Individual differences in working memory capacity: more evidence for a general capacity theory

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Individual Differences
in Working Memory
Capacity: More
Evidence for a General
Capacity Theory
Andrew R.A. Conway
Version of record first published: 15
Oct 2010.
To cite this article: Andrew R.A. Conway (1996): Individual Differences
in Working Memory Capacity: More Evidence for a General Capacity
Theory, Memory, 4:6, 577-590
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Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 Individual Differences in Working Memory Capacity:
More Evidence for a General Capacity Theory
Georgia Institute of Technology, USA The causes of the positive relationship between comprehension and measures ofworking mem ory capacity rem ain unclear. This study tests three hypotheses for therelationship by equating the difficulty, for 48 individual subjects, of processingdemands in complex working m emory tasks. Even with difficulty of processingequated, the relationship between number of words recalled in the workingmemory measure and comprehension remained high and significant. The resultsfavour a general capacity view. We suggest that high working memory spansubjects have more limited-capacity attentional resources available to them thanlow span subjects and that individual differences in working memory capacity willhave implications for any task that requires controlled effortful processing.
In the two decades that have followed the sem inal work of Baddeley and Hitch(1974), evidence supporting the relationship between working memory capacityand cognitive performance has steadily accumulated (for a review, see Engle,1995). However, it remains unclear exactly why this relationship occurs. Thepurpose of the current study is to test three competing hypoth eses that have beenproposed to accou nt for the relationship between working memory capacity andreading com prehension. As such, this introduction will proceed with a briefreview of the three competing hypoth eses.
Pascual-Leone (1970) argued that keeping schem es active requires attentional Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 control or mental energy and that the amount of m ental power or M -spaceincreases developm entally as a result of biological or epigenetic factors. Case Requests for reprints should be sent to Andrew R.A. Conway, Department of Psychology, University of South Carolina, Columbia, SC 29208, USA. Email: conwaya@black.cla.sc.edu This work was supported by Grant RO1-HD27490-01A1 from the National Institute of Child Health and Human Development and Grant F49620-93-1-0336 from the Air Force Office ofScientific Research. We would like to thank Stephen Tuholski for assistance with designing thematerials for the study.
Ó 1996 Psychology Press, an imprint of Erlbaum (UK) Taylor & Francis Ltd (1974) extended the ideas of Pascual-Leone to suggest that differences in M -space are responsible for individual as well as developm ental differences incognition. However, he argued that increases in measured M -space do not resultfrom an increase in attentional resources but as a result of a speed-up in m entaloperations as they becom e more automatic. Th e attentional resources freed bythe automatisation of m ental operations can be used to keep other schem es in theactive portion of m emory. Although the Neo-Piagetian approach has beenprimarily used to understand the development of cognition, the ideas m ay alsobe helpful in efforts to explain individual differences at a given stage ofdevelopm ent. W e have referred to this approach to the relationship betweenworking memory capacity and higher-level cognition as the general processinghypothesis because Case (1985) viewed the operations that becom e automatisedas general to a wide variety of tasks (Engle, Cantor, & Carullo, 1992).
Baddeley and Hitch (1974) argued that working memory is a com plex system used both for the storage of information and for the com putational processing ofthat inform ation. They proposed the central executive as a flexible but lim ited-capacity work space. The central executive is used for both storage andprocessingÐ consequently, when greater effort is required to process informa-tion, less capacity remains for the storage of that information. They alsoproposed a variety of data representation systems including one for speechinformation called the articulatory loop and one for visual and spatialinform ation called the visuo-spatial sketchpad. Both Case’ s theory and Baddeleyand Hitch’ s theory propose a moment-to-moment trade-off between resourcesallocated for storage and resources allocated for processing.
Following the logic of Baddeley and Hitch (1974) and Case (1974), Danem an and Carpenter (1980, 1983 ) hypothe sised that the correlation between workingm emory capacity and higher-level tasks like reading comprehension will onlyoccur if the processing com ponent of the working mem ory task is of the sam etype as is required by the higher-level task. This would lead to the sam e type oftrade-off in the higher-level task as would occur in the working memory task.
