, the expected immediate recall performance for each subject was computed by summing the H values for all items correctly learned by that subject during acquisition. Richardson & Underwood (1957) report that the summed Hs for each subject provide a valid estimate for predicting performance on a test for immediate recall. Once an estimate of immediate recall was derived for each subject. individual loss scores were computed by subtracting each subject’s delayed recall score from their predicted immediate score. The results of this analysis indicated that the loss scores for 2nd (M = 1.7 pairs) and 4th (M = 1.3 pairs) were not significantly different from one another, F(1, 58) = 1.44. This finding corroborates the lack of developmental differences in retention suggested by the SPA curves in Fig. 2. Because no other statistical measures are appropriate for the SPA. the number of observations (ns) upon which each SPA curve is based becomes useful when considering the issue of reliability. Therefore, Appendix B shows the number of observations that yielded each data point for all of the SPA curves reported in this paper. The fact that the smallest sample size in Fig. 2 was II = 30 (the largest was n = 107) suggests that the obtained SPA curves are fairly reliable estimates of the effect of item difficulty upon recall. It therefore appears that attempts to assess retention rates will be confounded when item-difficulty effects are ignored, even when subjects are given the same opportunity to learn. Study 2 further explored this notion by imposing another control for learner differences, in addition to providing an equal opportunity to learn. Therefore, all children received six study-test trials as in Study 1. However, 4th graders received a list of 18 paired associates compared to only 14 pairs for 2nd graders. Pilot studies determined that these list lengths would ensure comparable acquisition levels (80% correct) if learning occurred across six study-test trials. Despite the joint effect of these two methodological controls, a pattern of findings similar to that of Study 1 was still expected. That is, traditional controls (whether in combination or alone) do not account for the greater associative strength that accrues to easy items acquired by fast compared to slow learners. Therefore, apparent differences in recall ability will remain confounded with differences in learning ability. Consequently, it was hypothesized that a modified SPA would indicate the absence of developmental differences whereas measures of absolute and conditionalized recall would spuriously suggest their presence.
’ This technique is only appropriate for the fixed-trial method using an equal number of to-be-learned items across groups. Therefore. loss scores were not derived for either Study 2 or Studv 3.
ASSESSING
RETENTION
355
IN CHILDREN
201
15-
-
Grade2
-
Grade4
Mean Number Correct
0 0
12
3
4
5
6
Learning Trial FIG. 3. children.
The mean
number
of pairs learned
throughout
acquisition
by 2nd and 4th grade
STUDY 2 Method Subjects. Children enrolled in the same public schools as Study 1 served as subjects. None had participated in the earlier study. A total of 30 2ndgrade (M = 88.2 months) and 30 4th-grade students (M = 125.6 months) were randomly selected from the pool of available subjects that had returned signed informed consent forms from their parents. Subjects were tested individually in sessions of about 40 min each. Materials and procedure. Two different lists of noun pairs were devised for each grade. The pairs in each list were randomly chosen from the pool of 56 nouns used in Study 1. List lengths for 2nd and 4th graders were 14 and 18 noun pairs respectively, since pilot studies indicated that a mean of 80% correctly learned could be expected when both grades receive six study-test trials. In all other respects, subjects were treated in the same manner as in Study 1. Therefore, items on the six study-test trials were presented at a 4 s rate and the unannounced test of cued recall occurred 48 h later. Materials on both acquisition and recall trials were presented in different random orders for each subject. Results and Discussion Acquisition. A one-way ANOVA comparing the percentage correct on the sixth learning trial indicated that both grades reached the same levels of learning, F < 1. The percentage correct was 82.4% (11.53 pairs) and 85.0% (15.23 pairs) for 2nd and 4th graders respectively. Hence, the attempt to equate percentage learned using different list lengths proved successful. Figure 3 shows the mean number correct as a function of grade and
356
ALVIN
Y. WANG
100 80 60 Percent Recall
40 20
FIG. number
4. The mean percentage recall of times an item was correctly
for 2nd and 4th grade learned.
children
as a function
of the
trial. The curves are quite similar to those reported in Fig. 1. A 2 (Grade) x 6 (Trial) ANOVA revealed that both main effects and their interaction were significant. Thus, 4th graders learned significantly more pairs than 2nd graders, F(1, 58) = 22.97, p < .OOl. In addition, the main effect of Trial indicated that learning progressed across all six study-test trials F(5, 290) = 401.35, p < .OOl. Finally, the Grade x Trial interaction suggested that older children learned at increasingly faster rates throughout acquisition compared to younger children F(5, 290) = 16.38. p < ,001. This replicates the acquisition data of Study 1. Recall. Retention was first assessed traditionally using absolute recall scores (max. = 14 or 18 correct) and then recall conditionalized against the number correct on the sixth learning trial. A one-way ANOVA evaluating absolute recall scores indicated higher levels of retention for 4th (13.2 pairs) compared to 2nd graders (7.8 pairs), F(1, 58) = 26.22, p < .OOl. The same ANOVA using conditionalized recall scores also suggested higher levels of retention for older (80.8%) compared to younger children (70.0%), F(1, 58) = 4.09, p < .05. Nevertheless, upon reevaluating the data using the SPA a pattern of results similar to Study 1 was obtained. Inspection of Fig. 4 indicates that when H is equated between 2nd and 4th graders the developmental differences that were suggested in acquisition (cf. Fig. 3) are no longer present during recall. Furthermore. in line with the results of Study 1. the SPA stands in contrast to the findings of the two traditional methods for assessing recall. This confirms the hypothesis that methodological controls for equating learner differences do not always provide an adequate means for disentangling the effects of learning upon measures of retention. Study 3 was designed to extend the findings of Studies 1 and 2 by using a different method for controlling learner differences. The previous two studies used the equal opportunity to learn method with or without ad-
ASSESSlNG
RETENTION
IN CHILDREN
357
justing list length. Both studies found that standard measures of recall (i.e., absolute and conditionalized scores) suggest developmental differences in recall ability whereas the modified SPA did not. Might the same pattern of findings occur if a common learning criterion was imposed upon all learners? To answer this question, Study 3 required children to study a paired associate list until the preestablished learning criterion (80% correct) was attained. One final consideration of Study 3 was whether the SPA’s null result for 2nd- versus 4th-grade comparisons would generalize across a wider age group. To test this possibility, children in the 7th grade were included in addition to 2nd and 4th graders. STUDY 3 Method
The subjects were 90 children (n = 30 at each grade) who attended either a public elementary or middle school in Central Florida. These students were in the 2nd (M = 92.7 months). 4th (M = 130.2 months), and 7th grade (M = 163.4 months). Subjects were randomly chosen from a pool of potential subjects that had returned signed consent forms from their parents. None had participated previously in a psychological study. Materials and procedure. The same pool of 56 nouns used previously provided the items for each paired associate list. List lengths of 10, 14, and 18 pairs were prepared for subjects in the 2nd, 4th, and 7th grades respectively. Pilot studies had indicated that these list lengths would ensure an approximately equal number of trials (4-5 trials) for each grade to reach the learning criterion of 80% correct. As before, two different lists were devised for each grade to reduce item effects, and a different studytest order was used for each child. Items were presented at a 4 s rate throughout learning and the unannounced test of cued recall followed the 48 h retention period. Subjects.
