Developmental changes in speed of processing central limiting mechanism or skill transfer

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/247639904 Developmental Changes in Speed of Processing: Central Limiting Mechanism or Skill Transfer? Article in Child Development · August 1988 DOI: 10.1111/j.1467-8624.1988.tb03267.x CITATIONS READS 16 25 3 authors, including: James Stigler Howard Nusbaum 88 PUBLICATIONS 6,288 CITATIONS 163 PUBLICATIONS 5,020 CITATIONS University of California, Los Angeles SEE PROFILE University of Chicago SEE PROFILE All content following this page was uploaded by Howard Nusbaum on 11 April 2015 The user has requested enhancement of the downloaded file All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately Developmental Changes in Speed of Processing: Central Limiting Mechanism or Skill Transfer? Author(s): James W Stigler, Howard C Nusbaum and Laurence Chalip Source: Child Development, Vol 59, No (Aug., 1988), pp 1144-1153 Published by: Wiley on behalf of the Society for Research in Child Development Stable URL: http://www.jstor.org/stable/1130281 Accessed: 11-04-2015 16:27 UTC REFERENCES Linked references are available on JSTOR for this article: http://www.jstor.org/stable/1130281?seq=1&cid=pdf-reference#references_tab_contents You may need to log in to JSTOR to access the linked references Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive We use information technology and tools to increase productivity and facilitate new forms of scholarship For more information about JSTOR, please contact support@jstor.org Wiley and Society for Research in Child Development are collaborating with JSTOR to digitize, preserve and extend access to Child Development http://www.jstor.org This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Conunentaries Developmental Changes in Speed of Processing: Central Limiting Mechanism or Skill Transfer? James W Stigler, Howard C Nusbaum, and Laurence Chalip Universityof Chicago HOWARD LAURENCE STIGLER, W.; NUSBAUM, JAMES C.; and CHALIP, Developmental Changes in DEVELOPMENT, Speed of Processing:Central Limiting Mechanismor Skill Transfer?CHILD 1988, 59, 1144-1153 In this article we examine Kail'sclaim that similarityin developmentalspeed-ofprocessing curves for tasks indicates that performanceon a wide range of cognitive tasks is constrainedby the growth of a central limiting mechanism.We argue that the "specificlearning" hypothesis, which Kail rejects,does not consider the role of transferof learningbetween tasks,and thus assumes that domain specificityof learningimplies complete domainindependence We demonstrate,throughsimulations,thatthe operationof a centrallimitingmechanismis neither sufficient nor necessary to generate the curves observed by Kail alternativemodels of skill transferare proposed, and the ability of each model to generate data similar to Kail's is demonstrated.It is concluded that the types of data collected by Kail are essentially incapable of identifying taskspecific and task-generalconstraintson performance In performing any complex cognitive task in an experiment, a subject can draw on a wealth of resources consisting of some combination of knowledge and skills Some of these capabilities may be limited by the maturational state of the subject; others may be limited by the amount of practice and experience the subject has had One challenge for the developmental cognitive psychologist is to specify how these different types of cognitive limitations interact to explain performance on particular tasks Where performance changes in similar ways across tasks, can these similarities be tied to general maturational factors or to specific experiences? In a recent Child Development article, Kail (1986) argues that the growth of a central limiting mechanism underlies age differences in speed of processing across a wide range of cognitive tasks Kail bases his argument on studies of speed of processing in two different tasks, name retrieval and mental rotation His basic claim is that performance in both tasks is governed by a central limiting mechanism such as the availability of cognitive resources As the child matures, the availability of mental resources increases, thus reducing a substantial constraint on performance Kail presents three pieces of evidence in support of his argument (1) The shape of the function relating speed of processing to age is similar across the two tasks that ostensibly measure different processes; (2) this function is better fit by an exponential function than by a hyperbolic curve, indicating that the cause of the performance improvements is not learning, since learning curves are almost always better described by hyperbolic curves; and (3) the correlation of mean response time across conditions between adults and children approaches unity At first glance, it would seem that the similarity between speed-of-processing curves for different tasks across ages should provide only the weakest kind of support for a single mechanism mediating performance After all, there are many ways in which processing similarities can arise without postulating a single, common underlying mechanism As Newell and Rosenbloom (1981) stated, af- This paper was written while the firstauthorwas supportedby a Spencer Fellowship fromthe National Academy of Education The authors gratefullyacknowledge the helpful comments of Robert Sternberg,Robert Kail, and an anonymousreviewer Also, thanksto RobertSiegler for his sharp eye, and to Kevin F Miller for comments on an earlier draft.Correspondencemay be addressed to the authorsat Departmentof BehavioralSciences, Universityof Chicago, 5730 South WoodlawnAvenue, Chicago, IL 60637 [Child Development,1988, 59, 1144-1153 ? 