They used a measure of working memory that required both processing andstorage of inform ation. Subjects read aloud sets of sentences and, at the end of a3±7-sentence set, they were required to recall the last word of each sentence.
Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 Daneman and Carpenter (1980) hypothesised that the processing or mental operations required to read the sentences would vary in efficienc y acrossindividuals and that a reader with more efficient processes would have moreworking mem ory capacity available for storage than would a reader with lessefficient processes. Thus, good readers should recall more of the last words thanpoor readers because they have more autom atised reading operations. W etherefore call this idea the task specific hypothesis. Daneman and Carpenter(1980) found that the number of words recalled in the reading span measure ofworking memory correlated quite well with global measures of reading such asthe Verbal Scholastic Aptitude Test (VSAT) as well as with m ore molecular measures such as the ability to correctly attribute a delayed pronominalreference.
Another possible explanation for the relationship between working memory capacity and comprehension is that high span subjects sim ply have m oreattentional resources to draw on than low span subjects, independent of the taskinvolved. According to this view, which we call the general capacity hypothesis,high working memory capacity individuals will have more attentional resourcesto perform a task regardless of the specific nature of the task. Of course,individuals will also vary in efficienc y of their mental operations in a specifictask, but, other things being equal, high working memory capacity individualswill still have m ore attentional resources available to them than low workingmemory capacity individuals. Thu s, there should be a relationship betweenworking m emory capacity and reading com prehension regardless of the specificprocessing component of the span task. All that is necessary is that theprocessing com ponent place some demand on attentional resources. Turner andEn gle (1989) tested this hypothesis by varying the processing com ponent of thereading span task. Instead of having subjects read sentences, they had subjectsperform m athematical operations. In this ``operation span task’ ’ , the subjectperforms simple mathematical operations while m aintaining words for laterrecall. Each operation is presented with a word and after each set of operation±word strings, the subject recalls the words. This task bears much surfacesimilarity to the reading span task except that, instead of reading, the subjectperforms mathem atical operations. W orking memory capacity or operation spanis defined as the number of words the subject can recall while successfullyperforming the m athematical problem s. Turner and Engle (1989) found thatoperation span correlated with VSAT as well as reading span. Furthermore,operation span and reading span accounted for about the sam e variance incom prehension. Engle, Cantor, and Carullo (1992) provided further support forthe general capacity hypoth esis in a study in which they examined performanceon a moving window version of the operation and reading span tasks.
The task specific hypoth esis, the general processing hypothe sis, and the general capacity hypoth esis all predict a correlation between reading span andVSAT. However, the hypoth eses differ on two other predictions. First, the Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 general capacity and the general processing hypotheses predict that operationspan will also correlate with VSAT (Turner & Engle, 1989). The task specifichypoth esis would not predict this correlation. Second, when viewing time on theprocessing com ponent of the span tasks is partialled out of the correlationbetween span and VSAT, the general capacity view predicts that the correlationwill remain significant. The task specific and general processing hypoth esesboth predict that partialling out viewing tim e would eliminate or dim inish thecorrelation between span and VSAT.
The results of Engle, Cantor, and Carullo (1992) clearly supported the general capacity hypothesis. Significant correlations were found betw een reading span, operation span, and VSAT. Furtherm ore, when viewing time waspartialled out of the correlation between span and VSAT, the correlationremained significant. Therefore, while statistically controlling for the time spenton the processing component of the span tasks, the storage component of thespan tasks still predicted comprehension ability. This clearly does not supporteither the task specific hypoth esis or the general processing hypoth esis.
Our approach in the current study is sim ilar to that of Engle, Cantor, and Carullo (1992). However, instead of statistically controlling for processingefficienc y, we hoped to equate, across subjects, the processing dem ands of anoperation span task. The logic for the experiment is sim ple. If the relationshipbetween working memory span and com prehension is driven by the trade-offbetween processing and storage, then equating the difficulty of the span taskshould elim inate the relationship. In contrast, if the relationship betweenworking memory span and comprehension is driven by attentional resourcesabove and beyond the trade-off between processing and storage, then equatingthe difficulty of the span task should not affect the relationship.