Results and Discussion Acquisition. A one-way ANOVA of the number of trials needed to reach criterion indicated no difference across the 2nd (M = 4.8), 4th (M = 4.3). and 7th grades (M = 4.4), F(2, 87) < 1. Thus, the different list lengths chosen proved to be successful in controlling the number of learning trials across grades. The learning curves shown in Fig. 5 are not unlike that reported in Studies 1 and 2. It should be noted that because some subjects needed fewer than four study-test trials to reach criterion, the n for each trial may be different than the total sample size at each grade. A 3 (Grade) x 4 (Trial) ANOVA analyzing the initial four study-test trials was per-
358
ALVIN
Y. WANG
-
Grade2
--e-
Grade4 Grade7
Mean Number Correct
n “.
0
I
I
I
I
1
I
1
2
3
4
5
6
Learning Trial FIG. 5. The grade children.
mean number
of pairs
learned
throughout
acquisition
by 2nd. 4th. and 7th
formed with ns of 21, 19, and 16 for the 2nd, 4th, and 7th grades respectively.3 Main effects for Grade, F(2, 53) = 28.31, p < .OOl, and Trial, F(3, 159) = 210.03, p < .OOl were found in addition to the Grade x Trial interaction, F(6, 159) = 26.85, p < .OOl. This mirrors exactly the pattern of acquisition data found in Studies 1 and 2. Thus. older children acquired items at a faster rate than younger children, and this advantage increased as learning progressed. Recd. A one-way ANOVA of absolute recall scores indicated a main effect of Grade in favor of the older children, F(2, 87) = 84.68, p < .OOl. The mean number of pairs recalled was 6.2, 9.8, and 16.3 for 2nd, 4th, and 7th graders respectively. Even when percentage recall was conditionalized against the number correct on the last learning trial, older children displayed an advantage, F(2, 87) = 7.32, p < .Ol. The respective conditionalized recall scores for 2nd, 4th, and 7th graders were 73.5%. 77.7%, and 92.3%. Once again, consideration of traditional measures of recall alone would lead one to suspect developmental differences in retention. However, as expected, the modified SPA applied to the same data presents an entirely different picture. As inspection of Fig. 6 reveals, the developmental differences that were apparent during acquisition are no longer present. And in marked contrast to the traditional recall measures just reported, the retention levels of younger and older children were highly comparable when H is equated. This pattern of findings strongly replicates the results of Studies 1 and 2. GENERAL
DISCUSSION
Three studies tested the notion that ontogenetic differences in retention that are suggested by traditional measures of recall would disappear when ’ ANOVAs using IIS, thereby reducing
data beyond the fourth their reliability.
trial
would
be based
on increasingly
smaller
ASSESSING
RETENTION
359
IN CHILDREN
80 Percent Recall
60 40
.-. a-* .-A
0 0
1 I 1
Number Correct
2 1 2
3 3
2nd 4th 7th
1
4 56 a iI 4 56
I
4th 7th
During Learning
FIG. 6. The mean percentage recall for 2nd, 4th. and 7th grade of the number of times an item was correctly learned.
children
as a function
item-difficulty (associative strength) is equated across age groups. The pattern of results across all three studies was consistent in documenting this claim. Specifically, two traditional measures of retention (absolute recall scores and conditionalized recall scores) suggested the presence of developmental differences in retention. However, reevaluation of the data using the SPA revealed that these differences were largely due to variations in the degree of original learning. This discrepancy between traditional measures and the SPA was found when learner differences were ostensibly equated using the fixed-trials method (Study l), the trials-tocriterion method (Study 2), or a combination of the two methods (Study 3). Furthermore, Studies 1 and 2 obtained this pattern of results when comparing 2nd and 4th graders, while Study 3 extended these findings to 7th grade children. The following conclusions seem warranted given this overall pattern of results: 1. When H (Underwood’s measure of item-difficulty or associative strength) is equated for 2nd, 4th, and 7th graders, retention appears to be constant throughout childhood. This is consistent with research indicating that retention rates remain invariant regardless of learning speed (in adults) or the type of material learned. For instance. fast and slow adult learners possessthe same rates of retention when their acquisition and retention scores are assessedusing the SPA (Underwood, 1954, 1964). Furthermore, paired associates, word lists, and sentences are all retained at the same rate by adult learners (Slamecka & McElree, 1983). 2. Two traditional, procedural controls are not wholly effective for equating learner differences (i.e., trials-to-criterion and fixed-trials) because the item-difficulty confound (measured by H) is ignored. However, the present studies suggest that the SPA can be successfully applied to
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ALVIN
Y. WANG
retention data collected by the customary means. In this event, spurious. age-related differences in recall will largely disappear. This conclusion may appear vulnerable in light of the argument that the null result obtained by the SPA is a statistically weak position from which to form opinions: particularly since there are no direct tests that statistically assess the reliability of SPA outcomes. However. it should be emphasized that this conclusion is grounded upon the consistent pattern of results obtained across three separate studies. That is. the SPA yielded a qualitatively distinct outcome compared to traditional measures of retention. Moreover, a statistical analysis based upon loss scores undertaken in Study 1 furnished additional support for the lack of developmental differences in retention as shown by the SPA. Finally, it should be reiterated that this pattern of results was obtained using different methods (criteria1 and fixed-trials) and across three age-groups. Thus, the SPA has called into question the adequacy of earlier attempts to cquatc learner differences that rely solely on procedural controls. 3. Perhaps the disparity that exists across several earlier studies regarding developmental differences in retention may now be resolved. Because neither criteria1 nor fixed-trial techniques are adequate methods for controlling learner differences. traditional measures of retention derived from these techniques will be confounded with differences in acquisition. For instance, several studies purporting to find superior retention in older children relied on a procedure (fixed-trials) that favored fast learners. Moreover. other studies reporting better retention in younger children used a lenient learning criterion (e.g., SC)‘% correct) which permitted more overlearning in slow learners. It should be noted that recent studies using criteria1 procedures have also yielded developmental differences in retention favoring older children (Brainerd, Kingma. & Howe. 1985; Brainerd et al., 1984; Brainerd & Reyna, 1990). It is possible that methodological practices common to all of these studies promote the occurrence of age-related effects in ways not inherent in the present studies. For instance. all of the studies in question used a stringent acquisition criterion (two errorless trials) in conjunction with the repeated-recall technique. It is likely that this methodology favors the formation of organizational strategies in older children, especially if used in combination with measures of free recall (Brainerd & Reyna. 1990). Because the ability to spontaneously engage effective organizational strategies develops during childhood (Best & Ornstein. 1986; Corsale & Ornstein, 1980) older children will more readily benefit from these learning conditions compared to younger children. Similarly, paired associate studies using stringent learning criteria (Brainerd. Kingma, & Howe, 1985) will support developmental differences in retention favoring older childrcn. In contrast. paired associate studies using lenient learning criteria provide relatively few opportunities for older children to generate elab-
