A New Model of Verbal Short-Term Memory

A New Model of Verbal Short-Term Memory

Sergio Morra

Universitadi Padova, Padua, Italy

Two experiments tested a neo-Piagetian model of verbal short-term memory andcompared it with the articulatory loop model. Experiment 1 (n 5 113, age range 9–11)tested word span for 2-, 3-, and 4-syllable words, with both visual and auditory presen-tation. Experiment 2 (with the same participants) tested recall of visually presentedsupraspan lists. Measures of M capacity (as conceived in Pascual-Leone’s neo-Piagetiantheory) and articulation rate were also used. The proposed model can account for theeffects of M capacity, word length, and presentation modality. The fit of this model to thedata was acceptable, and parameter estimates were consistent across experiments. Fur-thermore, a correlation was found between M capacity and word span which resistedpartialling out of age and articulation rate.© 2000 Academic Press

Key Words:short-term memory; model; neo-Piagetian; visual presentation; auditorypresentation; word length; M capacity; goodness of fit.

Neo-Piagetian theories (e.g., Case, 1985; Demetriou, 1988; Halford, 1993)have emphasized the role of working memory in cognitive development, buttraditionally have not been connected with the dominant approach in workingmemory research (e.g., Baddeley, 1986). More recently, investigators (e.g., deRibaupierre & Bailleux, 1994) have suggested that it would be desirable to relatethese two approaches. In this article I provide such an integrative approach byusing a neo-Piagetian model that takes into account the effects of word length,presentation modality, and use of supraspan lists, which are often reported inworking memory research.

Baddeley’s model includes a set of peripheral short-term stores—including anarticulatory loop, a phonological store, and a visuospatial sketch pad. The modelalso includes a central executive, which is assumed to have both attentional andstorage functions, although its capacity and the way it works still seem to belargely undetermined (see Allport, Styles, & Hsieh, 1994; Baddeley, 1996;Lehto, 1996). Among the several short-term stores suggested, only the articula-

Thanks are due to Chiara Stoffel, Francesca Rizzotti, and Antonia Sartori for collecting and scoringdata, and to Sandro Bettella for computer programming. The author now works at the University ofGenova, Italy.

Address correspondence and reprint requests to Sergio Morra, DISA—sezione Psicologia, vico S.Antonio 5/7, 16126 Genoa, Italy. E-mail: [email protected].

Journal of Experimental Child Psychology75, 191–227 (2000)doi:10.1006/jecp.1999.2536, available online at http://www.idealibrary.com on

0022-0965/00 $35.00Copyright © 2000 by Academic Press

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tory loop’s capacity has been estimated. It was suggested that verbal short-termmemory (STM) is time-limited; that is, one can recall as much as can be spokenin about 1.5 or 2 s (Baddeley, 1986, 1992; Baddeley, Lewis, & Vallar, 1984;Baddeley, Thomson, & Buchanan, 1975; Hulme & Tordoff, 1989; Schweickert& Boruff, 1986). Given the finding that there are differences in recall when wordlength varies, it appeared that span depends on stimuli rehearsal rate. Baddeleyet al. (1984) also suggested that two components—an articulatory loop and aphonological store—are needed to account for different verbal STM phenomena.However, they attributed the word-length effect, and therefore the time-limitedcapacity, to the articulatory loop, not to the phonological store. Nicolson (1981)and subsequent studies also suggested that the articulatory loop can account forthe development of verbal STM from the age of 4 to adulthood.

However, this version of the loop model faces conflicting evidence. In contrastto early studies cited above, recent researchers (e.g., Cowan et al., 1994; Henry,1994) have shown that the ratio of recall to articulation rate is not constant andthat the intercept of the regression line of short-term memory span on articulationrate is often above zero. The articulatory loop cannot, therefore, fully account forverbal STM. Hulme, Maugham, and Brown (1991) found that word familiarityaffects the intercept of the span-to-speech-rate regression line. They concludedthat their results were incompatible with the widespread unitary view of STMspan in which all storage occurs within an articulatory loop. Hitch, Halliday, andLittler (1989) and Morra (1990) also drew similar conclusions.

