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Controlled and automatic processing during mental rotation
JOURNAL
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
51,
337-347
(1991)
Controlled and Automatic Processing during Mental Rotation ROBERT KAIL
In two experiments. Y- and IO-year-olds and adults were tested on a mental rotation task in which they judged whether stimuli presented in different orientations were letters or mirror-images of letters. The mental rotation task was performed alone on 48 trials and concurrently with a memory task on 4X additional trials. The concurrent memory task in Experiment 1 was recalling digits; in Experiment 2, recalling positions in a matrix. The key result was that the slope of the function relating response time to stimulus orientation was the same when the mental rotation task was performed alone and when performed concurrently with the memory task. This result is interpreted as showing that mental rotation is an automatic process for both children and adults. 11 1YYl Acadcnllc Prw. Inc.
Age differences are common on tasks that involve speeded performance. Typical are results reported by Bisanz, Danner, and Resnick (1979), who used a name retrieval task in which subjects determined whether pairs of pictures were identical physically or in name. Subjects judged name similarity more slowly than physical similarity, and the difference was used to estimate the time needed to retrieve the name of the stimulus. Eightyear-olds retrieved the names of common objects in 282 ms; times for lo-, 12-, and 19-year-olds were 210, 142, and 115 ms, respectively. Thus, in this study, 19-year-olds retrieved names in less than half of the time needed by 8-year-olds. A similar pattern was found by Kail, Pellegrino, and Carter (1980) using a mental rotation task in which subjects judged whether letters presented in different orientations were actual letters or mirror images of letters. The slope of the function that relates response time to the orientation of the letter was used to estimate rate of mental rotation of the letter. Eight-year-olds mentally rotated letters at a rate of 7.01 This research was supported by NICHD grant lYY47. I am grateful to Laura Curry, Shohini Sinha Tom, and Ric Waits for their help in testing subjects and analyzing the data. 1 also wish to acknowledge the helpful comments of John Belmont and Michael Corballis on a previous draft of this manuscript. Requests for reprints should be sent to Robert Kail. Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907.
331 0022-0965191
$3.00
CopyrIght ‘9 1991 hy Acadcmc Press. Inc. All rqhts of reproductm ,n any fcm,, rcscrved
338
ROBERT
KAll
ms/degree of rotation; rates for 11- and 19-year-olds were 4.72 and 4.0 ms/degree. The results of these studies typify developmental change on many tasks: Processing time decreases considerably during childhood and continues to decrease, though less rapidly, in adolescence (e.g., Kail, 1988). These age differences have been explained in terms of increased processing resources with age. That is, in information-processing theories (e.g. 1 Shiffrin & Dumais, 1981), performance on many cognitive tasks requires processing resources, sometimes referred to as mental effort or attention. Increasing processing resources leads to increases in speed of processing, even if all other factors (e.g., strategies) are held constant (Anderson. 1983). Consequently, age-related increases in the amount of processing resources available could produce age-related change in processing time. The effect of processing resources on speeded performance has been examined in research with dual-task paradigms. Subjects perform tasks alone as well as concurrently. If both tasks require limited processing resources, then concurrent performance should be worse than performance when the tasks arc performed alone. In the case of mental rotation, for example, if rate of mental rotation reflects the availability of limited processing resources, then the slope of the function relating response time to orientation should be steeper when the task is performed concurrently with a resource-demanding task than when performed alone. Such a dual-task paradigm was used by Corballis (1986) to study adults’ mental rotation. Subjects performed a mental rotation task involving familiar letters alone. or in conjunction with memory tasks. The key result was that the slope of the mental rotation function was the same when the task was performed alone and when performed concurrently with the memory tasks. Apparently, mental rotation of letters was performed automatically, that is, without drawing upon processing resources. Because adults’ rate of mental rotation apparently does not depend upon processing resources, age differences in rate of mental rotation cannot be due solely to developmental change in processing resources. However, a revised version of the explanation in terms of processing resources is possible. one that invokes the distinction between automatic and controlled processes (Logan, 1985; Shiffrin & Dumais. 1981). As described above, automatic processes require little or no allocation of processing resources. In addition, automatic processes are assumed to be fast and obligatory, in the sense that once initiated. they are carried through to completion (Logan & Cowan, 1984). In contrast. controlled processes require attentional resources, are slower than automatic processes, and can be halted. According to this line of reasoning, age diffcrcnccs in rate of mental rotation might reflect the fact that mental rotation is automatic for adults but controlled for children. In dual-task experiments. the prediction would be an interaction hetwecn age. load.