ASSESSING
RETENTION
361
IN CHILDREN
orative strategies.4 However, as the number of acquisition trials increases, the opportunity for developing organizational strategies also greatly increases (Wang, 1983). Thus, paired associate studies using stringent learning criteria (Brainerd, Kingma, & Howe, 1985) will report strong developmental differences in retention favoring older children. The conclusion reached by Brainerd and his colleagues in the aforementioned studies is that age-related differences in retention are primarily retrieval-based rather than storage-based failures. This is not incompatible with the present finding that retention rates may be invariant during childhood. Because the present studies did not encourage subjective organization, or manipulate differential use of encoding or retrieval strategies (e.g., orienting tasks or categorized lists), the measures of retention reported would largely reflect the contribution of storage or availability factors. Indeed, when a distinction is made between storage forgetting and retrieval forgetting, developmental differences in retention are limited only to the latter type of forgetting (Brainerd et al., 1984; Brainerd et al.. 1985). APPENDIX
A
Below are the formulas used to derive the logarithmic baselines for the SPA curves depicted in Figs. 2, 4, and 6. These formulas represent the best-fit functions that describe the performance of each grade throughout acquisition. Corresponding levels of H for each grade can be obtained when the values zero through six (possible number correct during learning) are substituted for N. The resulting Hs are the bases whereby the abscissas for all SPA curves may be plotted. Best-fit Fig. 2 Grade Grade Fig. 4 Grade Grade Fig. 6 Grade Grade Grade
function
Variance
explained
2 4
H = loo-100.94e H = lOO-110.12e-
zI’v “*
( r’ = .99) ( i = .99)
2 4
H = 100-102.9Ye H = lOO-llO.gOe~
Liiy IXN
(i (i
= .YY) = .99)
2 4 7
H = 100-94.31~~ H = lOO-87.58eH = 100~84.02e
(? (i (i
= .Yh) = .93) = .95)
“,’ ‘W 35N
(%)
’ The fact that neither Study 2 nor Study 3 of the present paper seem to favor younger children should not invalidate this argument. The primary reason is that different list-lengths across grades were used in conjunction with a learning criterion of 80%. The consequence was that older children needed about the same number of acquisition trials as, younger children-not all that dissimilar from the standard fixed-trial procedure.
362
ALVIN
Y. WANG
APPENDIX
B
Below are the number of observations (ns) upon which each data point along an SPA curve was based. Number
Fig. 2 Grade Grade Fig. 4 Grade Grade Fig. 6 Grade Grade Grade
correct
during
learning
0
I
2
3
4
5
h
2 4
Y3 39
46 40
30 46
45 56
6X 82
80 107
5x 50
2 4
69 so
47 39
50 so
hb 77
hl 104
h8 130
5Y YO
2 4 7
37 37 20
70 8’) 117
61 104 137
45 95 139
42 55 00
23 19 38
II II 10
REFERENCES Best,
D. L.. & Omstein. P. A. (1986). Children’s generalization and communication of mnemonic organizational strategies. Developmental Psycholu~y. 22, 845-853. Brainerd, C. J., Howe, M. L., Kingma, .I.. & Brainerd, S. H. (1984). On the measurement of storage and retrieval contributions to memory development. Journal of Experimental Child Psychology. 37, 478-499. Brainerd, C. J., Kingma. J.. & Howe. M. L. (1985). On the development of forgetting. Child Development, 56, 1103-t 119. Brainerd, C. .I., & Reyna. V. F. (1990). Can age x learnability interactions explain the development of forgetting’? Developmenfa/ Psychology, 26, 194-203. Chechile. R. A., Richman, C. L.. Topinka. C., & Ehrensbcck, K. (19X1). A developmental study of the storage and retrieval of information. Child Development, 52, 151-250. Corsale. K., &: Ornstein, P. A. (1980). Developmental changes in children’s use of semantic information in recall. Journul of Experimenrul Child Psychology, 30, 23 I-245. Dempster, F. N. (1984). Conditions affecting test performance: A developmental study. Journal of Experimental Child Psychology. 31, 65-77. Fajnsztcjn-Pollack, G. (1973). A developmental study of decay rate in long-term memory. Journui of Experimental Child Psychology:y. 16, 125-?35. Foos. P. W., Sabol, M. A.. Corral. G.. S: Mobley. L. (1987). Age diffcrcnces in primary and secondary memory. Bulletin 01 the Psychonomic Society. 25, 15% 160. Howe, M. L.. & Hunter. M. A. (lYX6). Long-term memory in adulthood: An examination of the development of storage and retrieval processes at acquisition and retention. Developmental Review, 6. 333-364. Longstreth. L. E., & Zoltan, V. (197X). Developmental changes in retention: Independent of age’? Journal of Experimenrul Child Psycholo~v. 26, 1 IS- 121. Richardson, J., & Underwood, B. .I. (lY.57). Comparing retention of vcrhal lists after different rates of acquisition. Journrd of General P~sychology. 56, 1X7-192. Salatas, H., & Flavell, J. H. (1976). Retrieval of recently learned information: Dcvelopmcnt of strategies and control skills. Child Development, 47, 941.-04X. Slamecka, N. J.. Xr McElree. B. (IYX3). Normal forpctting of verbal lists as ;I function 01
ASSESSING
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their degree of learning. Journal of Experimental Psychology: Learning, Memory, & Cognition, 9, 384-397. Underwood. B. J. (1954). Speed of learning and amount retained: A consideration of methodology. Psychological Bulletin, 51, 276-282. Underwood, B. J. (1964). Degree of learning and the measurement of forgetting,. Journal of Verbal Learning and Verbal Behavior, 3, 112-129. Underwood, B. J. (1972). Are we overloading memory? In A. W. Melton & II. Martin (Eds.), Coding processes in human memory. Washington, D. C.: Winston. Walen. S. R. (1970). Recall in children and adults. Journal of Verbal Learning and Verbal Behavior, 9, 94-98. Wang, A. Y. (1983). Individual differences in learning speed. Journal of Experimental Psychology: Learning, Memory, and Cognition, 9, 300-312. Wang, A. Y.. & RiCharde, S. R. (1987). Development of memory-monitoring and selfefficacy in children. Psychological Reports, 60, 647-658. RECEIVED:
August
24. 1989; REVISED: August
2. 1990.