1988 by the Societyfor Researchin Child Development,Inc All rightsreserved.0009-3920/88/5904-0031$01.00] This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Stigler, Nusbaum, and Chalip ter finding similarities in the shapes of learning curves across a wide range of tasks, "We not wish to assert that such an effect stems from a single cause or mechanism Indeed, its apparent ubiquity might seem to indicate multiple explanations" (p 16) Their conclusion is that the regularity in the shape of learning curves is based on more general features of the learning system or situation rather than on the postulation of some specific common, cognitive mechanism Following the same line of argument, the similarity of processing speed curves reported by Kail may be better accounted for by a more general view of the performance of these tasks rather than by hypothesizing a single, central limiting mechanism However, Kail's argument is based on all three lines of evidence taken together to rule out an alternative interpretation of developmental changes in cognitive processing According to this alternative account, called the specific learning hypothesis, developmental changes in speed of processing are due to the cumulative effects of learning and experience rather than to maturational changes in some general mechanism An examination of Kail's proposal for evaluating the contrasted hypotheses of specific learning and a central limiting mechanism reveals the assumptions underlying both hypotheses: [One] way to evaluate these hypotheses is to comparepatternsof developmentalchange acrosstasks Assume that change in processing speed reflects the acquisition of task-specific proceduralor declarativeknowledge Presumablythe events (e.g., specific experiences, maturationalchanges) that produce increased speed for some process X are independent of those events thatyield increases in speed of a second process Y Because the events that facilitate the two processes are independent, there is no necessary relation between developmental change in the speeds of these processes Of course, task-relevantknowledge could develop in parallel for particulartasks, resulting in identical growth functions, but this must be the exception rather than the rule if the hypothesis of taskspecific change is to have much heuristicvalue In contrast,if performanceon any speeded taskis limited by a generalmechanism,then the same pattern of growth in processing speed is expected across tasks [Kail, 1986, p 970] Kail argues that according to any version of the specific learning hypothesis that has "heuristic value," similarities in developmental speed-of-processing curves across tasks will only occur by coincidence, which is "the exception rather than the rule." In other words, Kail's assumption is that domain 1145 specificity of learning implies complete domain independence of the effects of learning It is our view that the version of the specific learning hypothesis that Kail pits against his central limiting mechanism hypothesis is highly restricted because it is limited to the case in which learning on one task is completely independent of learning on any other task This limitation may be unwarranted, in that there are few cognitive tasks that are so independent as to use completely different sets of skills and resources To assume that learning on any two tasks is completely independent precludes the possibility that transfer might occur between tasks Although it is possible that the specific learning hypothesis, as described by Kail, may be ruled out by Kail's data, we not believe his data militate against less restricted versions of a specific learning hypothesis A broader interpretation of specific learning, which we call the skill transfer hypothesis, may redress some of the limitations in Kail's formulation of specific learning Furthermore, models of skill transfer may provide us with an alternative explanation of evidence cited by Kail as support for a central limiting mechanism The question of interest is not whether domain-specific or general changes occurfor they both certainly occur-but rather which kind of change is primary Are these changes driven by specific learning, or by the independent growth of some general mechanism that applies to all tasks? We contend that the data reported by Kail are equivocal with respect to differentiating a central limiting mechanism from a skill transfer account of age-related changes in processing speed The Central Limiting Mechanism Hypothesis Before we argue that the skill transfer hypothesis can plausibly account for developmental changes in speed of processing, it is worth considering the central limiting mechanism hypothesis a