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

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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

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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 4 (Aug., 1988), pp 1144-1153

Published by: Wiley on behalf of the Society for Research in Child Development

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Conunentaries

Central Limiting Mechanism or Skill Transfer?

James W Stigler, Howard C Nusbaum,

and Laurence Chalip

University of Chicago

STIGLER, JAMES W.; NUSBAUM, HOWARD C.; and CHALIP, LAURENCE Developmental Changes in Speed of Processing: Central Limiting Mechanism or Skill Transfer? CHILD DEVELOPMENT, 1988,

59, 1144-1153 In this article we examine Kail's claim that similarity in developmental speed-of- processing curves for 2 tasks indicates that performance on a wide range of cognitive tasks is constrained by the growth of a central limiting mechanism We argue that the "specific learning" hypothesis, which Kail rejects, does not consider the role of transfer of learning between tasks, and thus assumes that domain specificity of learning implies complete domain independence We demonstrate, through simulations, that the operation of a central limiting mechanism is neither sufficient nor necessary to generate the curves observed by Kail 3 alternative models of skill transfer are 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 task- specific and task-general constraints on performance

In performing any complex cognitive task

in an experiment, a subject can draw on a

wealth of resources consisting of some combi-

nation of knowledge and skills Some of these

capabilities may be limited by the matura-

tional state of the subject; others may be lim-

ited 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 similar-

ities 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 pre- sents 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 ap- proaches 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 postulat- ing a single, common underlying mechanism

As Newell and Rosenbloom (1981) stated, af-

This paper was written while the first author was supported by a Spencer Fellowship from the National Academy of Education The authors gratefully acknowledge the helpful comments of Robert Sternberg, Robert Kail, and an anonymous reviewer Also, thanks to Robert Siegler for his sharp eye, and to Kevin F Miller for comments on an earlier draft Correspondence may be ad- dressed to the authors at Department of Behavioral Sciences, University of Chicago, 5730 South Woodlawn Avenue, Chicago, IL 60637

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ter finding similarities in the shapes of learn-

ing curves across a wide range of tasks, "We

do 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 conclu-

sion is that the regularity in the shape of

learning curves is based on more general fea-

tures of the learning system or situation rather

than on the postulation of some specific com-

mon, cognitive mechanism Following the

same line of argument, the similarity of pro-

cessing 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 develop-

mental changes in cognitive processing Ac-

cording 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 hypoth-

eses of specific learning and a central limiting

mechanism reveals the assumptions underly-

ing both hypotheses:

[One] way to evaluate these hypotheses is to com-

pare patterns of developmental change across tasks

Assume that change in processing speed reflects

the acquisition of task-specific procedural or de-

clarative knowledge Presumably the events (e.g.,

specific experiences, maturational changes) that

produce increased speed for some process X are

independent of those events that yield increases in

speed of a second process Y Because the events

that facilitate the two processes are independent,

there is no necessary relation between develop-

mental change in the speeds of these processes Of

course, task-relevant knowledge could develop in

parallel for particular tasks, resulting in identical

growth functions, but this must be the exception

rather than the rule if the hypothesis of task-

specific change is to have much heuristic value In

contrast, if performance on any speeded task is lim-

ited by a general mechanism, 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 develop-

mental 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

Stigler, Nusbaum, and Chalip 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 unwar- ranted, 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 do 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 occur- for they both certainly do 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 cor- rect

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-

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1146 Child Development

iting mechanism could play different limiting

roles in two tasks (e.g., affecting the asymp-

tote for one and the slope for the other), in

which case performance curves for the two

tasks would not necessarily be similar A cen-

tral 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 alterna-

tive roles for a limiting mechanism may affect

the shape of a processing speed curve in very

different ways Alternatively, the central lim-

iting 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 dif-

ferent characteristic functions (e.g., one hy-

perbolic 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 ef-

fects of a single limiting mechanism that con-

strains 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 develop-

ment 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 per-

formance 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 gov-

ern 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 pro-

cessing 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 fol-

lows the assumptions we have outlined, it can

take almost any specific form

The top two panels of Figure 1 show

simulated developmental speed-of-process-

ing 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

0

100

Age (years)

Task B

9

4

8 R(t+1) = R(t)- 09 (R(t)- 1/LM(t))

7 -

6-

5 -

4

2

Age (years)

Growth of Limiting Mechanism 1.0

0.8 0.6- 0.4-

0.2

Age (years)

FIG 1.-Simulation of the effect of a central limiting mechanism on two tasks, A (top panel) and

B (middle panel) Performance on these tasks is described by the same general function However, the growth of the limiting mechanism (shown in the bottom panel) sets the performance asymptote for Task B, and it modifies the increment of performance improvement for Task A