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
51,
Assessing Developmental ALVIN
Three
studies
dependent
during
incidental studies ologically
recall differed (i.e..
were
displayed
better
ontogenetic of acquisition
to
Differences
in Retention
Y. WANG
determine
In all
of paired with respect trials-to-criterion
grade group was also results across all three measures of absolute were reevaluated that statistically retention largely
designed
childhood.
338-363 (lYY1)
studies
whether 2nd
and
retention 4th
rates
graders
were
agefor
associates following a 48 h retention period. These to how degree of learning was controlled methodor fixed-trials), and in the case of Study 3 a 7th
included. Despite variations in procedure, studies was remarkably consistent. Specifically, and conditionalized recall suggested that
retention
are tested
than
younger
children.
However.
the
pattern traditional older children
when
the
same
of
data
using a technique (Underwood’s successive probability analysis) controls for degree of learning, developmental difference\ in disappeared. This finding suggests that many earlier reports of
changes in retention pcrformancc on
are due measurch
to the persistent and confounding of rccsll. c I’MI .\GNkrnlC rrc\\.
effect\ ,,,c
This paper attempts to clarify the debate concerning the effect of age upon retention rates during childhood. Specifically. do younger or older children perform better on long-term tests of recall? A review of some relevant studies suggeststhat despite the apparent simplicity of this question, there is little agreement regarding its answer. Indeed, a review of some representative studies yields every conceivable developmental outcome when the retention rates of younger and older children arc compared. For instance. some studies have found that rctention ability increases with age (Brainerd, Howe, Kingma. & Brainerd. 1984; Brainerd & Reyna, 1YYO;Chechile, Richman. Topinka. & Ehrensbeck. IYXl; Howe Kr Hunter. lYX6; Longstreth & Zoltan, IY78; Salatas bi Flavcll, lY76). This is compatible with the popular assumption that memory should improve with overall cognitive maturation. However, Portions Psychological assistance anonymous Reprints of Central
of in
the data Association.
wcrc
data collection. reviewer helped may hc obtained Florida. Orlando.
New
presented Orlean>,
at the I%S annual LA. I would like
meeting to thank
The comments of C. J. Braincrd. make this a better paper. from Alvin Y. Wang. Dcpartmcnt FL 31816.
of the Southcastcrn Lori Phillips for D.
W.
Abbott.
of Psychology.
and LJnivcrslty
her an
ASSESSING
RETENTION
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349
other investigations have reported the reverse finding; that is, superior long-term recall for younger compared to older children (Dempster, 1984; Walen, 1970). There are even a few studies suggesting that no ontogenetic changes in retention occur during childhood (Fajnsztejn-Pollack, 1973; Foos, Sabol, Corral, & Mobley, 1987). Is there any way by which these disparate findings may be reconciled? One possiblity is that this lack of consensus reflects the use of inadequate controls for equating learner differences during acquisition. Because measures of learning and retention tend to be correlated, uncontaminated measures of retention must somehow equate the amount learned by fast versus slow learners by the end of acquisiton (Underwood, 1954). Typically, older children learn faster than younger children; this was the case in all of the aforementioned developmental studies. Consequently, if the degree of original learning for younger and older children is not equated, measures of retention will necessarily be confounded with acquisition performance (Brainerd & Reyna. 1990; Dempster, lYX4). Two established procedures for equating learner differences hdve been used: the trials-to-criterion and the fixed-trials techniques. However, it may be that these traditional controls do not successfully equate learner differences as intended (Underwood, 1954). In the fixed-trials procedure, fast learners have a greater opportunity than slow learners to overlearn easy items. On the other hand. when a lenient trials-to-criterion technique is used, slow learners are more likely to overlearn easy items. However, a stringent acquisition criterion (e.g., two or more errorless trials) may provide greater opportunities for fast learners to develop effective learning strategies or encodings compared to slow learners (Wang, lY83). Thus. inconsistencies found across earlier studies may be due to the ineffcctiveness of traditional techniques for controlling degree of original learning. The Successive Probability Analysis The Successive Probability Analysis (SPA) was developed by Underwood (1954, 1964) for two reasons. First, it was designed to avoid the item-difficulty confound associated with traditional methods of control. Second, there is the cost-effective savings of needing to collect only delayed recall scores. Because the long-term retention of individual subjects is assessed against their degree of original learning (described below), subjects provide their own “baseline” data. Consequently, only one-half of the subjects are needed for the SPA compared to traditional procedures that require both immediate and delayed recall groups. The SPA requires an item-by-item assessment of associative strength (H) for each learning condition or age group. Measures of H are initially derived from the probability that an item was correctly learned at each trial of acquisition. After a constant number of trials, low H values rep-
350
ALVIN
Y. WANG
resent slow learning whereas high H values indicate more rapid acquisition rates. The H for each item is calculated by observing whether an item was correctly learned by a given trial as a function of the number of times it was correctly learned on the previous acquisition trial. For illustrative purposes, consider a study involving only three study-test trials during acquisition. The SPA would record whether an item was learned on trial 2 and also tally whether that item was correctly given on the first trial of acquisition. The SPA then continues to the next trial so that an item correctly learned on trial 3 is tabulated as a function of its learning history on trial 2. Thus, H values represent the probability that an item will be correctly learned on trial N + 1 given that it was learned a particular number of times on previous N trials. With sufficient sample size the average H values typically result in smooth “associative growth” curves for younger versus older children. The curves for each group are then fitted with exponential functions using a natural log (e) formula as seen below: H = 100 - Xr
“!’