In order to equate processing across subjects, we first determined each subject’ s capability on operations exactly like those used in the operation spantask. Therefore, we had subjects perform mathematical operations of varyingdifficulty. From their perform ance on these operations, we designed threeoperation span tasks in which the mathematical operations were ``tailored’ ’ tothe m athematical ability of the subject.
The three hypoth eses outlined earlier make different predictions regarding the correlations between our new operation span tasks and VSAT. The taskspecific hypoth esis would not predict a correlation between VSAT and ouroperation span tasks with processing dem and equated. This is because the viewargues that individuals differ in span because of their differing ability toperform the processing com ponent of the task. Therefore, if each subject is atthe same point on the performance function for the processing component, theindividual differences in the span score should disappear and the relationshipbetween the span score and reading com prehe nsion should disapp ear.
Similarly, the general processing hypoth esis would predict the absence ofsignificant correlations between VSAT and our new operation span tasks with Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 processing demand equated. This is because individual differences in span are argued to result from individual differences in the am ount of operation spacerequired by the processing portion of the task. Therefore, if each subject usesthe sam e am ount of operation space, they will each have the same amount ofresidual storage space for rem embering words. Unlike the other tw o views, thegeneral capacity hypoth esis would still predict significant correlations betweenVSAT and our new operation span tasks with processing dem and equated. Thisis because the view argues that individuals differ in the total amount ofattentional resources available to them . Therefore, regardless of the demand ofthe processing com ponent of the task, individual differences in span willremain.
Forty-eight undergraduates from the University of South Carolina participated inthe study. All were tested individually in each of the three sessions, receivedcourse credit for participation, and signed permission for access to theirScholastic Aptitude Test (SAT) scores from university files. To ensure a widerange of com prehension skill, we chose subjects based on their Verbal SAT score.
W e specified five VSAT intervals; 200±340, 350±440, 450±540, 550±640, and650±800; and chose 6, 12, 12, 12, and 6 subjects from each interval, respectively.
All the tasks reported here were conducted using an IBM PS/2 computer and a VGAmonitor. The original operation span task was programmed using Turbo Pascalsoftware. The mathematical operations and the new operation span tasks wereprogrammed using Micro Experimental Laboratory (MEL) software (Schneider, 1988).
Each subject participated in three experimental sessions. In the first session thesubject perform ed the original operation span task and a backward letter task,both of which are normally adm inistered to hundreds of subjects each semesterin our lab. The backward letter task is not totally germane to the current problembut the results are presented for completeness. In the second session the subjectperformed a series of mathematical operations to determ ine the points at whichthey would achieve approxim ately 75% , 85% , and 95% accuracy. The series ofoperations was designed as a hierarchy in terms of difficulty. In the third sessionthe subject performed three new operation span tasks in which the difficulty ofthe mathematical operations was manipulated to conform to the levels ofdifficulty ascertained in the secon d session.
This task was the sam e operation span task previously used in our lab (Conway & Engle, 1994). For each subject, a pool of Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 66 mathem atical operations was randomly paired with a pool of 66 to-be-rem em bered words (taken from LaPointe & Engle, 1990). During the task,subjects were presented with operation±word strings, e.g. (8/4) + 2 = 4 ? BIRD.
Each operation required the subject to multiply or divide two integers and thenadd or subtract a third integer, i.e. (8/4) + 2 = 4. The integers ranged from 1 to 10.
The subject was to read the operation aloud, say ``yes’ ’ or ``no’ ’ , to indicate if the number to the right of the equal sign was the correct answer, and then saythe word aloud. After the subject said the word, the experimenter im mediatelypressed a key, and another operation±w ord string was presented. This processcontinued until a question m ark cued the subject to write the to-be-remem beredwords, in order, on a response sheet. The number of operation±word strings per series varied from two to six. Three series of each leng th were performed, andthe order of series length was random ised. The first three series, each of length2, served as practice. A subject’ s span score was the sum of the correctlyrecalled words for trials that were perfectly recalled in correct order. Forexample, if a subject recalled all the series of length 2 in correct order and one ofthe series of length 3 in correct order, their span score would be 9 (2 + 2 + 2 + 3).