MENTAL
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and orientation: Children’s but not adults’ rate of mental rotation should be slower when the mental rotation task is performed concurrently than when the task is performed alone. The two experiments reported here were designed to assess this prediction. In both experiments, children and adults performed a mental rotation task twice: once alone and once in conjunction with a memory task. The memory tasks, similar to those used by Corballis (1986), were digit span and recall of positions within matrices. Two memory tasks were used in order to assess the generality of any effects associated with concurrent task performance. The difficulty of the memory task was equated for children and adults, thereby assuring that the memory task made comparable demands on resources for children and adults. Because the experiments differed only in the type of memory task, they are reported together. METHOD
Subjects
Participating in Experiment 1 were 24 children and 24 adults, with an equal number of males and females at each age. The mean ages of the two groups were 9.8 (range = 8.5-11.25) and 20.92 (18.42-34.08) years, respectively. Participating in Experiment 2 were 16 children and 16 adults, with equal numbers of males and females at each age. The mean ages of the two groups were 10.10 (9.42-11.92) and 20.11 (18.58-22.33) years, respectively. Most of the children in both experiments attended grades 3 and 4 in an elementary school in a small town in the midwestern United States. Each was paid $1 for participating. Three children lived in a different city in the midwestern United States. They had been recruited via advertisements and were paid $5. The adults were undergraduates at Purdue University and participated to satisfy a course requirement. Materials
For the digit span task used in Experiment 1, random sequences of digits were generated, subject to the constraints that (a) a digit appear only once in each sequence, and (b) three or more digits in ascending or descending order (e.g., 5, 6, 7) were not allowed. Two sets of sequences of 4-8 digits were constructed in this manner. The matrix recall task used in Experiment 2 was designed to be similar to digit span, Specifically, matrices consisted of 16 cells arranged in a 4 x 4 matrix (illustrated in Fig. 1 of Kail & Siegel, 1977). To assess matrix recall, 2 matrices were constructed with 4 Xs placed in cells of the matrices, 2 matrices included 5 Xs. and so on. up to 2 matrices with 9 Xs. Xs were placed randomly in the 16 cells, subject to the constraints that (1) the Xs
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not form a symmetrical pattern, and (2) no row or column be completely filled with XS. During both assessment of matrix recall and mental rotation trials, subjects studied the matrix for 5 s. They recalled by printing Xs on a blank matrix. The stimuli for the mental rotation task consisted of the capital letters F, G, P, and R. Each was presented on a computer monitor in six different orientations (0, 30, 60, 90, 120, and 150 degrees clockwise from the vertical), once as a letter and once as a mirror-image of a letter. This resulted in 48 trials (4 stimuli x 6 orientations x 2 presentations). Stimuli were ordered randomly subject to the constraints that (1) each block of 12 stimuli consisted of one stimulus derived from each combination of 6 orientations and 2 responses. and (2) the correct response (e.g., “letter” versus “not a letter”) was required on no more than 3 successive trials, Procedure The procedure used in Experiment 1 is described here and changes for Experiment 2 are described later. Digit span was assessed first. Starting with a sequence of 4 digits. the experimenter pronounced each digit at a rate of approximately I digit/s. After presentation of the last digit, the subject was asked to recall the digits in the correct sequence. If recall was entirely correct, the procedure was repeated with another set of four digits. If the second recall was also correct, the number of digits was increased by one. This procedure was repeated until subjects recalled a set of digits inaccurately. Digit span was defined as the largest set of digits for which subjects recalled both sequences perfectly. Following the digit span task were 12 practice trials with the mental rotation task. Next, there were two blocks of 48 trials of the mental rotation task. One block of trials included digit span as the concurrent task: the other block was performed without a concurrent task. Order of presentation of the concurrent task in the first or second block of trials was counterbalanced across subjects. For trials without the concurrent task. a fixation circle appeared on the center of the computer monitor. After 1 s. the stimulus appeared in the center of the monitor and remained there until subjects responded by pressing one of two keys on the keyboard. A correct answer was followed by “+ + + + +” on the screen; an incorrect answer. by ” ~ - - - - “. The next trial began after approximately 3 s. Subjects were told to answer as rapidly as they could, but not so rapidly that they made lots of mistakes. For trials with the concurrent memory task, each trial began with the instructions on the computer screen, “Remember these numbers,” at which point the experimenter read a sequence of digits. with the exact number set to the subject’s digit span. After pronouncing the last digit. the experimenter pressed a button that resulted in presentation of the fixation circle. Presentation of the stimuli and feedback followed, as de-
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scribed above. However, subjects were instructed to recall the digits immediately after responding to the mental rotation task. The experimenter recorded their recall, then pushed a button to initiate the next trial. For these trials, subjects were reminded of the requirement to respond rapidly; they were also told to be sure to try to remember all of the digits. The procedures for Experiment 2 differed only in that matrix recall was the concurrent task. Assessment of matrix recall was followed by 12 practice mental rotation trials and 2 blocks of 48 mental rotation test trials. In Experiment 1, testing required approximately 20 min for children and 15 for adults. In Experiment 2, testing required approximately 40 for children and 30 for adults. RESULTS
I begin by describing the findings for the primary dependent ,variablc, response time on the mental rotation task. Then I describe performance on the recall tasks. Because of the large number of variables, (Y was set to .Ol since (Y set to .05 would yield an unacceptably high experimentwise error rate. Errors were infrequent on the mental rotation task and followed patterns reported previously (e.g., Kail, 1988). Consequently, they are not described here. Response
Time on the Mental Rotation
Task
For each combination of orientation, response, and task condition (singlc- versus dual-task), a mean response time was calculated for each individual, using times on correct responses only. Response times within each condition were then compared to the condition mean; times greater than twice the mean were deleted and the mean was recalculated. Fewer than 1% of the response times were deleted in this manner. These data were then analyzed with a 2 (age) x 2 (sex) x 2 (order) x 2 (task condition) x 2 (response) x 6 (orientation) analysis of variance. Experiment 1. Figure 1 (left panel) shows response times for children and adults under both conditions, as a function of orientation. For these data, main effects of age, F(1, 40) = 94.86, p < .Ol. and orientation. F(5. 200) = 36.33, p < .Ol. were qualified by the interaction between these variables, F(S, 200) = 5.62, p < .Ol. The interaction reflected a common pattern typically interpreted as representing age differences in rate of mental rotation: Response time increased as a function of orientation for both children and adults, but more rapidly for children. Of principal interest are effects associated with task condition. The main effect was significant, F(1, 40) = 21.08, p < .Ol, reflecting the fact that single-task responses were 206 ms faster than those in the dual-task condition. The interaction of age and task condition was not significant, F < 1, nor was the interaction of these variables with orientation, F <
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DIGIT SPAN
FIG.