little more closely Kail suggests that only a central limiting mechanism could reasonably generate his data His fundamental claim is that if two processes are limited by the same general mechanism, the performance curves will necessarily have the same shape But this is not necessarily correct It is not sufficient to merely suggest that performance in both tasks is limited by the same mechanism; it also is necessary to specify how the mechanism limits performance It is quite possible that a single lim- This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions 1146 Child Development iting mechanism could play different limiting roles in two tasks (e.g., affecting the asymptote for one and the slope for the other), in which case performance curves for the two tasks would not necessarily be similar A central limiting mechanism may constrain the rate at which information is processed by a system or it may constrain the total amount of information being processed These alternative roles for a limiting mechanism may affect the shape of a processing speed curve in very different ways Alternatively, the central limiting mechanism may have the same limiting role for two tasks (e.g., setting the slope for both), yet the two tasks may be mediated by different processes that are described by different characteristic functions (e.g., one hyperbolic and the other linear) Kail has neither specified how the central limiting mechanism would affect performance on his two tasks, nor has he given any rationale for his implicit assumption that the mechanism affects both tasks in the same way We can demonstrate the differential effects of a single limiting mechanism that constrains the rate modifier of one process and the asymptote of another by using a simple mathematical model The model is based on the following assumptions First, we assume that we can describe the change in processing speed of a system with a single difference equation, such that the overall response time is monotonically decreasing with development This means that gains in processing speed are not lost with normal development Second, we assume that there is some limit on processing speed that represents optimal performance in the fully developed adult Third, we assume that developmental improvements in response speed are proportionate to the distance from this asymptote According to Kail's account, the capacity of a central limiting mechanism grows with age In our model, this capacity serves to govern changes in performance on specific tasks, which are described by difference equations We constructed two models, one for each task For one task, available capacity limits the processing speed rate, and the asymptote is fixed, while for the other task, capacity sets the asymptote and the processing speed rate is fixed As long as the difference equation follows the assumptions we have outlined, it can take almost any specific form The top two panels of Figure show simulated developmental speed-of-processing curves for two different tasks, A (shown in the top panel) and B (shown in the bottom panel) Task performance was simulated us- Task A 400 N(t+1)= N(t) - 8LM(t) (N(t) - 115) 300 ( 200 100 10 14 18 22 Age(years) Task B R(t+1)=R(t)-.09(R(t)-1/LM(t)) - 654 10 14 18 22 Age(years) Growth of Limiting Mechanism 1.0 0.8 0.60.40.2 10 14 18 22 Age(years) FIG 1.-Simulation of the effect of a central limiting mechanismon two tasks,A (top panel) and B (middle panel) Performanceon these tasksis described by the same generalfunction.However,the growth of the limiting mechanism (shown in the bottom panel) sets the performanceasymptotefor Task B, and it modifies the increment of performance improvementfor TaskA This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Stigler, Nusbaum, and Chalip ing the same difference equation for both tasks, but with different parametersfor each so thatthe range of performancewould reflect absolute differences between the two tasks Remember that it is the shape of the curves that is importantand not the absolute levels of performance Equation (1), which was used to simulate these tasks, is based on the activation equation used by McClelland and Rumelhart (1981) The choice of this model for performance improvements is based on a view of changes in performance as an accumulation process In this equation, pi(t) representsperformanceon task i at time t, and a and b are constants that modify the input I and the minimum performanceasymptoteA pi(t + 1) = pi(t) - aI[p1(t) - bA] (1) The bottom panel of Figure shows the hypothesized growth of a central limiting mechanism with age The growth of this mechanism over time is described by equation (2), which is simply another variationof the activation equation in which capacity is increased by a constant proportion (gJ is a constant in this simulation) of the difference between the asymptoteM and the currentcapacity available c(t + 1) = c(t) + gJ[M - lc(t)] (2) Although both tasks are limited by the growth of a central limiting mechanism, this mechanism limits performance in two very different ways In Task A (shown in the top panel), the asymptote for processing is a constantand capacityLM(t) limits the proportion by which performance