Furthermore, several authors have questioned whether articulation time reallydoes account for word-length effect in subvocal rehearsal, offering alternativeexplanations that include verbal output interference (Cowan et al., 1992; Henry,1991b), proactive interference (Nairne, Neath, & Serra, 1997), and complexity ofspeech programming (Caplan, Rochon, & Waters, 1992; Lovatt, Avons, &Masterson, 2000; Service, 1998). Brown and Hulme (1995) and Neath andNairne (1995) provided computational evidence that a word-length effect couldbe produced by any of several mechanisms of forgetting. Moreover, verbal STMspan is affected by variables that have little or no effect on articulation rate, suchas semantic variables (e.g., Poirier & Saint-Aubin, 1995), grammar class (Tehan& Humphreys, 1988), word frequency or familiarity (e.g., Henry & Millar, 1991;Hulme et al., 1997), and order of the stimulus words (Brooks & Watkins, 1990).

Finally, developmental research shows that rehearsal skill only partly accountsfor age-related changes in STM span (Cowan, Cartwright, Winterowd, & Sherk,1987; Cowan et al., 1994; Henry, 1991a; Hitch, Halliday, & Littler, 1989). Kailand Park (1994) suggested that articulation rate increase is an outcome of theincrease of processing speed with age, but they also found an age effect onmemory span not explained by either processing speed or articulation rate.

Various modified versions of the articulatory loop model have been proposed(Brown & Hulme, 1995; Burgess & Hitch, 1992; Cowan, 1992; Cowan et al.,1992, 1994; Gathercole, 1997; Henry, 1991b; Hulme et al., 1991). These will be

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considered in the general discussion. In revising Baddeley’s model, some authorsalso considered the finding of an above-zero intercept in the regression line ofSTM span on articulation rate. Hitch, Halliday, and Littler (1989) suggested thata positive intercept may reflect a contribution of the central executive to memoryspan, Nicolson and Fawcett (1991) proposed instead a phonological store, andHulme et al. (1991) argued that it represents a long-term memory contribution.The model presented here is closest to the suggestion of Hitch et al. However,it also tries to increase conceptual and quantitative precision by using neo-Piagetian theoretical constructs to replace that of ahomunculus-like centralexecutive. Rehearsal is also considered important; but no form of specificallytime-limited storage is assumed.

The present model elaborates upon the idea thatactivation can be a validalternative to storage as the basic metaphor for short-term memory (Cowan,1988; Engle, Cantor, & Carullo, 1992). Instead of positing the existence oftime-limited capacity stores, these authors consider how activation of somecognitive representations decreases during processing.

This model rests on a neo-Piagetian theory—the theory of constructive oper-ators (Pascual-Leone, 1987; Pascual-Leone & Goodman, 1979)—which includestwo types of constructs: schemes and general-purpose operators. FollowingPiaget,figurative schemes represent states of affairs, whileoperativeschemesrepresent procedures that transform either states of affairs or their mental repre-sentations. Schemes can be activated either by perceptual input or by variousinternal sources of activation. Rehearsal mechanisms are conceived not as limitedstores (such as the articulatory loop) but rather as specific operative schemes(e.g., a verbal rehearsal operative). As such, they have no “capacity” of their own,but their activation follows the same rules as that of any other scheme.

The theory of constructive operators posits a number of general-purposemechanisms that serve to increase or decrease activation of schemes or togenerate new ones. Four are relevant here. TheM operator (Mental energy) isconsidered as a limited amount of attentional resources that increases with ageand can be used by executive schemes to activate other schemes. It is conceivedas a general-purpose attentional mechanism, but not as “the single” resource. TheI operator(Interrupt) has a complementary control function; that is, it inhibits (ordeactivates) schemes. TheF operator(Field) consists in increased activation ofthose schemes that are facilitated by stimulus–response compatibility or Gestaltprinciples. TheL operator (Learning) allows activation, at reduced attentionalcost, of schemes belonging to a learned superscheme or structure (as in autom-atization).