I.
Response
the stimulus. (open squares) recalled positions
digits.
time
on
the
mental
children Results
and in the
separately conditions.
for
Results
in the
right
panel
POSITION
rotation
task
as a function
adults in the alone left panel are from are
from
Experiment
RECALL
of the
orientation
ot
(filled squares) and concurrent Experiment 1 in which subjects 2 in which
subjects
recalled
in a matrix.
1. As shown in Fig. 1, for both children and adults, at all orientations responsesin the single-task condition were about 200 ms faster than those in the concurrent condition. Two other effects were significant, neither central to the aims of the present study. Responseswere 116 ms faster on letters than mirror-image letters, F(1, 40) = 17.38, p < .Ol. The three-way interaction involving age, sex, and order was significant. F(1, 40) = 11.48, p < .Ol. This interaction can be interpreted in two ways (Reese, 1990). One interpretation is simply in terms of differences in subjects assigned to the various experimental conditions. For children, girls tested in the sequence concurrent/alone responded 374 ms faster than boys, while boys tested in the sequence alone/concurrent responded 775 ms faster than girls. For adults. men tested in the sequence concurrent/alone responded 152 ms faster than women, while women tested in the sequence alone/concurrent responded 216 ms faster than men. Another interpretation is based on the fact that the condition by trial block (1 vs 2) interaction is confounded in the three-way interaction of age. sex, and order. Examination of the condition by trial block interaction, separately for each combination of age and sex. revealed three patterns: (1) for boys and for women, response times in the concurrent condition decreased from block 1 to block 2, but response times in the single-task condition increased; (7) for girls, the opposite pattern was seen; and (3) for men, responsesin the two conditions did not change from block 1 to block 2. Experiment 2. Figure 1 (right panel) shows mean response times for
MENTAL
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children and adults. Main effects of age, F(1, 24) = 46.16, p < .Ol, and orientation, F(5, 120) = 31.29, p < .Ol, were qualified by the interaction between these variables, F(5, 120) = 5.71, p < .Ol. As in Experiment 1, this interaction reflected the pattern associated with age differences in rate of mental rotation. The main effect of response was significant: responses were 122 ms faster on letters than mirror-image letters, F(1, 24) = 12.0, p < .Ol.
The principal results concern effects associated with task condition. The main effect was significant, F(1, 40) = 21.08, p < .Ol, reflecting the fact that responses in the alone condition were 288 ms faster than those in the concurrent condition. Notably, the interaction of task condition and orientation was not significant, F < 1, nor was the three-way interaction of these variables with age, F < 1. As shown in Fig. 1, the effect of condition was essentially constant across orientation. Supplementary analyses. Analyses of Experiments 1 and 2 individually both yielded nonsignificant Fs for all interactions involving task condition and orientation. This result is consistent with the conclusion that, for both children and adults, the mental rotation component of task performance is accomplished automatically. Because this conclusion is based upon accepting the null hypothesis, an additional analysis was conducted in which the data from the two experiments were pooled. Despite the increased power of the analysis, the interaction between age. orientation,
of Recall Performance
The size of subjects’ digit spans (i.e., from the initial assessment, the largest set of digits in which both sequences were recalled correctly) and the analogous measure for position recall were analyzed with a 2 (age) x 2 (sex) x 2 (order) analysis of variance. Experiment 1. Adults’ span was greater than children’s, but the effect was larger for males (6.83 and 4.83 for men and boys, respectively) than for females (5.67 and 4.75 for women and girls, respectively). With (Yset to .Ol, there were marginally significant main effects of age and sex, Fs(1.
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40) 2 5.80, ps < .05, as well as a marginally significant interaction between these two variables, F(l, 40) = 4.42. p < .05. Experiment 2. Adults recalled larger matrices than did children, with means of 5.13 and 4.0, respectively, F( 1, _74) = 15.67, p < .Ol. No other effects were significant. Recall During
the Mental Rotation
Tash
The percentage of trials of the mental rotation task in which recall (of digits in Experiment 1. positions in Experiment 2) was perfectly accurate was analyzed with a 2 (age) x 2 (sex) x 2 (order) x 7 (response) x 6 (orientation) analysis of variance. Experiment I: digit recall. No effects were significant. Experiment 2: recall of positions. Adults recalled positions accurately on 72.9%) of the trials, compared to 35.3% for children, F( 1, 24) = 43.53. p < .Ol. Males recalled positions more accurately than did females. with means of 64.5% and 42.7%~ respectively. F(l. 24) = 15.38, p c .Ol. Recall decreased slightly with increases in the orientation of the letter. F(S, 120) = 3.05. p < .Ol. with means of 54.3. 60.16, S7.4. 49.6, S2.3, and 47.7, for O-150 degrees, respectively. This change occurred at the same rate for children and adults, indicated by the nonsignificant interaction between age and orientation. F Y-CI. Discussion In the present research, results reported by Corballis (lYX6) were replicated for both children and adults. That is. for both children and adults, the slope of the function relating response time to stimulus orientation was the same when the task was performed alone and when it was performed concurrently with a memory task. Perhaps the most straightforward interpretation of this finding is the one offered initially by Corballis (19%). namely. that mental rotation is executed automatically. That is. apparently neither adults nor children require processing resources to execute the mental rotation component of task performance. By this interpretation, age differences in rate of mental rotation cannot reflect a developmental transition from controlled to automatic processing because mental rotation is automatic for children as well as adults. Two alternative explanations must be considered before concluding that mental rotation is automatic. The first explanation stems from the finding, in Experiment 2, that recall dcclincd slightly as a function of the orientation of the mental rotation stimulus. This might mean that available resources are exceeded when subjects attempt to remember positions and perform difficult mental rotation problems (e.g., 150 degree orientations). Perhaps this resulted in less accurate recall but not poorer mental rotation performance because children and adults chose to emphasize mental ro-