This score was originally reported by Turner and Engle (1989), and consistentlycorrelates with VSAT (Cantor & Engle, 1993 ; Cantor, Engle, & Hamilton, 1991 ;Engle, Cantor, & Carullo, 1992; Engle, Nations, & Cantor, 1990 ; LaPointe &Engle, 1990). Each subject’ s accuracy on the operations was also recorded. Ifaccuracy was below 85% , the subject was not used in the experiment.
The backward letter task consisted of auditory presentation of strings of random letters, chosen from the pool of all consonantsexcept w. The letters were recorded in a fem ale voice at a rate of one letter persecond and the word ``recall’ ’ was spoken in the sam e voice after the last letter.
The lists of letters varied in length from two to eight, with three trials at eachlength. Th e subject was required to write the list in the reverse order on an answersheet. If a subject could not recall a letter, they were to leave a blank space for thatletter. The sam e scoring procedure was used as with the operation span tasks.
The purpose of this session was to determine each subject’ s performance on mathematical operations of varying difficulty(see Table 1). The subject’ s performance during this session determined theoperations to be used in the subsequent operation span tasks. Before perform ingthe mathematical operations, the subject was given ``number recognition’ ’ trialsto fam iliarise them with the keyboard. A number was presented in the centre ofthe com puter screen and the subject pressed the correspondin g key on thenumeric keypad on the right-hand side of the keyboard. Each subject performed20 of these trials.
Each subject then perform ed 375 operations in 25 blocks of 15 trials. Each block contained one operation from each of the 15 types of mathem aticaloperations selected in a pilot study1. The order of presentation of the 15 types Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 within a block was random.
1 A pilot study with approximately 100 subjects was conducted to select the mathematical operations used in sessions 2 and 3. A series of 20 types of operations that we intuited to range indifficulty from very easy to very difficult were used. Each subject received 15 operations of each ofthe 20 types at a rate of three seconds per operation. The subject was to type the correct digit solutionto the operation within the three-second period or the item was counted as an error. The pilot studyverified the intuitive order of difficulty of the operations but found that five of the types of operationswere either too difficult for our subjects to solve in three seconds or were indiscriminable from othertypes of operations. This left a series of 15 types of mathematical operations that ranged in difficultyfrom ``2 + 5 = ?’ ’ to ``(22 + 34)/7 = ?’ ’ . These types of operations were used in the study reported hereand are shown in Table 1.
Ty pes of M a the m atical O pe ra tions U sed R ((a /10) *10 + 1, (a /10 ± 1) *10 + 9) The form of the operation is followed by the range of possible integer values for a, b, and c. The values for a, b, and c were chosen such that the answer of the operation would be an integer between1 and 9. Formation of the last operation type listed in the Table, (a + b) / c, required an algorithm thatfirst assigned a value to c [R (2, 9)], then a temporary value to a [c * R (2, 9)], then a value to b[R (2, a)], and then a final value for a (a ± b), based on the value of b.
An operation appeared on the computer screen (e.g. 2 + 3 = ?) and the subject’ s task was to enter the answer using the num eric keypad on the right-hand side of the keyboard within three seconds of the onset of the operation. Ifthe subject did not respond in three seconds, the trial was scored as an error andthe next trial began.
Response accuracy was recorded by the com puter. If the subject made fewer than three errors (92% accuracy or better) on an operation type, thatoperation type was designated as the operation type to be used in the ``easy’ ’span task for that subject. If the subject made three, four, or five errors Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 (between 80% and 88% accuracy) on an operation type, that operation typewas designated as the operation type to be used in the ``m oderate’ ’ span taskfor that subject. If the subject m ade six, seven, or eight errors (between 68%and 76% accuracy) on an operation type, that operation type was designatedas the operation type to be used in the ``difficult’ ’ span task for that subject.