In this generalized formula, the H for each item is a function of X (asymptotic value of the curve), b (exponent representing slope), and N (number correct during learning). The value 100 occurs because this is the theoretical limit (100% correct) of each learning curve. The significance of these formulas is that a common dimension of associative strength (i.e., item-difficulty) is now available for comparing the retention rates between groups. After obtaining the respective curve-fitting formulas for each age group, values of N can be substituted in the equation to solve for their respective Hs. If there are six study-test trials during acquisition, then N can take on the values from zero to six correct. This is the basis for the multiple abscissas seen in Figs. 2, 4, and 6. Once the abscissas have been established, the actual probability of recall (y-axis) is plotted as a function of the number of times an item was correctly learned (x-axis). Now it is possible to determine which values of N would produce equivalent measures of H for different age groups. For instance, compare the logarithmic abscissas of 2nd and 4th graders in Fig. 2. Older children required four correct learning trials for an item whereas younger children needed about six correct trials to reach comparable levels of associative strength. Thus, controlling learning rate in terms of H (rather than methodologically) is the basis whereby the SPA statistically equates for learner differences. Despite wide variations in learning speed, there are no differences in the retention rates of fast versus slow adult learners when the SPA is employed (Underwood, 1954, 1064). In fact. it has been suggested that material equated for H will have the same probability of being recalled
ASSESSING
RETENTION
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351
regardless of who is recalling the material (Underwood, 1972). Consequently, it is plausible that earlier reports of developmental differences in retention may be due to persistent item-difficulty confounds (termed “memorability gradients” by Brainerd & Reyna, 1990) rather than to ontogenetic changes in retention per se. The Present Studies
The three studies reported here used a modified version of the SPA’ for evaluating the retention rates of younger and older children. Moreover, the SPA was applied to learning and retention data that had been obtained in the traditional manner-the criterion and fixed-trials techniques. This was done so that an omnibus comparison across all of these control techniques could be undertaken. The present studies compared 2nd and 4th graders who were given an incidental test of cued recall for paired associates following a 48 h retention period. These studies differed in that one or the other traditional method of control was used, and in the case of Study 3, a 7th grade group was also included. Two related hypotheses guided the design of these three studies. The first hypothesis was that developmental differences in retention would be found using traditional techniques for evaluating recall. Because traditional procedures (and their associated measures of absolute or conditionalized recall) do not adequately equate for differences in learning speed across groups, any group differences that emerge in acquisition might still exist during recall. The second hypothesis was that by applying the SPA to the same data, any retention differences that were previously indicated by traditional analyses would now decrease or disappear. This seemed a reasonable outcome since the SPA would factor out any itemdifficulty effects not adequately controlled by either the criteria1 or fixedtrials method. STUDY
1
Method Subjects. The subjects were 30 2nd-grade (M = 86.3 months) and 30 4th-grade (M = 123.2 months) students attending two public elementary schools in Central Florida. They were randomly selected from a pool of potential subjects that returned signed informed consent forms from their parents. None had previously participated in a psychological study. Materials. Two different lists comprising 14 noun pairs each were devised with the restriction that pair members possess no discernable re’ A modified version of Underwood’s SPA was used here since no attempt WAS made to project associative growth curves to a seventh hypothetical acquisition trial. Therefore, all of the best-fit functions (see Appendix A) are based upon actual acquisition data without using any extrapolated data.
352
ALVIN
Y. WANG
12 IO 8
Mean Number Correct
6 4 2 0 0
1
2
3
4
5
6
Learning Trial FIG.
I.
The
mean
number
of pairs
learned
throughout
acquisition
hy 2nd
and
4th
gr;lde
children.
lationship to one another. Both lists contained simple, concrete nouns used previously by Wang & RiCharde (1987). In order to control for item effects, each list was learned by one-half of the children from each grade, Furthermore, different presentation orders for both acquisition and recall trials were generated for each child so that serial learning would be minimized. Procedure. Children were tested individually in sessions lasting approximately 30 min. During acquisition, all subjects learned a list of 14 noun pairs across 6 study-test trials. Both members of a paired associate were presented simultaneously on study trials whereas only the stimulus words followed by blank lines were shown on test trials. On test trials subjects were instructed to say aloud the response word they thought was presented with each stimulus word. Items on both study and test trials were presented at a 4 s rate using 4 x 6 inch index cards. The unannounced test of cued recall occurred 4X h after acquisition. A list of the original 14 stimulus words was shown with instructions to write down the correct response word next to the appropriate stimulus word. Children were encouraged to guess during the 5 min period of cued recall. Results und Discussim Acquisition. Figure 1 shows the mean number of correct pairs learned for each grade across the 6 study-test trials of acquisition. A 2 (Grade) x 6 (Trial) Analysis of Variance (ANOVA) revealed a main effect for Trial. F(5, 290) = 322.99, 19 < .OOl, and a highly significant Grade x Trial interaction, F(5, 290) = 594.01. p < ,001. The main effect of Grade was marginally significant. F (I, 58) = 2.60, p < .lO. This overall pattern of results suggests that while initial learning scores were comparable for
ASSESSING
Percent Recall
RETENTION
353
IN CHILDREN
40 -
.-.