speed can increase at each age (by setting I in eq [1]) This role for a central limiting mechanism might be viewed as developmental increases in the efficiency of cognitive processing By comparison,in Task B (shown in the middle panel), the central limiting mechanism, LM(t), sets the asymptote of performance, A As capacity grows, the asymptote limiting performancedecreases, so processing time is reduced This could be viewed as a physiological change with development that permitsthe response system to generatefaster responses, or as a change in the speed with which certain mental processes are carried out Thus, as we outlined above, there are two different ways in which cognitive processing can be constrainedby a limiting mechanism The developmental speed-of-processing curves shown in Figure have very different 1147 shapes despite being governed by the same limiting mechanism These simulationresults illustratean importantpoint: the fact that two tasks are limited by the same central mechanism is not sufficientto guaranteethe similarity of their performancecurves The assumption that all tasks limited by the same mechanism will have the same shape is unwarranted.The simple invocationof a central limiting mechanism is not sufficientto generate similar performancecurves without substantialelaborationof how the mechanismoperates in limiting task performance The Skill Transfer Hypothesis While it may be true that a general limiting mechanismcould, under certaincircumstances, result in curves with similar shapes, it is our contention that substantialtransferof skills between tasks could the same The fact that transfermodels can account for performancesimilaritiesacrosstaskswas demonstratedlong ago in a series of papers by Ferguson (1954, 1956, 1959) If an increase in speed of processing in Task A leads to a correspondingincrease in speed of processing in Task B, for whatever reason, the developmental functionsfor the two tasks will tend to resemble each other In Kail'sstudy,the two taskswere chosen because "for both cognitive theorists and psychometric theorists, mental rotation and name retrieval represent distinct processes" (p 971) Kail's claim is that mental rotation loads psychometrically on spatial ability, while name retrieval loads on verbal ability This reported difference in psychometric loading suggests that there may be minimal overlap among the processes that mediate these tasks This processing distinction between tasks is importantfor Kail's argument If the tasks were not distinct, then developmental similaritiesbetween tasks could be attributedto the common structureof the tasks, making it unnecessary to invoke a more general mechanism We question whether Kail'stwo tasks are distinct enough to claim that there is no processing overlap between them Although it may be true that "name retrieval" tasks, in general, load on verbal ability, there is some evidence suggesting that the matching task used by Kail may load more highly on spatial ability than on verbal ability List, Keating, and Meiman (1985) used a task that was structurallysimilar to that used by Kail, except that the stimuli were letters of the alphabet instead of pictures of common objects Although matching letters should be more of This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions 1148 Child Development a verbal task than matching pictures of objects, List et al found that the only psychometric loadings for their task were spatial-not verbal Questions of psychometric loading aside, the real issue is the extent to which these tasks share any component skills that could lead to transfer Even if mental rotation is related to spatial aptitude and name retrieval is related to verbal aptitude, if these tasks depend on a single central limiting mechanism, then by definition (Shiffrin & Dumais, 1981), these tasks must be at least partially dependent on the operation of control processes in memory (see Shiffrin, 1976) The subject must access, maintain, and manipulate information from memory in both tasks, and it is unlikely that these very general control processes all are unique to either mental rotation or name retrieval If any of these basic skills are used to carry out both tasks, we would expect transfer between them Although we have argued that transfer could occur between two different tasks such as mental rotation and name retrieval, how likely is such transfer? Data relevant to this question have been reported in a recent, interesting paper by Kail (1987) In this study, Kail trained one group of subjects on mental rotation and a second group on memory scanning Following training, each group was given the other group's training task as a transfer task So the group trained on mental rotation received the memory search task as a transfer task, and the group trained on memory search received the mental rotation task to measure transfer The results for both groups showed significant transfer of training between these very different tasks Based on these results and on the preceding arguments, we believe that it is plausible to assume transfer between mental rotation and name retrieval as measured by Kail Three models of skill transfer.