If m ore than one operation type qualified for use in the span tasks (i.e. thesubject responded at 100% accuracy on more than one operation type) thenthe operation type defined as m ore difficult by the pilot study was chosen asthe operation type to be used in the span task. If no operation type qualifiedfor either the easy, moderate, or difficult span task then the subject did no tparticipate in the study.
Operation Span Tasks with Maths Difficulty Manipulated and Controlled for Each subject performed three operation span tasks; easy, m oderate, and difficult. The procedure for each span task was exactly the sam eas the procedure for the original operation span task (described earlier). The onlydifference between the tasks was the type of mathematical operations used. Forthe ``easy’ ’ span task, the subject received the operation type on which he or shem ade fewer than three errors in the previous session. For the ``moderate’ ’ spantask, the subject received the operation type on which he or she m ade three, four,or five errors in the previous session. For the ``difficult’ ’ span task, the subjectreceived the operation type on which he or she made six, seven, or eight errors inthe previous session. The order of the three tasks was counterbalanced acrosssubjects within each VSAT range.
Three pools of 66 high-frequency concrete noun s (taken from Carrol, Davies, & Richm an, 1971 ) were random ised for the easy, moderate, and difficult spantasks. Therefore, an individual subject received different words for the easy,m oderate, and difficult span tasks, but the sam e words and the sam e order ofwords were used for each subject.
In addition to obtaining each subject’ s span score, we recorded the time the subject spent reading the operation and word. This ``viewing time’ ’ began whenthe experim enter pressed a key to present the operation±w ord pair and endedwhen the experimenter pressed a key indicating the subject had finished readingthe operation±word pair, which led to the presentation of the next operation±word pair. During this time, the subject was to read the mathem atical operationaloud, say ``yes’ ’ or ``no’ ’ to indicate whether the given answer was correct orincorrect, and say the word.
Descriptive statistics for the dependent measures of greatest interest are reportedin Table 2. As can be seen, error rates were relatively low and varied onlyslightly as a function of difficulty. This was supported by a one-way repeatedm easures ANOVA on error rate. The main effect for difficulty was m arginallysignificant, F(2,90) = 2.87, P = 0.06, MSe = 4.31. Simple com parisons showed Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 that significantly fewer errors were made in the easy span task (M = 1.06) than in the difficult span task, (M = 2.02) F(1,45) = 8.02, P < 0.01. No other simplecomparisons were significant.
Our manipulation of difficulty was successful because subjects were slower in the difficult span task than in the moderate span task, and faster in the easyspan task than in the moderate span task. This was supported by a one wayrepeated measures ANOVA on viewing tim e2. The main effect for difficulty wassignificant, F(2,90) = 19.36, P < 0.01, M Se = 507,47 2 and pair-w ise com parisons 2 The viewing time data for two subjects were not recorded because of a computer error. One subject was from the 650±800 VSAT range and the other was from the 550±640 VSAT range.
M ean and (standard deviation). The span and backward letter measures are the sum of the correctly recalled items for trials that were perfectly recalled in correct order. The viewing time data are inmilliseconds and the error rate data are proportions.
showed that all levels of difficulty significantly differed from one another (forall, P < 0.01).
The number of words recalled in the operation span task did not vary as a function of difficulty. This was supported by a one-way repeated measuresANOVA on operation span. The main effect for difficulty was not significant,F(2,90) < 1, M Se = 27.85.
W e calculated reliability measures for our operation span tasks with mathem atical difficulty manipulated. In each of our operation span tasks, thesubject was presented with 15 series of operation±word pairs. These series variedin leng th from two to six operation±w ord pairs per series and there were threeseries of each length, 2, 3, 4, 5, and 6. Therefore, for each operation span task, wecalculated three submeasures, each derived from five operation±word pair seriesof length 2, 3, 4, 5, and 6. W e calculated Cronbach’ s alpha for the easy, m oderate,and difficult span tasks based on these subm easures. Cronbach’ s alpha for theeasy, moderate, and difficult tasks is 0.80, 0.84, and 0.84 respectively.
Intercorrelations among the span measures and VSAT are reported in Table 3. All of the correlations in the Table are significant (for all, P < 0.01).