2nd
t-t
4th
2nd 0
1
2
3
4
56 4th
0
Number Corrkt C&g Lear%& FIG. 2. The mean percentage recall for 2nd and 4th grade children as a function of the number of times an item was correctly learned (note the different logarithmic baselines due to different Hs).
all subjects, older children learned at increasingly faster rates as acquisition progressed. Recall. Long-term retention was evaluated using two traditional scoring methods in addition to the SPA. The traditional methods analyzed either absolute recall scores (max. = 14 pairs) or the percentage recalled conditionalized against the number correct on the last learning trial. A one-way ANOVA using absolute recall scores indicated that 4th graders (M = 12.0 pairs) retained significantly more pairs than 2nd graders (M = 7.7 pairs), F(I, 58) = 33.49, p < .OOl. Evaluating the conditionalized recall scores by the same ANOVA also suggested superior retention for older (M = 84.5%) compared to younger children (M = 74.8%). F(1, 58) = 5.72, p < .05. However, as noted earlier, interpretation of traditional recall measures is problematic given that they do not attempt to equate learner differences in associative strength (H). Consequently, preliminary conclusions are unwise despite the direction of the two reported ANOVAs. Therefore, the SPA was applied to the data of Study 1 to determine whether consideration of H would produce a different outcome. Figure 2 shows the cued recall performance of 2nd and 4th graders when recall is reevaluated using the SPA (see Appendix A). Notice that there are different logarithmic scales along the abscissa associated with each grade (faster accelerating H values are associated with older children throughout all the present studies). In comparison to their acquisition curves, there is no discernable difference in the overall recall ability of younger versus older children. This also stands in marked contrast to the two traditional. albeit imperfect measures of retention reported earlier. Nevertheless, it may be argued that a visual comparison of SPA curves may not wholly justify any conclusions that differ markedly from that which was obtained using traditional analyses. To counter this argument,
354
ALVIN
Y. WANG
a statistical technique which uses SPA data to derive loss scores was used.’ In this technique, the expected immediate recall performance for each subject was computed by summing the H values for all items correctly learned by that subject during acquisition. Richardson & Underwood (1957) report that the summed Hs for each subject provide a valid estimate for predicting performance on a test for immediate recall. Once an estimate of immediate recall was derived for each subject. individual loss scores were computed by subtracting each subject’s delayed recall score from their predicted immediate score. The results of this analysis indicated that the loss scores for 2nd (M = 1.7 pairs) and 4th (M = 1.3 pairs) were not significantly different from one another, F(1, 58) = 1.44. This finding corroborates the lack of developmental differences in retention suggested by the SPA curves in Fig. 2. Because no other statistical measures are appropriate for the SPA. the number of observations (ns) upon which each SPA curve is based becomes useful when considering the issue of reliability. Therefore, Appendix B shows the number of observations that yielded each data point for all of the SPA curves reported in this paper. The fact that the smallest sample size in Fig. 2 was II = 30 (the largest was n = 107) suggests that the obtained SPA curves are fairly reliable estimates of the effect of item difficulty upon recall. It therefore appears that attempts to assess retention rates will be confounded when item-difficulty effects are ignored, even when subjects are given the same opportunity to learn. Study 2 further explored this notion by imposing another control for learner differences, in addition to providing an equal opportunity to learn. Therefore, all children received six study-test trials as in Study 1. However, 4th graders received a list of 18 paired associates compared to only 14 pairs for 2nd graders. Pilot studies determined that these list lengths would ensure comparable acquisition levels (80% correct) if learning occurred across six study-test trials. Despite the joint effect of these two methodological controls, a pattern of findings similar to that of Study 1 was still expected. That is, traditional controls (whether in combination or alone) do not account for the greater associative strength that accrues to easy items acquired by fast compared to slow learners. Therefore, apparent differences in recall ability will remain confounded with differences in learning ability. Consequently, it was hypothesized that a modified SPA would indicate the absence of developmental differences whereas measures of absolute and conditionalized recall would spuriously suggest their presence.
’ This technique is only appropriate for the fixed-trial method using an equal number of to-be-learned items across groups. Therefore. loss scores were not derived for either Study 2 or Studv 3.
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IN CHILDREN
201
15-
-
Grade2
-
Grade4
Mean Number Correct
0 0
12
3
4
5
6
Learning Trial FIG. 3. children.
The mean
number
of pairs learned
throughout
acquisition
by 2nd and 4th grade
STUDY 2 Method Subjects. Children enrolled in the same public schools as Study 1 served as subjects. None had participated in the earlier study. A total of 30 2ndgrade (M = 88.2 months) and 30 4th-grade students (M = 125.6 months) were randomly selected from the pool of available subjects that had returned signed informed consent forms from their parents. Subjects were tested individually in sessions of about 40 min each. Materials and procedure. Two different lists of noun pairs were devised for each grade. The pairs in each list were randomly chosen from the pool of 56 nouns used in Study 1. List lengths for 2nd and 4th graders were 14 and 18 noun pairs respectively, since pilot studies indicated that a mean of 80% correctly learned could be expected when both grades receive six study-test trials. In all other respects, subjects were treated in the same manner as in Study 1. Therefore, items on the six study-test trials were presented at a 4 s rate and the unannounced test of cued recall occurred 48 h later. Materials on both acquisition and recall trials were presented in different random orders for each subject. Results and Discussion Acquisition. A one-way ANOVA comparing the percentage correct on the sixth learning trial indicated that both grades reached the same levels of learning, F < 1. The percentage correct was 82.4% (11.53 pairs) and 85.0% (15.23 pairs) for 2nd and 4th graders respectively. Hence, the attempt to equate percentage learned using different list lengths proved successful. Figure 3 shows the mean number correct as a function of grade and
356
ALVIN
Y. WANG
100 80 60 Percent Recall
40 20
FIG. number
4. The mean percentage recall of times an item was correctly
for 2nd and 4th grade learned.