-Given that transfer could occur between different tasks, it is important to demonstrate that the effects of this transfer could result in data similar to those reported by Kail The basic attribute of a model of transfer is that as performance increases on one task, there are proportionate increases in performance on the transfer tasks This does not, by itself, indicate how transfer is accomplished We propose that one mechanism of transfer between tasks is by the improvement of shared component skills Practice on a particular task improves the skills that mediate it Performance of a second task that is mediated by any of the improved skills should show improvement as well Figure shows three general models of skill transfer that could account for similarity among speed-of-processing curves in different tasks In Transfer Model (shown in the top panel), performance on either of two tasks leads to direct improvement on the other task This is the most general view of transfer since it does not specify the mechanism by which transfer occurs In this model, if transfer is symmetric, then the speed-of-processing curves will have the same shape; to the degree to which transfer is asymmetric, the shapes of the curves will be similar but not identical The two panels of Figure show simulations of the name retrieval and mental rotation tasks based on direct transfer between these tasks These simulations are based on equation (1) in which I is set to the performance level for the other task In other words, increments in response speed are modified by the performance level of the other task The performance level of one task serves as input governing changes in the performance of the other task The asymptote A is set to a different value for each task reflecting the different scales of performance In this simulation, performance starts at some initial level for both tasks, and the more performance on each task improves, the more the other task benefits Since both tasks are engaged in simultaneously, the performance curves are directly coupled Both curves have the same shape as a result of transfer Tranfer Model (shown in the middle panel of Fig 2) is a more elaborated form of Transfer Model By this account, task performance may depend on both task-specific and task-shared skills This model assumes that skills are strengthened or improved by practice so that performance of a task improves each of the underlying skills (both task-specific and task-shared) which in turn improves performance To the extent that a task depends on a particular skill, improvements in that skill will result in better task performance If a skill is shared between tasks and both tasks depend on this skill, improvements in the shared skill will largely determine the shape of the performance curves for both tasks Furthermore, if the shapes of the underlying skill-growth curves are generally similar across tasks, the shape of the performance curves will be generally similar as well, assuming that the characteristic functions for task performance are the same and the shared skills play the same role in carrying out both tasks The upper two panels of Figure show the performance curves for simulations of the This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Stigler, Nusbaum, and Chalip 1149 Transfer Model I age age task task Transfer Model age task age I task skll skill skil2 Transfer Model age age task task skill I FIG.2.-Three models of skill transferdue to specific learning In TransferModel (top panel), changes in performanceof one taskdirectlyaffectperformanceof a second taskand vice versa.In Transfer Model (middle panel), tasks are performedby a combinationof shared and specific skills, and performance on one task affects performanceof a second taskby improvingcommonskills In TransferModel (bottompanel), two tasks are mediated primarilyby a common skill; increases in the proficiencyof this skill improveperformanceof both taskseven thoughthe performanceof these taskshas little, if any, effect on the level of the skill name retrieval and mental rotation tasks based on Transfer Model Each task was simulated using equation (1) with I being set by the sum of the levels of two skills-one common and one task-specific In this model, there are three different skills One skill is specific to each task and one is shared between them The rate of performance improvement on each task is governed by the sum of the levels of the two skills that mediate the task The task-common and taskspecific skills are weighted equally The growth of the three skills (shown in the bottom panel) is based on equation (2) For each skill, the asymptote is set to and the value of J depends on whether the skill is task-specific or task-common For taskspecific skills, J is set to the performance level of the appropriate task The input governing the growth of a task-specific skill is the performance level of the task mediated by that skill For the task-common skill, J is the sum of the performance level of both tasks Thus in this model there is a feedback loop between tasks and skills: Performing a task serves to improve component skills, which in turn further improves task performance Note that the two different tasks have the same