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tation performance at the expense of position recall. This seems implausible in light of task instructions that gave equal emphasis to both tasks. However, this explanation could be evaluated in future research by asking subjects to perform the task concurrently under instructions that varied the emphasis on the two tasks. Another alternate interpretation of the present results hinges on the nature of the recall tasks used here. Some theorists claim that resources are not general but instead form multiple pools, such as verbal and spatial resources (Wickens & Benel, 1982). If the recall tasks did not tap the same pool of resources needed to execute the mental rotation task, rate of mental rotation should be the same for concurrent and alone conditions. There are three difficulties with this explanation. First, two memory tasks that might well tap different pools-digit span tapping the verbal pool and position recall the spatial pool-had the same influence on rate of mental rotation. Second, overall responses were slower when the mental rotation task was performed concurrently than when it was performed alone. This suggests that the recall tasks tapped the same resources needed for the encoding, comparison, and response phases of mental rotation performance. Given this result. one would have to propose that performance on the memory task as well as the encoding, comparison, and response processes of the mental rotation task tap a common pool of resources while the mental rotation process taps a unique resource. Third, if multiple pools of resources are proposed to explain the present results, then the earlier findings of a common rate of developmental change across tasks can be explained only by assuming (I) that all of the processes known to conform to a common developmental function tap the same pool of resources. or (2) that the tasks tap distinct pools. but these develop at the same rate. Assuming that the present results, at the very least, cast do,ubt on a developmental transition from controlled to automatic processing, what mechanism might explain age-related change in processing speed? One possibility is based upon an analogy to computer hardward (Salthouse 6i Kail, 1983). If two computers have identical software but one machine has a slower cycle time (i.e., the time for the central processor to execute a single instruction), that machine will execute all processes more slowly, by an amount that depends upon the total number of instructions to be executed. The human analog to cycle time might be the time to match productions to the contexts of working memory or it might consist of the time to execute the action side of productions (e.g., Klahr, 1989). In any cast, according to this interpretation, children’s responses should be increasingly slower than adults’. reflecting the fact that each cognitive instruction takes longer to execute. One implication of rhis view. which has been explored at length in studies of cognitive aging (e.g.. Cerclla, 1985) is that children’s response
346
ROBERT
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~~
, III), A,&
~.
1 I-, I
~’ b’-
~1-.b:N,J
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FIG. 2. Children’s mean response times plotted as a function of adults‘ mean response times in corresponding conditions. The 24 points represent orthogonal combination of six orientations, two conditions. and two experiments. Filled squares depict single-task performance in Experiments I and 2; open squares. concurrent performance.
times should be a multiple of adults’ response times. That is, if children’s response times are plotted as a function of adults’ response times in corresponding conditions, the function should be linear. Furthermore, the slope, which provides an estimate of the factor by which children execute responses more slowly than adults, should be greater than 1. Consistent with this prediction, Fig. 2 shows that children’s response times in the two experiments increase linearly as a function of adults’ response times in corresponding conditions (r = .91) with the slope of 1.87 (see Fig. 2). This outcome supports any explanation of the present results in terms of mechanisms that yield a constant age difference in speeded performance. including the possibility of developmental change in cycle time. REFERENCES Anderson, J. R. (1983). The architecture rjfcogrilion. Cambridge. MA: Harvard University Press. Bisanz, J.. Danner, F., Bi Resnick, L. B. (1979). Changes with age in measures of processing efficiency. Child Developmenr. 50, 132-141. Cerella, J. (lY85). Information-processing rates in the elderly. Psychological Bollerin, 98, 67-83. Corballis, M. C. (1986). Is mental rotation controlled or automatic? Memory & Cugnitiorl, 14, 1244128. Kail, R. (198X). Developmental functions for speeds of cognitive processes. Journnl 01 Experimental Child Psychology. 45. 339-364. Kail. R.. Pellegrino. J.. & Carter, P. (1980). Developmental change in mental rotation. Journal of Experimenlal Child Psychology. 29, 102-l 16. Kail. R. V., & Siegel, A. W. (1977). Sex differences in retention of verbal and spatial characteristics of stimuli. Journal of Experimental Child Psycholo,ty, 23, 341-347.
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ROTATION
Klahr,
347
D. (1989). Information-processing approaches. In R. Vasta (Ed.), Annuls of child development (Vol. 6. pp. 133-185). Greenwich, CT: JAI Press. Logan, G. D. (1985). Skill and automaticity: Relations, implications, and future directions. Canadian Journal of Psychology, 39, 3617386. Logan, G. D.. & Cowan, W. B. (1984). On the ability to inhibit thoughts and action: A theory of an act of control. Psychological Review, 91, 295-327. Reese, H. W. (1990). On the interpretation of within-subjects Latin-square designs. Unpublished manuscript. Salthouse, T. A., & Kail, R. (1983). Memory development throughout the life span: The role of processing rate. In P. B. Baltes and D. G. Brim (Ed.). Life-span development and behavior (Vol. 5, pp. 89-116). New York: Academic Press. Shiffrin, R. M., & Dumais, S. T. (1981). The development of automatism. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 111-140). Hillsdale. NJ: Erlbaum. Wickens. C. D., & Benel, D. C. R. (1982). The development of time-sharing skills. In J. A. S. Kelso & J. E. Clark (Eds.), The development of movement control and coordination (pp. 253-272). New York/London: Wiley. RECEIVED:
April
19, 1990: REVISED: August
23, 1990.