children
as a function
of the
trial. The curves are quite similar to those reported in Fig. 1. A 2 (Grade) x 6 (Trial) ANOVA revealed that both main effects and their interaction were significant. Thus, 4th graders learned significantly more pairs than 2nd graders, F(1, 58) = 22.97, p < .OOl. In addition, the main effect of Trial indicated that learning progressed across all six study-test trials F(5, 290) = 401.35, p < .OOl. Finally, the Grade x Trial interaction suggested that older children learned at increasingly faster rates throughout acquisition compared to younger children F(5, 290) = 16.38. p < ,001. This replicates the acquisition data of Study 1. Recall. Retention was first assessed traditionally using absolute recall scores (max. = 14 or 18 correct) and then recall conditionalized against the number correct on the sixth learning trial. A one-way ANOVA evaluating absolute recall scores indicated higher levels of retention for 4th (13.2 pairs) compared to 2nd graders (7.8 pairs), F(1, 58) = 26.22, p < .OOl. The same ANOVA using conditionalized recall scores also suggested higher levels of retention for older (80.8%) compared to younger children (70.0%), F(1, 58) = 4.09, p < .05. Nevertheless, upon reevaluating the data using the SPA a pattern of results similar to Study 1 was obtained. Inspection of Fig. 4 indicates that when H is equated between 2nd and 4th graders the developmental differences that were suggested in acquisition (cf. Fig. 3) are no longer present during recall. Furthermore. in line with the results of Study 1. the SPA stands in contrast to the findings of the two traditional methods for assessing recall. This confirms the hypothesis that methodological controls for equating learner differences do not always provide an adequate means for disentangling the effects of learning upon measures of retention. Study 3 was designed to extend the findings of Studies 1 and 2 by using a different method for controlling learner differences. The previous two studies used the equal opportunity to learn method with or without ad-
ASSESSlNG
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357
justing list length. Both studies found that standard measures of recall (i.e., absolute and conditionalized scores) suggest developmental differences in recall ability whereas the modified SPA did not. Might the same pattern of findings occur if a common learning criterion was imposed upon all learners? To answer this question, Study 3 required children to study a paired associate list until the preestablished learning criterion (80% correct) was attained. One final consideration of Study 3 was whether the SPA’s null result for 2nd- versus 4th-grade comparisons would generalize across a wider age group. To test this possibility, children in the 7th grade were included in addition to 2nd and 4th graders. STUDY 3 Method
The subjects were 90 children (n = 30 at each grade) who attended either a public elementary or middle school in Central Florida. These students were in the 2nd (M = 92.7 months). 4th (M = 130.2 months), and 7th grade (M = 163.4 months). Subjects were randomly chosen from a pool of potential subjects that had returned signed consent forms from their parents. None had participated previously in a psychological study. Materials and procedure. The same pool of 56 nouns used previously provided the items for each paired associate list. List lengths of 10, 14, and 18 pairs were prepared for subjects in the 2nd, 4th, and 7th grades respectively. Pilot studies had indicated that these list lengths would ensure an approximately equal number of trials (4-5 trials) for each grade to reach the learning criterion of 80% correct. As before, two different lists were devised for each grade to reduce item effects, and a different studytest order was used for each child. Items were presented at a 4 s rate throughout learning and the unannounced test of cued recall followed the 48 h retention period. Subjects.
Results and Discussion Acquisition. A one-way ANOVA of the number of trials needed to reach criterion indicated no difference across the 2nd (M = 4.8), 4th (M = 4.3). and 7th grades (M = 4.4), F(2, 87) < 1. Thus, the different list lengths chosen proved to be successful in controlling the number of learning trials across grades. The learning curves shown in Fig. 5 are not unlike that reported in Studies 1 and 2. It should be noted that because some subjects needed fewer than four study-test trials to reach criterion, the n for each trial may be different than the total sample size at each grade. A 3 (Grade) x 4 (Trial) ANOVA analyzing the initial four study-test trials was per-
358
ALVIN
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-
Grade2
--e-
Grade4 Grade7
Mean Number Correct
n “.
0
I
I
I
I
1
I
1
2
3
4
5
6
Learning Trial FIG. 5. The grade children.
mean number
of pairs
learned
throughout
acquisition
by 2nd. 4th. and 7th
formed with ns of 21, 19, and 16 for the 2nd, 4th, and 7th grades respectively.3 Main effects for Grade, F(2, 53) = 28.31, p < .OOl, and Trial, F(3, 159) = 210.03, p < .OOl were found in addition to the Grade x Trial interaction, F(6, 159) = 26.85, p < .OOl. This mirrors exactly the pattern of acquisition data found in Studies 1 and 2. Thus. older children acquired items at a faster rate than younger children, and this advantage increased as learning progressed. Recd. A one-way ANOVA of absolute recall scores indicated a main effect of Grade in favor of the older children, F(2, 87) = 84.68, p < .OOl. The mean number of pairs recalled was 6.2, 9.8, and 16.3 for 2nd, 4th, and 7th graders respectively. Even when percentage recall was conditionalized against the number correct on the last learning trial, older children displayed an advantage, F(2, 87) = 7.32, p < .Ol. The respective conditionalized recall scores for 2nd, 4th, and 7th graders were 73.5%. 77.7%, and 92.3%. Once again, consideration of traditional measures of recall alone would lead one to suspect developmental differences in retention. However, as expected, the modified SPA applied to the same data presents an entirely different picture. As inspection of Fig. 6 reveals, the developmental differences that were apparent during acquisition are no longer present. And in marked contrast to the traditional recall measures just reported, the retention levels of younger and older children were highly comparable when H is equated. This pattern of findings strongly replicates the results of Studies 1 and 2. GENERAL
DISCUSSION
Three studies tested the notion that ontogenetic differences in retention that are suggested by traditional measures of recall would disappear when ’ ANOVAs using IIS, thereby reducing
data beyond the fourth their reliability.
trial
would
be based
on increasingly
smaller
ASSESSING
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80 Percent Recall
60 40
.-. a-* .-A
0 0
1 I 1
Number Correct
2 1 2
3 3
2nd 4th 7th
1
4 56 a iI 4 56
I
4th 7th
During Learning
FIG. 6. The mean percentage recall for 2nd, 4th. and 7th grade of the number of times an item was correctly learned.