shape in their performance curves, despite the fact that each depends partly on an independent, task-specific skill in addition to the one skill that is common to both Moreover, these curves are the same shape, despite the fact that the independent skill curves are quite different Finally, Transfer Model (shown in the bottom panel of Fig 2) is perhaps the most telling, as it is computationally indiscriminable from Kail's model of a general limiting mechanism According to Tranfer Model 3, the tasks performed by subjects in a particular experiment are transfer tasks These tasks This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Child Development 1150 Name Retrieval Name Retrieval 400 400 N(t+1) = N(t) - 3(CS(t) + NS(t))(R(t)- 115) N(t+1) = N(t)- 05R(t) (N(t)- 115) 300 "300 e 200 200 100 100 10 6 10 14 18 22 14 18 22 Age(years) Mental Rotation Age (years) MentalRotation 7- 8- (R(t)- 2.5) R(t+1)=R(t)- OO11N(t) 7- 4g 6- S5o 4 - 3(CS(t) + RS(t))(R(t)- 2.5) R(t+1) = RWt) 10 14 18 22 - Age (years) Skill Development 1.0 10 14 18 22 0.8 Age (years) FIG.3.-A simulationof TransferModel anddirectcouplingbetweentwo tasks Symmetric with age so thatthe curves improvesperformance havethe sameshape to CS(t) 0.6 0.4 - SRS(t} NS(t) / 0.2 have little, if any, direct influence on the skills that mediate their performance Instead, tasks such as name retrieval and mental rotation, which are not practiced extensively inside or outside the lab, really only probe the state of skills already developed independently in some other context If performance of these transfer tasks depends largely on shared skills that were learned outside of the lab and on new skills that must be developed on first encounter with the tasks, it seems likely that the independently learned (but shared) skills will dominate performance and determine the shape of the performance curves for both tasks 0.0 10 14 18 22 Age (years) FIc 4.-A simulation of Transfer Model Name retrieval (top panel) and mental rotation (middle panel) are mediated by one common skill and one task-specificskill Developmentalchanges in processing speed are a result of the sum of the two skill levels for each task Changes in the common skill CS(t), the name retrievalskill NS(t), and the mental rotationskill RS(t)are shown in the bottom panel Despite differencesin the shapes of the growth of the individual skills, developmental changes in processing speed for the two tasks are similar Thiscanbe seen in the toptwo panelsof constant proportion of the difference between Figure5, whichshowa simulationof Transfer the asymptote and the current skill level The Model using equation (1) for modeling task bottom panel of Figure shows the growth skill growth For each task, I in equation (1) is mance of the two tasks This model is compu- Improvements in performance are governed by the level of the mediating skill However, the skill grows independently of the tasks as a of a central limiting mechanism because in this model the limiting mechanism is the level of proficiency of the mediating skill performanceand equation(2) for modeling curve for the shared skill that limits perfor- set to the previouslevel of the commonskill tationally indistinguishable from Kail's view This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Stigler, Nusbaum, and Chalip Name Retrieval 400 N(t+1)= N(t)- 5CS(t) (N(t)- 115) 300 !200- 100 10 14 18 Age(years) Mental Rotation 10 22 1151 Given the type of data presented by Kail and the type of argumentshe makes regarding the similarityof curve shapes, there is no way to distinguish between a central limiting mechanismbased on resourceavailabilityand a skill transfermodel in which performance is constrained by the proficiency of skills learned outside the laboratory.The only argument advanced by Kail against a learning model is based on his claim that the performance curves he observed are best fit by an exponential function Since previous studies examining learning data have concluded that learning data are best described by a hyperbolic function (e.g., Newell & Rosenbloom, 1981), Kail concludes that the exponential shape of his data argues against a learning account such as that provided by Transfer Model R(t+1) = R(t) - 5CS(t) (R(t) - 2.5) Before accepting Kail's argument concerning the shapes of the developmental curves, it is importantto note two differences between Kail's results and those of Newell 64 and Rosenbloom (1981) Kail's data were obtained by sampling different groups of subjects at different ages, whereas the learning data analyzed by Newell and Rosenbloom were generally sampled within individuals acrosstime In other words, Kail'sdataare not generated by practice Although Kail noted this difference, it is not clear how it will affect 22 18 14 10 the shapes of the resulting curves A more Age(years) importantpoint aboutKail'sdataconcernsthe CommonSkill Development magnitude of the difference between the fits of exponential and hyperbolic functions 1.0 Whereas in some of the studies examined by Newell and Rosenbloom the difference be0.8 tween curves was large enough to have practical significance within the domain being learned, this is definitely not the case with S0.6 Kail's data Not only is the difference in fit between hyperbolic and exponential curves not statisticallyreliable for Kail'sdata,as Kail 0.4 himself acknowledges, but we contend that the differences between the curves are too small to be meaningful, and therefore they 0.2 should not be interpreted 22 14 18 10 Age(years) Figure shows the theoretical curves FIG.5.