Perform ance on the original operation span task correlates highly withperformance on the span tasks in which we manipulated m athem atical difficulty.
Also, we found the intercorrelations between the new span tasks to be highly Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 significant. M ost importantly, all of the span tasks; original, easy, m oderate, anddifficult; significantly correlate with VSAT. This suggests that individualdifferences in span are not accounted for by differing ability on the processingcom ponent of complex span tasks, such as operation span. These results supportthe general capacity hypothesis and fail to support both the task specifichypoth esis and the general processing hypoth esis.
Although the intercorrelations among the various span measures are allconsiderable and significant, we can ask whether the measures account for Intercorrela tions B etw e en S pan Ta sks a nd V S A T comm on variance in VSAT. There are several ways we can converge on ananswer to this question. One way is to use a forward selection procedure todeterm ine the amount of new variance the m easures account for in VSAT. Table4 shows the results of the forward selection procedure. The easy operation spantask accou nted for 33% of the varianc e in VSAT, the original operation spanaccou nted for an additional 10% , backward letter accounted for an additional3% , and the moderate and difficult accounted for 1% additional each but thelatter two were not significant. All of the measures combined accounted for 48%of the variance in VSAT but the bulk of that was contributed by a singlem easure, the easy operation span.
To determ ine whether the efficiency of processing for an individual inm athematical operations played any role in the relationship between the numberof words recalled and the Verbal SAT, we calculated partial correlationsbetween VSAT and our span m easures while statistically controlling for viewingtim e. If the general processing hypoth esis is correct, these correlations shouldbecome non-significant. Th e partial correlations are reported in Table 5. Thecorrelations between the span tasks and VSAT remain virtually unchanged and,obviou sly, significant when viewing tim e is partialled out (for all, P < 0.01).
Therefore, the significant correlations between the span tasks and VSAT are notdue to the am ount of tim e required to process the operation±w ord pair.
Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 R es ults of R eg ression A na lyses of V aria n ce in V S A T C orre lations B etw e en V S A T an d S pa n Tas ks B efore an d A fter Partialling O ut Th e purpose of this study was to investigate the relationship between workingmemory capacity and reading com prehension, and to provide a test of threecom peting hypoth eses proposed to accou nt for this relationship. W e used theoperation span task because it was possible to systematically vary the difficultyof the processing com ponent of the task. W e equated the processing dem and ofthe operation span task across subjects and systematically manipulated the leve lof difficulty across three conditions. The correlations between these threeconditions and reading com prehension, as operationalised by VSAT, rangedfrom 0.49 to 0.62 and did not differ statistically from the original version of theoperation span which correlated 0.59 with VSATÐ for all pair-w ise com par-isons, t(45) < 1.43, P > 0.10. Further, these correlations were undiminished whenwe partialled out the time that subjects spent viewing the operation±w ord string.
Th e general capacity hypoth esis can explain these results but the task specificand general processing hypotheses cannot.
The general capacity m odel of working memory was first proposed by Engle, Cantor, and Carullo (1992). The m odel assum ed that working m emory consistsof knowledge units in long-term declarative memory which are currently activebeyond som e critical threshold. The model also assumed that knowledge unitsvary in their level of activation and that the total am ount of activation availableto the system is limited. The total amount of activation available to eachindividual varies, and it is this varianc e that causes individual differences inworking memory capacity. Cantor and Engle (1993) provided support for the Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 general capacity model by reporting that the am ount of activation available tolong-term memory, as measured by the fact retrieval task (Anderson, 1974),statistically accounted for the correlation between operation span and VSAT.
A recent study condu cted in our lab (Conway & Engle, 1994), however, has convinced us that it is not sufficient to sim ply say that high- and low-spansubjects differ in the total amount of activation available to them. A furtherqualification for the general capacity model is that individual differences willonly reveal themselves in tasks that force the subject to engage in controlledeffortful processing. If the task allows for automatic processing, then thelimited-capacity resource we call working m emory will not be taxed. Indeed, Conway and Engle (1994) found that individual differences in working m emorycapacity were important in a memory search task that required controlledprocessing, but were not im portant in a m emory search task that allowed forautom atic processing. Thus, we now believe that individual differences on thecomplex W M measures correspond to differences in general, controlled,effortful, attentional resources.