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
51,
337-347
(1991)
Controlled and Automatic Processing during Mental Rotation ROBERT KAIL
In two experiments. Y- and IO-year-olds and adults were tested on a mental rotation task in which they judged whether stimuli presented in different orientations were letters or mirror-images of letters. The mental rotation task was performed alone on 48 trials and concurrently with a memory task on 4X additional trials. The concurrent memory task in Experiment 1 was recalling digits; in Experiment 2, recalling positions in a matrix. The key result was that the slope of the function relating response time to stimulus orientation was the same when the mental rotation task was performed alone and when performed concurrently with the memory task. This result is interpreted as showing that mental rotation is an automatic process for both children and adults. 11 1YYl Acadcnllc Prw. Inc.
Age differences are common on tasks that involve speeded performance. Typical are results reported by Bisanz, Danner, and Resnick (1979), who used a name retrieval task in which subjects determined whether pairs of pictures were identical physically or in name. Subjects judged name similarity more slowly than physical similarity, and the difference was used to estimate the time needed to retrieve the name of the stimulus. Eightyear-olds retrieved the names of common objects in 282 ms; times for lo-, 12-, and 19-year-olds were 210, 142, and 115 ms, respectively. Thus, in this study, 19-year-olds retrieved names in less than half of the time needed by 8-year-olds. A similar pattern was found by Kail, Pellegrino, and Carter (1980) using a mental rotation task in which subjects judged whether letters presented in different orientations were actual letters or mirror images of letters. The slope of the function that relates response time to the orientation of the letter was used to estimate rate of mental rotation of the letter. Eight-year-olds mentally rotated letters at a rate of 7.01 This research was supported by NICHD grant lYY47. I am grateful to Laura Curry, Shohini Sinha Tom, and Ric Waits for their help in testing subjects and analyzing the data. 1 also wish to acknowledge the helpful comments of John Belmont and Michael Corballis on a previous draft of this manuscript. Requests for reprints should be sent to Robert Kail. Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907.
331 0022-0965191
$3.00
CopyrIght ‘9 1991 hy Acadcmc Press. Inc. All rqhts of reproductm ,n any fcm,, rcscrved
338
ROBERT
KAll
ms/degree of rotation; rates for 11- and 19-year-olds were 4.72 and 4.0 ms/degree. The results of these studies typify developmental change on many tasks: Processing time decreases considerably during childhood and continues to decrease, though less rapidly, in adolescence (e.g., Kail, 1988). These age differences have been explained in terms of increased processing resources with age. That is, in information-processing theories (e.g. 1 Shiffrin & Dumais, 1981), performance on many cognitive tasks requires processing resources, sometimes referred to as mental effort or attention. Increasing processing resources leads to increases in speed of processing, even if all other factors (e.g., strategies) are held constant (Anderson. 1983). Consequently, age-related increases in the amount of processing resources available could produce age-related change in processing time. The effect of processing resources on speeded performance has been examined in research with dual-task paradigms. Subjects perform tasks alone as well as concurrently. If both tasks require limited processing resources, then concurrent performance should be worse than performance when the tasks arc performed alone. In the case of mental rotation, for example, if rate of mental rotation reflects the availability of limited processing resources, then the slope of the function relating response time to orientation should be steeper when the task is performed concurrently with a resource-demanding task than when performed alone. Such a dual-task paradigm was used by Corballis (1986) to study adults’ mental rotation. Subjects performed a mental rotation task involving familiar letters alone. or in conjunction with memory tasks. The key result was that the slope of the mental rotation function was the same when the task was performed alone and when performed concurrently with the memory tasks. Apparently, mental rotation of letters was performed automatically, that is, without drawing upon processing resources. Because adults’ rate of mental rotation apparently does not depend upon processing resources, age differences in rate of mental rotation cannot be due solely to developmental change in processing resources. However, a revised version of the explanation in terms of processing resources is possible. one that invokes the distinction between automatic and controlled processes (Logan, 1985; Shiffrin & Dumais. 1981). As described above, automatic processes require little or no allocation of processing resources. In addition, automatic processes are assumed to be fast and obligatory, in the sense that once initiated. they are carried through to completion (Logan & Cowan, 1984). In contrast. controlled processes require attentional resources, are slower than automatic processes, and can be halted. According to this line of reasoning, age diffcrcnccs in rate of mental rotation might reflect the fact that mental rotation is automatic for adults but controlled for children. In dual-task experiments. the prediction would be an interaction hetwecn age. load.