In line with the view that every scheme functions as an integrated cognitiveunit, Pascual-Leone (1970) assumed that activation by the M operator of anyscheme requires the same amount of attentional energy. Further, he suggestedthat 3-year-olds have an M operator capacity sufficient to activate executiveschemes for the current task plus one (operative or figurative) scheme (i.e.,e 1

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1) and that capacity increases by one additional scheme approximately every 2years through adolescence.

Building on Pascual-Leone’s work, Burtis (1982) modeled encoding andretrieval processes in a short-term memory task. His model successfully ac-counted for the effects of M capacity and chunking in recall of visually presentedsupraspan sets of consonants. It did not, however, consider the word-length effector other effects often attributed to phonological encoding. The purpose of themodel described here was thus to preserve Burtis’s theoretical structure, revisingand extending it to consider the roles of rehearsal, presentation modality, anddifferences between materials (such as varying word lengths). The main goals ofthis paper are to describe the model and to test its goodness of fit.

In a pilot experiment, children aged 6 to 9 years heard, for immediate recall,lists of two-, three-, and four-syllable words, following a span procedure.Experiment 1 compared memory span for lists of different-length words pre-sented visually or aurally to children aged 9 to 11. In Experiment 2 supraspanlists were used instead of a conventional span procedure. In all experiments, themodel’s predictions depend on the participants’ M capacity, and on a single freeparameter (explained in the Model section). The model is evaluated by itsgoodness of fit to the empirical data, and by the consistency of estimates acrossexperiments.

A further aim of these experiments was to compare articulation rate and Mcapacity as predictors of individual differences in verbal STM. The correlationbetween articulation rate and STM performance is often regarded as evidence forthe articulatory loop model (e.g., Baddeley, 1986; Hulme & Tordoff, 1989; butsee Cowan et al., 1994). Although articulation rate has already been comparedwith time for item identification (Hitch, Halliday, & Littler, 1989, 1993) and withgeneral processing speed (Kail & Park, 1994), it has not been compared with Mcapacity.

MODEL

While the time-limited articulatory loop model accounts easily for the word-length effect, it can hardly accommodate those findings, reviewed in the intro-duction, which suggest that verbal short-term memory is not time-limited. Bycontrast, Burtis (1982) accounts well for relationships between M capacity,chunking, and STM but did not explain other phenomena. What is thereforeneeded is a new developmental model that integrates both M capacity andexperimental conditions as sources of variance. This section presents a generaloverview of such a model, and the Appendix supplies more formal detail. For thesake of readability, Table 1 presents a list of symbols used in this paper, most ofwhich are commonly used in the operator-logic notation of the theory of con-structive operators.

The experiments reported below used unrelated, well-learned words for con-crete referents, so that children may be presumed to have figurative schemes that

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represent them. When the items are presented, the child’s encoding operationsenable activation of these figurative schemes. Some schemes are kept fullyactivated by the M operator during the retention interval, but once availableresources are exceeded, activation decreases for the remaining items. Probabilityof recalling the latter items depends on the relative amount of activation thatschemes still have.

At recall, there is no longer direct activation from input, because the stimuliare absent. In a short-term memory task in which items are unrelated, neither Fnor L activation occurs. (Such activation would occur if the items could bechunked together.) I therefore assume that the schemes representing stimuluswords can either be kept fully activated by the M operator or be partly activebecause their activation has not yet dropped to zero.

Some operative schemes are activated for encoding, rehearsal, and retrieval inSTM tasks. Operative schemes do not represent items to be reported, but insteadrepresent processing operations. They, too, consume part of the M capacity inorder to be activated (except when they have other sources of activation).