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ing the same difference equation for both

tasks, but with different parameters for each

so that the range of performance would reflect

absolute differences between the two tasks

Remember that it is the shape of the curves

that is important and not the absolute levels of

performance

Equation (1), which was used to simulate

these tasks, is based on the activation equa-

tion used by McClelland and Rumelhart

(1981) The choice of this model for perfor-

mance improvements is based on a view of

changes in performance as an accumulation

process In this equation, pi(t) represents per-

formance on task i at time t, and a and b are

constants that modify the input I and the

minimum performance asymptote A

pi(t + 1) = pi(t) - aI[p1(t) - bA] (1)

The bottom panel of Figure 1 shows the

hypothesized growth of a central limiting

mechanism with age The growth of this

mechanism over time is described by equa-

tion (2), which is simply another variation of

the activation equation in which capacity is

increased by a constant proportion (gJ is a

constant in this simulation) of the difference

between the asymptote M and the current ca-

pacity 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 con-

stant and capacity LM(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 mecha-

nism, LM(t), sets the asymptote of perfor-

mance, A As capacity grows, the asymptote

limiting performance decreases, so processing

time is reduced This could be viewed as a

physiological change with development that

permits the response system to generate faster

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 constrained by a limiting mechanism

The developmental speed-of-processing

curves shown in Figure 1 have very different

Stigler, Nusbaum, and Chalip 1147 shapes despite being governed by the same limiting mechanism These simulation results illustrate an important point: the fact that two tasks are limited by the same central mechanism is not sufficient to guarantee the similarity of their performance curves The assumption that all tasks limited by the same mechanism will have the same shape is un- warranted The simple invocation of a central limiting mechanism is not sufficient to generate similar performance curves without substantial elaboration of how the mechanism op- erates in limiting task performance

The Skill Transfer Hypothesis While it may be true that a general limiting mechanism could, under certain circum- stances, result in curves with similar shapes,

it is our contention that substantial transfer of skills between tasks could do the same The fact that transfer models can account for performance similarities across tasks was demonstrated long ago in a series of papers by Fer- guson (1954, 1956, 1959) If an increase in speed of processing in Task A leads to a cor- responding increase in speed of processing in Task B, for whatever reason, the developmental functions for the two tasks will tend to resemble each other

In Kail's study, the two tasks were 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 important for Kail's argument

If the tasks were not distinct, then developmental similarities between tasks could be at- tributed to the common structure of the tasks, making it unnecessary to invoke a more general mechanism

We question whether Kail's two 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 structurally similar to that used by Kail, ex- cept that the stimuli were letters of the al- phabet instead of pictures of common objects Although matching letters should be more of

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a verbal task than matching pictures of

objects, List et al found that the only

psychometric loadings for their task were spa-

tial-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 re-

lated to spatial aptitude and name retrieval is

related to verbal aptitude, if these tasks de-

pend on a single central limiting mechanism,

then by definition (Shiffrin & Dumais, 1981),

these tasks must be at least partially depen-

dent 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 trans-

fer 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, in-

teresting paper by Kail (1987) In this study,

Kail trained one group of subjects on mental

rotation and a second group on memory scan-

ning 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 mem-

ory search received the mental rotation task to

measure transfer The results for both groups

showed significant transfer of training be-

tween these very different tasks Based on

these results and on the preceding arguments,

we believe that it is plausible to assume trans-

fer between mental rotation and name re-

trieval 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 per-

formance increases on one task, there are pro-

portionate 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 2 shows three general models of skill transfer that could account for similarity among speed-of-processing curves in different tasks In Transfer Model 1 (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 de- gree to which transfer is asymmetric, the shapes of the curves will be similar but not identical

The two panels of Figure 3 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 simulta- neously, the performance curves are directly coupled Both curves have the same shape as

a result of transfer

Tranfer Model 2 (shown in the middle panel of Fig 2) is a more elaborated form of Transfer Model 1 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 carry- ing out both tasks

The upper two panels of Figure 4 show the performance curves for simulations of the

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Stigler, Nusbaum, and Chalip 1149

Transfer Model I

task 1 task 2

Transfer Model 2

task 1 task 2

skll 1 skil2 skill 3

Transfer Model 3

task 1 task 2

skill I

FIG 2.-Three models of skill transfer due to specific learning In Transfer Model 1 (top panel), changes in performance of one task directly affect performance of a second task and vice versa In Transfer Model 2 (middle panel), tasks are performed by a combination of shared and specific skills, and performance on one task affects performance of a second task by improving common skills In Transfer Model 3 (bottom panel), two tasks are mediated primarily by a common skill; increases in the proficiency of this skill improve performance of both tasks even though the performance of these tasks has little, if any, effect

on the level of the skill

name retrieval and mental rotation tasks

based on Transfer Model 2 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 be-

tween them The rate of performance im-

provement on each task is governed by the

sum of the levels of the two skills that

mediate the task The task-common and task-

specific 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 1 and

the value of J depends on whether the skill

is task-specific or task-common For task-

specific skills, J is set to the performance level

of the appropriate task The input governing

the growth of a task-specific skill is the per-

formance 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 3 (shown in the bottom panel of Fig 2) is perhaps the most telling, as it is computationally indiscrimin- able 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