MENTAL
ROTATION
339
and orientation: Children’s but not adults’ rate of mental rotation should be slower when the mental rotation task is performed concurrently than when the task is performed alone. The two experiments reported here were designed to assess this prediction. In both experiments, children and adults performed a mental rotation task twice: once alone and once in conjunction with a memory task. The memory tasks, similar to those used by Corballis (1986), were digit span and recall of positions within matrices. Two memory tasks were used in order to assess the generality of any effects associated with concurrent task performance. The difficulty of the memory task was equated for children and adults, thereby assuring that the memory task made comparable demands on resources for children and adults. Because the experiments differed only in the type of memory task, they are reported together. METHOD
Subjects
Participating in Experiment 1 were 24 children and 24 adults, with an equal number of males and females at each age. The mean ages of the two groups were 9.8 (range = 8.5-11.25) and 20.92 (18.42-34.08) years, respectively. Participating in Experiment 2 were 16 children and 16 adults, with equal numbers of males and females at each age. The mean ages of the two groups were 10.10 (9.42-11.92) and 20.11 (18.58-22.33) years, respectively. Most of the children in both experiments attended grades 3 and 4 in an elementary school in a small town in the midwestern United States. Each was paid $1 for participating. Three children lived in a different city in the midwestern United States. They had been recruited via advertisements and were paid $5. The adults were undergraduates at Purdue University and participated to satisfy a course requirement. Materials
For the digit span task used in Experiment 1, random sequences of digits were generated, subject to the constraints that (a) a digit appear only once in each sequence, and (b) three or more digits in ascending or descending order (e.g., 5, 6, 7) were not allowed. Two sets of sequences of 4-8 digits were constructed in this manner. The matrix recall task used in Experiment 2 was designed to be similar to digit span, Specifically, matrices consisted of 16 cells arranged in a 4 x 4 matrix (illustrated in Fig. 1 of Kail & Siegel, 1977). To assess matrix recall, 2 matrices were constructed with 4 Xs placed in cells of the matrices, 2 matrices included 5 Xs. and so on. up to 2 matrices with 9 Xs. Xs were placed randomly in the 16 cells, subject to the constraints that (1) the Xs
340
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not form a symmetrical pattern, and (2) no row or column be completely filled with XS. During both assessment of matrix recall and mental rotation trials, subjects studied the matrix for 5 s. They recalled by printing Xs on a blank matrix. The stimuli for the mental rotation task consisted of the capital letters F, G, P, and R. Each was presented on a computer monitor in six different orientations (0, 30, 60, 90, 120, and 150 degrees clockwise from the vertical), once as a letter and once as a mirror-image of a letter. This resulted in 48 trials (4 stimuli x 6 orientations x 2 presentations). Stimuli were ordered randomly subject to the constraints that (1) each block of 12 stimuli consisted of one stimulus derived from each combination of 6 orientations and 2 responses. and (2) the correct response (e.g., “letter” versus “not a letter”) was required on no more than 3 successive trials, Procedure The procedure used in Experiment 1 is described here and changes for Experiment 2 are described later. Digit span was assessed first. Starting with a sequence of 4 digits. the experimenter pronounced each digit at a rate of approximately I digit/s. After presentation of the last digit, the subject was asked to recall the digits in the correct sequence. If recall was entirely correct, the procedure was repeated with another set of four digits. If the second recall was also correct, the number of digits was increased by one. This procedure was repeated until subjects recalled a set of digits inaccurately. Digit span was defined as the largest set of digits for which subjects recalled both sequences perfectly. Following the digit span task were 12 practice trials with the mental rotation task. Next, there were two blocks of 48 trials of the mental rotation task. One block of trials included digit span as the concurrent task: the other block was performed without a concurrent task. Order of presentation of the concurrent task in the first or second block of trials was counterbalanced across subjects. For trials without the concurrent task. a fixation circle appeared on the center of the computer monitor. After 1 s. the stimulus appeared in the center of the monitor and remained there until subjects responded by pressing one of two keys on the keyboard. A correct answer was followed by “+ + + + +” on the screen; an incorrect answer. by ” ~ - - - - “. The next trial began after approximately 3 s. Subjects were told to answer as rapidly as they could, but not so rapidly that they made lots of mistakes. For trials with the concurrent memory task, each trial began with the instructions on the computer screen, “Remember these numbers,” at which point the experimenter read a sequence of digits. with the exact number set to the subject’s digit span. After pronouncing the last digit. the experimenter pressed a button that resulted in presentation of the fixation circle. Presentation of the stimuli and feedback followed, as de-
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scribed above. However, subjects were instructed to recall the digits immediately after responding to the mental rotation task. The experimenter recorded their recall, then pushed a button to initiate the next trial. For these trials, subjects were reminded of the requirement to respond rapidly; they were also told to be sure to try to remember all of the digits. The procedures for Experiment 2 differed only in that matrix recall was the concurrent task. Assessment of matrix recall was followed by 12 practice mental rotation trials and 2 blocks of 48 mental rotation test trials. In Experiment 1, testing required approximately 20 min for children and 15 for adults. In Experiment 2, testing required approximately 40 for children and 30 for adults. RESULTS
I begin by describing the findings for the primary dependent ,variablc, response time on the mental rotation task. Then I describe performance on the recall tasks. Because of the large number of variables, (Y was set to .Ol since (Y set to .05 would yield an unacceptably high experimentwise error rate. Errors were infrequent on the mental rotation task and followed patterns reported previously (e.g., Kail, 1988). Consequently, they are not described here. Response
Time on the Mental Rotation
Task