In serial recall, specific operative schemes could keep track of presentationorder. Subvocal rehearsal is a convenient option, though not the only possible

TABLE 1List of Symbols Used in the Theory of Constructive Operators and in this Model

Symbol Meaning

M (operator) A central attentional resource that can activate a limited number of schemes.F (operator) Processes that enhance activation of schemes according to Gestalt field

principles or stimulus–response compatibility.L (operator) Processes that enhance activation of schemes as a consequence of

overlearning (i.e., a spread of activation among constituents of a well-learned structure).

I (operator) A central attentional control process (“interrupt”) that reduces activation ofcurrently irrelevant schemes.

« Executive schemes (e.g., current goals or monitoring processes). Specifically,«Lisn, «Read, and«Rec stand for the goals of listening to, reading, andrecalling the word lists.

f Figurative schemes (representations of objects or states of affairs).c Operative schemes (mental blueprints for transformations or actions).

Specifically,cCode, cReh, andcRetr stand for the operations of encoding,rehearsing, and retrieving words.

e A small, constant amount of the M operator capacity, necessary to activatethe executive schemes.

k The number of figurative and operative schemes that can be simultaneouslyactivated by a subject’s M operator.

i A free parameter, specific to this model, that represents activation decrease.W1, W2, etc. The first, second, etc., word in a list.fW1, fW2, etc. The representations of the first, second, etc., word in a list.UW1, UW2, etc. Utterances of the first, second, etc., word.

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one. I suggest that rehearsal serves not only to refresh stimuli traces, but alsomainly to encode serial order with less effort than would be required by otherstrategies. For instance, activating a set of ordering tags could be more effortful.(For a discussion of order representation, see also Brown, 1997.)

Modeling Performance with Rehearsal

Suppose that a person subvocally rehearses articulatory codes. As the firstword is presented, an encoding operative scheme and a figurative scheme for thatword are activated. As the second word is presented, the encoding operative isstill necessary, as well as a second figurative scheme. At the same time, arehearsal operative scheme can be activated to rehearse the scheme that repre-sents the first word, and so on. If that person’s M operator has the capacity toactivatek operative or figurative schemes, as soon as it becomes fully engagedwith the two encodeand rehearseoperatives plusk 2 2 figuratives (i.e., themental representations ofk 2 2 words), other previously activated schemes startto lose activation.

In the case of auditory presentation, however, I assume that articulatory and/oracoustic encoding of the stimuli is highly compatible and automatized. Thisassumption can be justified, for example, with reference to Penney’s claim that“a subject cannot voluntarily prevent entry of an auditory item into short-termmemory,” while “in the visual modality, . . . generation of the phonological codeis not automatic” (Penney, 1989, pp. 399–400; see also Baddeley et al., 1984).Assuming that item encoding is automatic with auditory presentation, only therehearse(not theencode) operative requires M capacity. Thus,k 2 1 (rather thank 2 2) figurative schemes can be kept active by the M operator during stimulipresentation. Another difference between visual and auditory presentation con-cerns the end-of-list signal. In visual presentation the signal is obviously arbitraryand conventional. Thus, participants must encode it (as a figurative scheme) inorder to decide to report the items. In contrast, in auditory presentation, theend-of-list signal may be either a conventional signal (e.g., a tone) or a habitualcomponent of human verbal communication (e.g., the experimenter turning tolook at the participant or slightly stressing the last item in the list). In auditorypresentation, if the end-of-list signal involves such nonarbitrary components,then one can assume that it is automatically encoded. In other words, it would notrequire M capacity.

As soon as some schemes start losing activation, probability of recalling themdecreases. I assume that the higher the number of decaying schemes at any givenpoint, the more they will interfere with each other. Thus, probability of recallinga partly activated scheme depends both on how long it has been decaying and onhow many partially activated schemes have interfered with it. In the presentmodel, I assume that activation decays at the same rate during input and recall,although this may well be an oversimplification.