children
as a function
item-difficulty (associative strength) is equated across age groups. The pattern of results across all three studies was consistent in documenting this claim. Specifically, two traditional measures of retention (absolute recall scores and conditionalized recall scores) suggested the presence of developmental differences in retention. However, reevaluation of the data using the SPA revealed that these differences were largely due to variations in the degree of original learning. This discrepancy between traditional measures and the SPA was found when learner differences were ostensibly equated using the fixed-trials method (Study l), the trials-tocriterion method (Study 2), or a combination of the two methods (Study 3). Furthermore, Studies 1 and 2 obtained this pattern of results when comparing 2nd and 4th graders, while Study 3 extended these findings to 7th grade children. The following conclusions seem warranted given this overall pattern of results: 1. When H (Underwood’s measure of item-difficulty or associative strength) is equated for 2nd, 4th, and 7th graders, retention appears to be constant throughout childhood. This is consistent with research indicating that retention rates remain invariant regardless of learning speed (in adults) or the type of material learned. For instance. fast and slow adult learners possessthe same rates of retention when their acquisition and retention scores are assessedusing the SPA (Underwood, 1954, 1964). Furthermore, paired associates, word lists, and sentences are all retained at the same rate by adult learners (Slamecka & McElree, 1983). 2. Two traditional, procedural controls are not wholly effective for equating learner differences (i.e., trials-to-criterion and fixed-trials) because the item-difficulty confound (measured by H) is ignored. However, the present studies suggest that the SPA can be successfully applied to
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ALVIN
Y. WANG
retention data collected by the customary means. In this event, spurious. age-related differences in recall will largely disappear. This conclusion may appear vulnerable in light of the argument that the null result obtained by the SPA is a statistically weak position from which to form opinions: particularly since there are no direct tests that statistically assess the reliability of SPA outcomes. However. it should be emphasized that this conclusion is grounded upon the consistent pattern of results obtained across three separate studies. That is. the SPA yielded a qualitatively distinct outcome compared to traditional measures of retention. Moreover, a statistical analysis based upon loss scores undertaken in Study 1 furnished additional support for the lack of developmental differences in retention as shown by the SPA. Finally, it should be reiterated that this pattern of results was obtained using different methods (criteria1 and fixed-trials) and across three age-groups. Thus, the SPA has called into question the adequacy of earlier attempts to cquatc learner differences that rely solely on procedural controls. 3. Perhaps the disparity that exists across several earlier studies regarding developmental differences in retention may now be resolved. Because neither criteria1 nor fixed-trial techniques are adequate methods for controlling learner differences. traditional measures of retention derived from these techniques will be confounded with differences in acquisition. For instance, several studies purporting to find superior retention in older children relied on a procedure (fixed-trials) that favored fast learners. Moreover. other studies reporting better retention in younger children used a lenient learning criterion (e.g., SC)‘% correct) which permitted more overlearning in slow learners. It should be noted that recent studies using criteria1 procedures have also yielded developmental differences in retention favoring older children (Brainerd, Kingma. & Howe. 1985; Brainerd et al., 1984; Brainerd & Reyna, 1990). It is possible that methodological practices common to all of these studies promote the occurrence of age-related effects in ways not inherent in the present studies. For instance. all of the studies in question used a stringent acquisition criterion (two errorless trials) in conjunction with the repeated-recall technique. It is likely that this methodology favors the formation of organizational strategies in older children, especially if used in combination with measures of free recall (Brainerd & Reyna. 1990). Because the ability to spontaneously engage effective organizational strategies develops during childhood (Best & Ornstein. 1986; Corsale & Ornstein, 1980) older children will more readily benefit from these learning conditions compared to younger children. Similarly, paired associate studies using stringent learning criteria (Brainerd. Kingma, & Howe, 1985) will support developmental differences in retention favoring older childrcn. In contrast. paired associate studies using lenient learning criteria provide relatively few opportunities for older children to generate elab-
ASSESSING
RETENTION
361
IN CHILDREN
orative strategies.4 However, as the number of acquisition trials increases, the opportunity for developing organizational strategies also greatly increases (Wang, 1983). Thus, paired associate studies using stringent learning criteria (Brainerd, Kingma, & Howe, 1985) will report strong developmental differences in retention favoring older children. The conclusion reached by Brainerd and his colleagues in the aforementioned studies is that age-related differences in retention are primarily retrieval-based rather than storage-based failures. This is not incompatible with the present finding that retention rates may be invariant during childhood. Because the present studies did not encourage subjective organization, or manipulate differential use of encoding or retrieval strategies (e.g., orienting tasks or categorized lists), the measures of retention reported would largely reflect the contribution of storage or availability factors. Indeed, when a distinction is made between storage forgetting and retrieval forgetting, developmental differences in retention are limited only to the latter type of forgetting (Brainerd et al., 1984; Brainerd et al.. 1985). APPENDIX
A
Below are the formulas used to derive the logarithmic baselines for the SPA curves depicted in Figs. 2, 4, and 6. These formulas represent the best-fit functions that describe the performance of each grade throughout acquisition. Corresponding levels of H for each grade can be obtained when the values zero through six (possible number correct during learning) are substituted for N. The resulting Hs are the bases whereby the abscissas for all SPA curves may be plotted. Best-fit Fig. 2 Grade Grade Fig. 4 Grade Grade Fig. 6 Grade Grade Grade
function
Variance
explained
2 4
H = loo-100.94e H = lOO-110.12e-
zI’v “*
( r’ = .99) ( i = .99)
2 4
H = 100-102.9Ye H = lOO-llO.gOe~
Liiy IXN
(i (i
= .YY) = .99)
2 4 7
H = 100-94.31~~ H = lOO-87.58eH = 100~84.02e
(? (i (i
= .Yh) = .93) = .95)
“,’ ‘W 35N
(%)
’ The fact that neither Study 2 nor Study 3 of the present paper seem to favor younger children should not invalidate this argument. The primary reason is that different list-lengths across grades were used in conjunction with a learning criterion of 80%. The consequence was that older children needed about the same number of acquisition trials as, younger children-not all that dissimilar from the standard fixed-trial procedure.
362
ALVIN
Y. WANG
APPENDIX
B
Below are the number of observations (ns) upon which each data point along an SPA curve was based. Number
Fig. 2 Grade Grade Fig. 4 Grade Grade Fig. 6 Grade Grade Grade
correct
during
learning
0
I
2
3
4
5
h
2 4
Y3 39
46 40
30 46
45 56
6X 82
80 107
5x 50
2 4
69 so
47 39
50 so
hb 77
hl 104
h8 130
5Y YO
2 4 7
37 37 20
70 8’) 117
61 104 137
45 95 139
42 55 00
23 19 38
II II 10
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RETENTION
IN CHILDREN
363
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August
24. 1989; REVISED: August
2. 1990.