For each combination of orientation, response, and task condition (singlc- versus dual-task), a mean response time was calculated for each individual, using times on correct responses only. Response times within each condition were then compared to the condition mean; times greater than twice the mean were deleted and the mean was recalculated. Fewer than 1% of the response times were deleted in this manner. These data were then analyzed with a 2 (age) x 2 (sex) x 2 (order) x 2 (task condition) x 2 (response) x 6 (orientation) analysis of variance. Experiment 1. Figure 1 (left panel) shows response times for children and adults under both conditions, as a function of orientation. For these data, main effects of age, F(1, 40) = 94.86, p < .Ol. and orientation. F(5. 200) = 36.33, p < .Ol. were qualified by the interaction between these variables, F(S, 200) = 5.62, p < .Ol. The interaction reflected a common pattern typically interpreted as representing age differences in rate of mental rotation: Response time increased as a function of orientation for both children and adults, but more rapidly for children. Of principal interest are effects associated with task condition. The main effect was significant, F(1, 40) = 21.08, p < .Ol, reflecting the fact that single-task responses were 206 ms faster than those in the dual-task condition. The interaction of age and task condition was not significant, F < 1, nor was the interaction of these variables with orientation, F <
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DIGIT SPAN
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1. As shown in Fig. 1, for both children and adults, at all orientations responsesin the single-task condition were about 200 ms faster than those in the concurrent condition. Two other effects were significant, neither central to the aims of the present study. Responseswere 116 ms faster on letters than mirror-image letters, F(1, 40) = 17.38, p < .Ol. The three-way interaction involving age, sex, and order was significant. F(1, 40) = 11.48, p < .Ol. This interaction can be interpreted in two ways (Reese, 1990). One interpretation is simply in terms of differences in subjects assigned to the various experimental conditions. For children, girls tested in the sequence concurrent/alone responded 374 ms faster than boys, while boys tested in the sequence alone/concurrent responded 775 ms faster than girls. For adults. men tested in the sequence concurrent/alone responded 152 ms faster than women, while women tested in the sequence alone/concurrent responded 216 ms faster than men. Another interpretation is based on the fact that the condition by trial block (1 vs 2) interaction is confounded in the three-way interaction of age. sex, and order. Examination of the condition by trial block interaction, separately for each combination of age and sex. revealed three patterns: (1) for boys and for women, response times in the concurrent condition decreased from block 1 to block 2, but response times in the single-task condition increased; (7) for girls, the opposite pattern was seen; and (3) for men, responsesin the two conditions did not change from block 1 to block 2. Experiment 2. Figure 1 (right panel) shows mean response times for
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children and adults. Main effects of age, F(1, 24) = 46.16, p < .Ol, and orientation, F(5, 120) = 31.29, p < .Ol, were qualified by the interaction between these variables, F(5, 120) = 5.71, p < .Ol. As in Experiment 1, this interaction reflected the pattern associated with age differences in rate of mental rotation. The main effect of response was significant: responses were 122 ms faster on letters than mirror-image letters, F(1, 24) = 12.0, p < .Ol.
The principal results concern effects associated with task condition. The main effect was significant, F(1, 40) = 21.08, p < .Ol, reflecting the fact that responses in the alone condition were 288 ms faster than those in the concurrent condition. Notably, the interaction of task condition and orientation was not significant, F < 1, nor was the three-way interaction of these variables with age, F < 1. As shown in Fig. 1, the effect of condition was essentially constant across orientation. Supplementary analyses. Analyses of Experiments 1 and 2 individually both yielded nonsignificant Fs for all interactions involving task condition and orientation. This result is consistent with the conclusion that, for both children and adults, the mental rotation component of task performance is accomplished automatically. Because this conclusion is based upon accepting the null hypothesis, an additional analysis was conducted in which the data from the two experiments were pooled. Despite the increased power of the analysis, the interaction between age. orientation,
of Recall Performance
The size of subjects’ digit spans (i.e., from the initial assessment, the largest set of digits in which both sequences were recalled correctly) and the analogous measure for position recall were analyzed with a 2 (age) x 2 (sex) x 2 (order) analysis of variance. Experiment 1. Adults’ span was greater than children’s, but the effect was larger for males (6.83 and 4.83 for men and boys, respectively) than for females (5.67 and 4.75 for women and girls, respectively). With (Yset to .Ol, there were marginally significant main effects of age and sex, Fs(1.
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40) 2 5.80, ps < .05, as well as a marginally significant interaction between these two variables, F(l, 40) = 4.42. p < .05. Experiment 2. Adults recalled larger matrices than did children, with means of 5.13 and 4.0, respectively, F( 1, _74) = 15.67, p < .Ol. No other effects were significant. Recall During
the Mental Rotation
Tash
The percentage of trials of the mental rotation task in which recall (of digits in Experiment 1. positions in Experiment 2) was perfectly accurate was analyzed with a 2 (age) x 2 (sex) x 2 (order) x 7 (response) x 6 (orientation) analysis of variance. Experiment I: digit recall. No effects were significant. Experiment 2: recall of positions. Adults recalled positions accurately on 72.9%) of the trials, compared to 35.3% for children, F( 1, 24) = 43.53. p < .Ol. Males recalled positions more accurately than did females. with means of 64.5% and 42.7%~ respectively. F(l. 24) = 15.38, p c .Ol. Recall decreased slightly with increases in the orientation of the letter. F(S, 120) = 3.05. p < .Ol. with means of 54.3. 60.16, S7.4. 49.6, S2.3, and 47.7, for O-150 degrees, respectively. This change occurred at the same rate for children and adults, indicated by the nonsignificant interaction between age and orientation. F Y-CI. Discussion In the present research, results reported by Corballis (lYX6) were replicated for both children and adults. That is. for both children and adults, the slope of the function relating response time to stimulus orientation was the same when the task was performed alone and when it was performed concurrently with a memory task. Perhaps the most straightforward interpretation of this finding is the one offered initially by Corballis (19%). namely. that mental rotation is executed automatically. That is. apparently neither adults nor children require processing resources to execute the mental rotation component of task performance. By this interpretation, age differences in rate of mental rotation cannot reflect a developmental transition from controlled to automatic processing because mental rotation is automatic for children as well as adults. Two alternative explanations must be considered before concluding that mental rotation is automatic. The first explanation stems from the finding, in Experiment 2, that recall dcclincd slightly as a function of the orientation of the mental rotation stimulus. This might mean that available resources are exceeded when subjects attempt to remember positions and perform difficult mental rotation problems (e.g., 150 degree orientations). Perhaps this resulted in less accurate recall but not poorer mental rotation performance because children and adults chose to emphasize mental ro-