Decreased activation of figurative schemes is expressed as parameteri (the

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model’s only free parameter), defined as the decrease in probability of recall ofan item per processing step and per decaying scheme. I assume that parameteriis specific to materials, such as articulatory codes for long or short words,confusable or nonconfusable consonants, digits, semantic codes, and so on. (It isconceivable thati may also vary according to some characteristic of the subjectpopulation, e.g., resistance to interference [Dempster, 1992], although this pos-sibility is not explored here.) The assumption thati is materials-specific impliesthat the word-length effect can be accounted for by a greater drop in activationof articulatory codes for long words than for short words during each processingstep.

The notion that a parameter can express decreasing recall probability iscommon to many models. What is specific to this model, however, are thefollowing assumptions: (a) activation will decrease only for those representationsthat are not focused on by a central attentional mechanism, that is, the Moperator; (b) activation decrease is proportional not only to time but also to thenumber of currently decaying schemes (e.g., if there are three decaying schemesat a given step, each of them will lose an amount of activation of 3i during thatstep); (c) being specific to materials, parameteri does not vary with otherexperimental conditions (such as presentation modality) or the individuals’ Mcapacity (which is independently represented in the model).

It might be asked why the model includes only one material-specific freeparameter but is silent about whether differences among materials are due torehearsal time, output interference, planning complexity, or a combination ofthese and other factors. The reason is twofold. First, it is desirable to keep themodel as simple as possible (a model with too many free parameters wouldprobably fit any set of data). Second, this model is based on two main ideas—(a)the role of a central attentional mechanism whose limited capacity is dividedbetween operative and figurative schemes and (b) decreasing recall probability ofthose schemes that are not kept activated by the M operator. If the model fits thedata well, then future research can make detailed exploration of the processingfactors affecting the value ofi. The advantage of this model is that it highlightsand quantifies the role of a specific, central attentional resource, the M operator,which most current models seem to neglect. Although testing the extent to whichfree parameteri is related to rehearsal time, output interference, and other factorswould be feasible, it goes beyond the scope of this series of experiments.

Modeling Performance without Rehearsal

Let us now consider an individual who does not use a subvocal rehearsalstrategy. In this case, I assume that if individuals can recall the first and the lastitems at all, they will recall them in the appropriate positions. Such positions areassumed to be salient, and as such, are activated by the F operator. Burgess andHitch (1992) make a similar assumption within a theoretically different account,while Cowan et al. (1992, Fig. 4) and Hulme et al. (1997, Fig. 5) also reportedevidence that the first and last position have a special advantage.

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Serial positions other than the first and last could be encoded by separateoperative schemes for each position in the sequence, or possibly guessed. In thiscase, in a three-item list, the first and third positions are salient and the secondis completely determined; in a four-item list, the first and fourth are salient, andthere is a .50 probability of guessing which item was the second and which thethird. In a five-item list, this probability becomes 1/6, and so on, with combina-torial increase.

If people tend to choose a strategy that maximizes performance while mini-mizing effort, then most adults will use subvocal rehearsal. There may beexceptions, but at present it is hard to make clear predictions about how far adultperformance is affected by alternative strategies. We can easily predict, however,that children do not use articulatory rehearsal if this consumes too much of theirlimited attentional resources (M capacity). It has been established that youngchildren seldom rehearse and that, although it is possible to train them to do so,such training is not completely successful (e.g., Cowan, Saults, Winterowd, &Sherk, 1991; Henry, 1991a; Hitch, Halliday, Dodd, & Littler, 1989). Guttentag(1984) demonstrated that rehearsal requires mental effort. Children may thereforenot follow this strategy because it demands excessive expenditure of attentionalcapacity.