-A simulationof TransferModel3 from Kail's Table plotted using Kail's estiDevelopmental changesin the speedof performing mated parametersfor the name retrievaltask two transfertasks,nameretrieval(toppanel)and (top panel) and the two mental rotationtasks mentalrotation(middlepanel),are identicalsince (the curve fromExperiment is shown in the theyrelyon the growthof a commonskill(bottom middle panel and the curve from Experiment on the is shown in the bottom panel) At the point panel)that is unaffectedby performance transfertasks of greatestdivergence forthe two mental rotation tasks, these curves differ only by tenths of milliseconds! There is no extant experimental paradigmthathas sufficientresolution to distinguish between two curves differing - This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions 1152 Child Development NameRetrieval(Expt.1) were distorted by random deletions of dots 400 300 " J Hyperbolic SExponential 2001 100 11 13 15 17 19 21 23 MentalRotation(Expt.1) 7- this correlationprovides convergingevidence for the claim that processing speed in children and adultsdiffersby the growthof a general limiting mechanism The problem with this line of evidence, Age (years) and the remainder were undistorted The correlation between response times across conditions was concluded to be one, following several analyses of the data According to Kail, " Hyperbolic SExponential as Kail points out at the end of his discussion of Experiment3, is that only some versions of the specific learninghypothesis can be differentiated fromthe central limiting mechanism hypothesis using this paradigm Those versions of the specific learning hypothesis that Kail is able to rule out are those in which it is assumed that the component processes of the mental rotationtask develop at considerably different rates Just as earlier we proposed that different cognitive skills may develop at 23 17 21 19 11 13 15 similarrates due to transfer,we propose with Age (years) greater confidence that the component processes of a single skill might develop at simiMentalRotation(Expt.2) lar rates.Given that the component processes of mental rotation are practiced together within the same task, we would expect that they should develop in substantiallythe same w54 "Hyperbolic way There is no reason to assume that each Exponential putative component develops accordingto its own schedule: The components are practiced S3together, in the same context, with the same stimuli, and the same conditions This is the 21 19 17 23 11 15 13 situation for all of these processes to optimal Age(years) develop together and to directly influence FIG.6.-A comparisonof best-fit hyperbolic each other, as in TransferModel and exponentialfunctions fromKail's(1986) Table Thus, Kail's interpretationof adult-child for name retrieval(top panel), mental rotationin Experiment (middle panel), and mental rotation RT correlationsfor performanceof the same in Experiment2 (bottompanel) task is as problematic as the comparison of age-relatedcurves acrosstasks, and for essentially the same reasons Stating that the paton this scale of response time As a result, it is tern of response times across conditions is not reasonable to assert that this tiny differ- similarbetween two groups of subjects is logence (which is neither statisticallysignificant ically equivalent to stating that the shapes of nor experimentally detectable) is useful evi- two curves are similar.The problem is simply dence against the skill-transferhypothesis that both hypotheses-central limiting mechanism and skill transfer-could produce a Effects of Learning on the similarpatternof response times acrosscondiComponent Processes of a Task tions In the equations Kail develops in the The final argument advanced by Kail against the specific learning account of devel- opmental changes in processing speed is based on a correlation of one between the performance of adults and children across conditions in a particulartask In Kail's Experiment 3, adults and children were instructedto distinguish between mirror-image letters and correctlydisplayed letters at a variety of orientations.Half of the letter patterns Appendix, he again assumes that domainspecific learning is best represented by the assumption of complete domain independence Conclusion In conclusion, an analysis of the results and interpretation presented by Kail reveals no strong evidence in support of the central limiting mechanism hypothesis The kind of This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions Stigler, Nusbaum, and Chalip data collected by Kail, we would argue, is essentially irrelevant to the task of discriminating the central limiting mechanism hypothesis from a family of transfermodels that represent the specific learning hypothesis Not only can transfermodels explain similar age-relatedtrends in processing speed across