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Name Retrieval

400

N(t+1) = N(t)- 05R(t) (N(t) - 115)

"300

100

6 10 14 18 22

Age (years) Mental Rotation

9

8 R(t+1)=R(t) - OO11N(t) (R(t) - 2.5)

7-

6-

o 4

S5-

4 -

6 10 14 18 22

Age (years) FIG 3.-A simulation of Transfer Model 1

Symmetric and direct coupling between two tasks

improves performance with age so that the curves

have the same shape

have little, if any, direct influence on the

skills that mediate their performance Instead,

tasks such as name retrieval and mental rota-

tion, which are not practiced extensively in-

side or outside the lab, really only probe the

state of skills already developed indepen-

dently 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

This can be seen in the top two panels of

Figure 5, which show a simulation of Transfer

Model 3 using equation (1) for modeling task

performance and equation (2) for modeling

skill growth For each task, I in equation (1) is

set to the previous level of the common skill

Improvements in performance are governed

by the level of the mediating skill However,

the skill grows independently of the tasks as a

Name Retrieval

400

N(t+1) = N(t) - 3(CS(t) + NS(t)) (R(t) - 115)

300

200

100

6 10 14 18 22

Age (years) Mental Rotation

9

8 R(t+1) = RWt) - 3(CS(t) + RS(t)) (R(t) - 2.5) 8-

4g

6 10 14 18 22

Age (years)

Skill Development

1.0

0.8

SRS(t}

0.2

0.0

6 10 14 18 22

Age (years)

FIc 4.-A simulation of Transfer Model 2 Name retrieval (top panel) and mental rotation (middle panel) are mediated by one common skill and one task-specific skill Developmental changes

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 retrieval skill NS(t), and the mental rotation skill RS(t) are shown in the bottom panel Despite differences in the shapes of the growth of the individual skills, developmental changes in processing speed for the two tasks are similar

constant proportion of the difference between the asymptote and the current skill level The bottom panel of Figure 5 shows the growth curve for the shared skill that limits performance of the two tasks This model is computationally indistinguishable from Kail's view

of a central limiting mechanism because in this model the limiting mechanism is the level of proficiency of the mediating skill

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Stigler, Nusbaum, and Chalip 1151 Name Retrieval

400

N(t+1) = N(t) - 5CS(t) (N(t) - 115)

300

!200-

100

Age (years)

Mental Rotation

10

R(t+1) = R(t) - 5CS(t) (R(t) - 2.5)

8 -

4 6-

4

2

Age (years) Common Skill Development

1.0

0.8

S0.6

0.4

0.2

Age (years)

FIG 5.-A simulation of Transfer Model 3

Developmental changes in the speed of performing

two transfer tasks, name retrieval (top panel) and

mental rotation (middle panel), are identical since

they rely on the growth of a common skill (bottom

panel) that is unaffected by performance on the

transfer tasks

Given the type of data presented by Kail and the type of arguments he makes regard- ing the similarity of curve shapes, there is no way to distinguish between a central limiting mechanism based on resource availability and

a skill transfer model 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 3

Before accepting Kail's argument con- cerning the shapes of the developmental curves, it is important to note two differences between Kail's results and those of Newell and Rosenbloom (1981) Kail's data were ob- tained by sampling different groups of subjects at different ages, whereas the learning data analyzed by Newell and Rosenbloom were generally sampled within individuals across time In other words, Kail's data are not generated by practice Although Kail noted this difference, it is not clear how it will affect the shapes of the resulting curves A more important point about Kail's data concerns the magnitude of the difference between the fits

of exponential and hyperbolic functions Whereas in some of the studies examined by Newell and Rosenbloom the difference between curves was large enough to have prac- tical significance within the domain being learned, this is definitely not the case with Kail's data Not only is the difference in fit between hyperbolic and exponential curves not statistically reliable for Kail's data, as Kail himself acknowledges, but we contend that the differences between the curves are too small to be meaningful, and therefore they should not be interpreted

Figure 6 shows the theoretical curves from Kail's Table 2 plotted using Kail's esti- mated parameters for the name retrieval task (top panel) and the two mental rotation tasks (the curve from Experiment 1 is shown in the middle panel and the curve from Experiment

2 is shown in the bottom panel) At the point

of greatest divergence for the two mental rotation tasks, these curves differ only by tenths

of milliseconds! There is no extant experi- mental paradigm that has sufficient resolution

to distinguish between two curves differing

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