The present model implies that individuals with an M capacity of less thane1 3 do not rehearse in the case of visual presentation—not because the rehearsaloperation is difficult in itself but because it requires too much of their attentionalcapacity: They do not have enough capacity to monitor rehearsal and at the sametime encode the current item. Theencodeand rehearseoperative schemes andthe representation of the current word are three distinct psychological units, eachof which demands its share of M capacity. In the case of auditory presentation,since the encoding operative scheme would not require a unit of M capacity theminimum M capacity needed for rehearsal would bee 1 2. The conditions forrehearsal in the present model are also consistent with the minimal ages forrehearsal reported in the relevant literature (e.g., Hitch et al., 1993; Hitch,Halliday, Schaafstal, & Heffernan, 1991), sincee 1 2 is the modal M capacityat 5–6 years, ande 1 3 is the modal capacity at 7–8 years of age (e.g.,Pascual-Leone, 1970).

Throughout this article, the model’s goodness of fit is tested on the basis of thestrict assumption that when item ordering creates some difficulty (i.e., with listsof four or more words), individuals who have enough M capacity to rehearse doso consistently, while those who do not have enough M capacity never userehearsal. No probabilistic correction is allowed for this assumption.

A PILOT EXPERIMENT

In a pilot experiment, from a total pool of 124 participants (57 girls and 67boys, mean age 8;0, range 5;10 to 9;9, living in Northern Italy, in a small townor its surrounding Alpine villages) 96 children were selected and tested for

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memory span, articulation rate, M capacity, and verbal ability. In order tomaximize accuracy of M-capacity measurement, we selected 24 children in eachgrade (1–4), those who had the smallest variation coefficient (i.e., standarddeviation/mean ratio) in the M-capacity measures. M capacity was operationallydefined as the average of the scores in three tests—Figural Intersections Test, Mr.Cucumber Test, and Counting Span Test (see method of Experiment 1 fordetails). For the memory span and the rapid articulation tasks, three sets of 10Italian nouns (of two, three, and four syllables, respectively) were used in thisand the subsequent experiments. The Vocabulary subtest from the Italian versionof the Wechsler Intelligence Scale for Children (Wechsler, 1974) and an adap-tation of the Verbal Fluency subtest from the Primary Mental Abilities (Thur-stone, 1941) were also used. The M-capacity tests were administered by oneexperimenter, and all other tasks by another.

The memory-span scores were analyzed with a 4 (age groups)3 3 (wordlengths) mixed-design ANOVA, which yielded significant effects of age,F(3,92) 5 25.84,p , .001, and word length,F(2, 184)5 78.50,p , .001, and anonsignificant interaction. Although there was a word-length effect, the resultswere only partly consistent with the articulatory loop model, since performancewas only worse in the case of four-syllable words. The difference between two-and three-syllable words was not significant. The ratio between span and artic-ulation rate (AR) increased from 1.67 s for the shortest words to 2.56 s for thelongest. The best fitting regression line, across 12 data points (four age groups3three word lengths) was Span5 2.501 0.685AR. This equation accounted for51.2% variance across word lengths and age groups; both its intercept (p , .001)and its slope (p , .02) were significantly different from zero. The finding of arelationship between memory span and articulation rate was thus replicated. Thefact that the intercept was much higher than zero contradicts a prediction ofBaddeley’s original time-limited articulatory loop model but confirms morerecent findings (e.g., Hulme et al., 1991).

The respective contribution of articulation rate and M capacity to word spandevelopment was assessed by correlational analyses. Children’s memory span forwords was positively correlated with both M capacity,r(94)5 .65,p , .001, andarticulation rate,r(94) 5 .55,p , .001. I then tested whether each of these twovariables still correlated with word span, with the other one and age partialledout. This analysis is necessary because memory span, articulation rate, and Mcapacity all increase with age. Since M capacity is conceived as a developmentalvariable, it may be noted that partialling out of age eliminates true variance.However, there are also individual differences in M capacity among subjects ofthe same age. Partialling out age eliminates one source of variance while leavingthe other intact, so partial correlations can be regarded as a particularly strict testof the relationship between M capacity and word memory span. With agepartialled out, memory span was correlated with both M capacity,r(93) 5 .50,p , .001, and articulation rate,r(93) 5 .32, p , .01. The correlation between