tasks, but some versions of the central limiting mechanism hypothesis would predict findings differentfromthose obtainedby Kail In essence, the argumentwe are making is similar to argumentsthat have been raised previously regarding the indistinguishability of two models given certaintypes of data For example, Anderson (1978) argued that analog and propositional models of mental imagery cannot be distinguished using behavioralevidence While we believe that currentpsychological data are insufficient to discriminate between transferand the growth of a central limiting mechanism, we not believe that such data are unobtainable We not question the general claim that cognitive processes may be limited by central resources or that these resources may change with maturation.Indeed, there is a great deal of evidence in cognitive psychology to support the existence of both central (e.g., Shiffrin, 1976) and domain-specific resources (e.g., Wickens, 1984), and in many cases, task performancewill be limited by the availabilityof both types of capacities However, we believe that it is equally importantto consider the types of skills and processes that are used to performan experimentaltask.The human information-processingsystem is not just resource-limited There is a very strong argument to be made for the role of procedural knowledge in governing task performance(see Kolers & Roediger, 1984), and it is importantto consider how age-relateddifferences in performance might be a consequence of learning and transfereffects A complete account of cognitive development must take into account both maturational changes in resource availabilityand the effects of learning and transferon skill acquisition and improvement But in order to understandthe relative importanceand functions of resources and skills in cognitive development, it is necessary to design experiments that are specifically directed at teasing apart the underlying sources of performance limitations in a wide range of cognitive tasks The results presented by Kail demonstrate only thatthere is some similarity between the changes that occur across certain tasks as the child develops However, a correlationaldesign can only describe the existence of such View publication stats 1153 similarities;it cannot determine the underlying cause The rejection of one highly restricted view of specific learning does not necessitate acceptanceof an accountbased on a central limiting mechanism when other views of specific learning, such as the skilltransfer hypothesis, can account for Kail's findings equally well References Anderson, J R (1978).Arguments concerningrepresentations formentalimagery,Psychological Review, 85, 249-277 Ferguson, G A (1954) On learning and human ability.CanadianJournalof Psychology,8, 95112 Ferguson,G A (1956).On transferand the abilities of man Canadian Journal of Psychology, 10, 121-131 Ferguson, G A (1959) Learningand human ability: A theoretical approach.In P H DuBois, W H Manning, & C J Spies (Eds.), Factor analysis and related techniques (pp 174-190) Washington, DC: Office of Naval Research (TechnicalReportNo 7) Kail, R (1986) Sources of age differencesin speed of processing.Child Development,57, 969-987 Kail, R (1987, April).Impact of extensive practice on speed of cognitive processes Paper presented at the biennial meetings of the Society for Researchin Child Development,Baltimore Kolers, P A., & Roediger, H L III (1984) Procedures of mind.Journal of VerbalLearningand Verbal Behavior,23, 425-449 List, J A., Keating, D P., & Merriman,W E (1985) Differences in memory retrieval: A constructvalidityinvestigation.Child Development, 56, 138-151 McClelland,J L., & Rumelhart,D E (1981) An interactive activationmodel of context effects in letter perception:Part1 An accountof basic findings.PsychologicalReview, 88, 375-407 Newell, A., & Rosenbloom, P S (1981) Mechanisms of skill acquisitionand the law of practice In J R Anderson (Ed.), Cognitive skills and their acquisition (pp 1-55) Hillsdale, NJ: Erlbaum Shiffrin,R M (1976).Capacitylimitationsin information processing, attention, and memory In W K Estes (Ed.), Handbook of learning and cognitive processes (pp 177-236) Hillsdale, NJ: LEA Shiffrin,R M., & Dumais, S T (1981).The development of automatism.In J R Anderson(Ed.), Cognitiveskills and their acquisition(pp 111140) Hillsdale, NJ: LEA Wickens, C D (1984) Processing resources in attention In R Parasuraman& D R Davies (Eds.), Varieties of attention (pp 63-102) New York:AcademicPress This content downloaded from 205.208.121.144 on Sat, 11 Apr 2015 16:27:51 UTC All use subject to JSTOR Terms and Conditions ... 1956, 1959) If an increase in speed of processing in Task A leads to a correspondingincrease in speed of processing in Task B, for whatever reason, the developmental functionsfor the two tasks... level of the mediating skill However, the skill grows independently of the tasks as a of a central limiting mechanism because in this model the limiting mechanism is the level of proficiency of. .. developmental changes in speed of processing, it is worth considering the central limiting mechanism hypothesis a little more closely Kail suggests that only a central limiting mechanism could