The question remains, why do we find that operation span predicts VSAT, even when the processing dem and of the task is equated for each subject? Theoperation span task, regardless of the demand of the processing component,requires the subject to switch attention constantly from one aspect of the task toanother. Subjects must perform a mathem atical operation and then encode aword, perform a mathem atical operation, and encode a word, and so on, untilthey are asked to recall the words. This type of attention switching requires thesubject to engage in controlled effortful processing. W e agree with Baddeleyand Hitch (1974) and Danem an and Carpenter (1980), that tapping bothprocessing and storage is necessary for a span task to be a good measure of acentral executive or working mem ory capacity. However, we argue that it is notthe demand of the processing component that is critical. W e argue that thesimple existence of a processing com ponent beyond the storage com ponent iswhat is required for a span task to be a good measure of working mem ory and agood predictor of m ore com plex cognitive behaviour, such as readingcomprehension. Of course, the processing compo nent has to be demandingenoug h that it forces the subject to shift attention away from the storagecomponent of the task and to engage in controlled effortful processing. Suppor tfor this argument com es from our finding that viewing time was a function oflevel of difficulty but the number of words recalled was not. Subjects spentnearly one second longer processing the operation±w ord pair in the difficultspan task than in the easy span task, yet the number of words recalled in eachtask was not statistically different. If the demand of the processing component ofthe task was the critical determ inant of span, then we should have found thenumber of words recalled to be a function of the level of difficulty of theoperations. However, if attention switching is the critical determinant of span, aswe argue, then level of difficulty will not have an effect on the number of words Downloaded by [Carnegie Mellon University] at 08:13 31 January 2013 recalled, as we found.
Towse and Hitch (1995) recently reported evidence in support of an attention-switching interpretation of developm ental differences in performanc eon the counting span task. They independently manipulated counting difficultyand counting time in the counting span task and found that difficulty did nothave an effect on span when time of counting was controlled. They argue, as wehave, that performance on span tasks such as reading span, operation±w ord span,and counting span is not driven by a trade-off between resources allocated toprocessing and storage. Their view differs from ours however, in that they arguethat the tim ing of the processing component of the task is critical to span performance. Thus, according to their view, span perform ance is driven by thetime spent away from the storage com ponent. The attention-switch itself is no tcritical; the tim e between successive switches is.
Our data do not support their view. W e found that viewing time was a function of level of difficulty, but the number of words recalled was not. That is,subjects spent longer on the processing component in the difficult span task thanin the easy span task, yet the number of words recalled in the two tasks was no tstatistically different. Furtherm ore, when we partialled viewing tim e out of thecorrelations between span and VSAT, the correlations remained virtuallyunchanged. Thus, we argue that the critical com ponent of the task is theattention-switch itself, not the trade-off in resources, and not the time spentprocessing.
One potential problem with our procedure is that the mathematical ability of each subject was tested under strict time constraint whereas the operation spantask is subject-paced. In the mathem atical operations session, the subject wasonly allowed three seconds to answer each m athem atical operation. In thesubsequent operation span tasks, the subject read the operation aloud at his orher own pace. One may argue that the nature of the processing underlying thesetwo tasks is quite different due to the differing tim e constraints. However, beforethe operation span tasks, we encouraged our subjects to perform the operationsas quickly as possible without sacrificing accuracy. Also, if the subject appearedto be perform ing the operations slowly in the operation span tasks, theexperimenter encouraged them to perform the operations more quickly.
Th erefore, we do not feel that this difference in procedure contaminated theoutcome of the experiment.
In conclusion, we argue that working memory is a very general resource which plays a role in a wide variety of cognitive tasks. Furtherm ore, we hope thecurrent article makes the point that it is not sufficient sim ply to identify arelationship between working memory and som e aspect of cognition. W e mustgo beyond the identification of the relationship and investigate exactly why therelationship occurs. Only then will we be able to understand fully the role ofworking mem ory in norm al human information processing.
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