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span and M capacity remained significant even with age and articulation ratepartialled out,r(92) 5 .41,p , .001. However, the correlation between span andarticulation rate, with age and M capacity partialled out, was nonsignificant,r(92) 5 .09. In order to control for verbal ability, vocabulary and verbal fluencyscores were also considered. With age, verbal fluency, and vocabulary partialledout, the correlation between memory span and M capacity was still significant,r(91) 5 .41, p , .001, whereas between span and articulation rate it was not,r(91) 5 .15.

The possibility can also be ruled out that the correlation between M capacityand word span is an artifact due to a high correlation between word span and oneparticular test among those included in the M-capacity battery. With both age andarticulation rate partialled out, word span correlated with the Figural Intersec-tions Test,r(92) 5 .23,p , .02, with the Counting Span Test,r(92) 5 .47,p ,.001, and with the Mr. Cucumber Test,r(92) 5 .22, p , .02.

These results suggest that the positive correlation between M capacity andmemory span is a robust phenomenon, at least in childhood, while the correlationbetween span and articulation rate might be due to other intervening variables. Inany case, it seems that articulation rate makes only a small contribution toindividual differences in memory span during childhood.

The model presented above was tested for goodness of fit to these data. Sinceit was assumed thati has different values for different materials, three separateestimations of this parameter were made, one for each word length. (SeeExperiment 1 below for the procedure for estimating parameters and testing forgoodness of fit.) The resulting values werei 5 .0124 for two-syllable,i 5 .0169for three-syllable, andi 5 .0298 for four-syllable words. The model’s goodnessof fit was tested in relation to three groups of subjects with M capacity ofe 1 2,e 1 3, ande 1 4, respectively. There were nine means (i.e., three M-capacitygroups by three word lengths), seven of which were correctly predicted by themodel. Only two of nine differences were significant (p , .05)—the modelpredicted a higher mean than observed with four-syllable words for subjects withM 5 e 1 3, and a lower mean than observed with three-syllable words forsubjects with M5 e 1 4. The variance of each distribution was also considered.The fit was worse for variances than for means, since observed variances tendedto be smaller than predicted by the model, five out of nine comparisons beingsignificant. Apart from this tendency to overestimate variances, this experimentprovided preliminary support for two conclusions: (a) M capacity seems topredict individual differences in word span better than does articulation rate, and(b) the proposed model shows a reasonable approximation to the data, at least asfar as the group means are concerned. In short, it accurately predicts the amountof memory-span increase as a function of M capacity.

However, this pilot experiment was limited in that it included only onepresentation modality, and only a span measure of short-term memory (but nomeasure with supraspan lists). In addition, subject selection ensured reliable

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measurement of M capacity, but could have affected the results in other, un-known ways. The following experiments were designed to test the model withina broader range of experimental conditions and with unselected samples.

EXPERIMENT 1

This experiment replicated the pilot experiment with an unselected sample,and also included visual presentation. It was designed to replicate the resultsfound in the pilot study, and to test whether the model can account for differencesbetween visual and auditory presentation. It was suggested earlier that theencoding operative scheme and the end-of-list signal do not require attentionalresources (M capacity) in auditory presentation. Fourth and fifth graders wererecruited as subjects, because they can easily read the visually presented stimuluswords.

Method

Participants. The participants were 58 fourth graders and 55 fifth graders(mean age 10;3, age range 8;11 to 11;5) from two middle-size towns in NorthernItaly. They comprised 53 girls and 60 boys. All children had normal or corrected-to-normal vision and no other relevant impairments. The sample included allfourth and fifth graders enrolled in the schools, with the exception of 7 childrenwho had reading difficulties, were mentally retarded, or were nonnative Italianspeakers.