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tation performance at the expense of position recall. This seems implausible in light of task instructions that gave equal emphasis to both tasks. However, this explanation could be evaluated in future research by asking subjects to perform the task concurrently under instructions that varied the emphasis on the two tasks. Another alternate interpretation of the present results hinges on the nature of the recall tasks used here. Some theorists claim that resources are not general but instead form multiple pools, such as verbal and spatial resources (Wickens & Benel, 1982). If the recall tasks did not tap the same pool of resources needed to execute the mental rotation task, rate of mental rotation should be the same for concurrent and alone conditions. There are three difficulties with this explanation. First, two memory tasks that might well tap different pools-digit span tapping the verbal pool and position recall the spatial pool-had the same influence on rate of mental rotation. Second, overall responses were slower when the mental rotation task was performed concurrently than when it was performed alone. This suggests that the recall tasks tapped the same resources needed for the encoding, comparison, and response phases of mental rotation performance. Given this result. one would have to propose that performance on the memory task as well as the encoding, comparison, and response processes of the mental rotation task tap a common pool of resources while the mental rotation process taps a unique resource. Third, if multiple pools of resources are proposed to explain the present results, then the earlier findings of a common rate of developmental change across tasks can be explained only by assuming (I) that all of the processes known to conform to a common developmental function tap the same pool of resources. or (2) that the tasks tap distinct pools. but these develop at the same rate. Assuming that the present results, at the very least, cast do,ubt on a developmental transition from controlled to automatic processing, what mechanism might explain age-related change in processing speed? One possibility is based upon an analogy to computer hardward (Salthouse 6i Kail, 1983). If two computers have identical software but one machine has a slower cycle time (i.e., the time for the central processor to execute a single instruction), that machine will execute all processes more slowly, by an amount that depends upon the total number of instructions to be executed. The human analog to cycle time might be the time to match productions to the contexts of working memory or it might consist of the time to execute the action side of productions (e.g., Klahr, 1989). In any cast, according to this interpretation, children’s responses should be increasingly slower than adults’. reflecting the fact that each cognitive instruction takes longer to execute. One implication of rhis view. which has been explored at length in studies of cognitive aging (e.g.. Cerclla, 1985) is that children’s response
346
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FIG. 2. Children’s mean response times plotted as a function of adults‘ mean response times in corresponding conditions. The 24 points represent orthogonal combination of six orientations, two conditions. and two experiments. Filled squares depict single-task performance in Experiments I and 2; open squares. concurrent performance.
times should be a multiple of adults’ response times. That is, if children’s response times are plotted as a function of adults’ response times in corresponding conditions, the function should be linear. Furthermore, the slope, which provides an estimate of the factor by which children execute responses more slowly than adults, should be greater than 1. Consistent with this prediction, Fig. 2 shows that children’s response times in the two experiments increase linearly as a function of adults’ response times in corresponding conditions (r = .91) with the slope of 1.87 (see Fig. 2). This outcome supports any explanation of the present results in terms of mechanisms that yield a constant age difference in speeded performance. including the possibility of developmental change in cycle time. REFERENCES Anderson, J. R. (1983). The architecture rjfcogrilion. Cambridge. MA: Harvard University Press. Bisanz, J.. Danner, F., Bi Resnick, L. B. (1979). Changes with age in measures of processing efficiency. Child Developmenr. 50, 132-141. Cerella, J. (lY85). Information-processing rates in the elderly. Psychological Bollerin, 98, 67-83. Corballis, M. C. (1986). Is mental rotation controlled or automatic? Memory & Cugnitiorl, 14, 1244128. Kail, R. (198X). Developmental functions for speeds of cognitive processes. Journnl 01 Experimental Child Psychology. 45. 339-364. Kail. R.. Pellegrino. J.. & Carter, P. (1980). Developmental change in mental rotation. Journal of Experimenlal Child Psychology. 29, 102-l 16. Kail. R. V., & Siegel, A. W. (1977). Sex differences in retention of verbal and spatial characteristics of stimuli. Journal of Experimental Child Psycholo,ty, 23, 341-347.
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Klahr,
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D. (1989). Information-processing approaches. In R. Vasta (Ed.), Annuls of child development (Vol. 6. pp. 133-185). Greenwich, CT: JAI Press. Logan, G. D. (1985). Skill and automaticity: Relations, implications, and future directions. Canadian Journal of Psychology, 39, 3617386. Logan, G. D.. & Cowan, W. B. (1984). On the ability to inhibit thoughts and action: A theory of an act of control. Psychological Review, 91, 295-327. Reese, H. W. (1990). On the interpretation of within-subjects Latin-square designs. Unpublished manuscript. Salthouse, T. A., & Kail, R. (1983). Memory development throughout the life span: The role of processing rate. In P. B. Baltes and D. G. Brim (Ed.). Life-span development and behavior (Vol. 5, pp. 89-116). New York: Academic Press. Shiffrin, R. M., & Dumais, S. T. (1981). The development of automatism. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 111-140). Hillsdale. NJ: Erlbaum. Wickens. C. D., & Benel, D. C. R. (1982). The development of time-sharing skills. In J. A. S. Kelso & J. E. Clark (Eds.), The development of movement control and coordination (pp. 253-272). New York/London: Wiley. RECEIVED:
April
19, 1990: REVISED: August
23, 1990.