Materials. Three sets of 10 concrete high-frequency Italian nouns (of two,three, and four syllables, respectively) were used. The word sets, drawn from 10semantic categories, do not differ in mean frequency according to De Mauro,Mancini, Vedovelli, and Voghera (1993),F(2, 27) 5 1.01, p 5 .38. Thetwo-syllable words were Zio (uncle), Merlo (blackbird), Pesca (peach), Sole(sun), Treno (train), Vaso (vase), Scarpe (shoes), Bagno (bathroom), Ape (bee),Rosa (rose). The three-syllable words were Sorella (sister), Rondine (swallow),Banana (banana), Nuvole (clouds), Corriera (long-distance bus), Pettine (comb),Maglione (sweater), Cucina (kitchen), Lumaca (snail), Geranio (geranium). Thefour-syllable words were Genitori (parents), Pappagallo (parrot), Mandarino(tangerine), Temporale (storm), Motoscafo (motorboat), Sigaretta (cigarette),Pantaloni (trousers), Corridoio (corridor), Tartatuga (turtle), Garofano (carna-tion). These were the same word sets previously used in the pilot experiment.Another set of 10 concrete nouns of different lengths was used for practice.

For the span task, 18 two-word sequences, 18 three-word sequences, etc., upto a maximum of seven words, were created by random selection—that is, sixlists of each length from each set. Increasingly long lists were used to assess wordspan; half of them were acoustically and half visually presented. The materialsfor each span trial consisted of one two-word list, one three-word list, etc., drawnfrom the same set. For the articulation task, each set was divided into five wordpairs.

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Three M-capacity tests were used: the Figural Intersections Test, Mr. Cucum-ber Test, and Counting Span Test. M capacity was operationally defined as theaverage of the three test scores (see Morra, 1994; Morra & Scopesi, 1997, forjustification of this procedure). Each of the M-capacity tests is based on theprinciple that all of its items have the same content but differ in processing load(Case, 1985; Morra, 1994; Pascual-Leone & Baillargeon, 1994). Since M capac-ity is considered a general resource, it is convenient to average across tests withdifferent content and response demands, although this means that the correlationsbetween different tests cannot be very high (Case, 1985; Morra, 1994).

The Figural Intersections Test comprises 36 items, each of which requires theintersection of a set of shapes to be found. The level of an item is determined bythe number of presented shapes, which ranges from two to nine. An individual’sscore is the number of levels at which at least 75% of responses are correct, plusone (for “level one,” not included in the test because no intersection is possiblewith one shape). For details, see Morra (1994) and Pascual-Leone and Baillar-geon (1994).

The Mr. Cucumber Test presents outline drawings of an extraterrestrial char-acter, with a number (from 1 to 8) of colored stickers attached to it. There arethree items per level, in ascending order. The child is shown a colorless shape andasked to indicate the positions of the stickers in the previously presented figure.One point is given for each consecutive level on which a person gets at least twoitems correct, plus one third of a point for each correct item beyond that level.Scores are rounded up/down to the nearest unit. For details, see Case (1985) andMorra (1994).

The Counting Span Test requires the subject to rapidly count aloud sets ofcolored dots and then recall the number of each set. The level of an item isdetermined by the number of sets it comprises, ranging from one to eight. Thescore is the highest level on which a child gets at least two items correct out ofthree. For details, see Case (1985) and Morra (1994).

Note that, if the articulatory loop model is correct, then these tests should havelow correlations with word span. Out of these tests, only the Counting Spanrequires verbal responses, and none of them is scored for serial recall ofinformation. Both the Figural Intersections Test and the Mr. Cucumber Test havevisuospatial content; the Figural Intersections Test does not demand any recall,and the Mr. Cucumber Test involves recall of simultaneously presented posi-tions. Only the Counting Span Test demands recall of verbal information;however, order errors are disregarded, and, more important, it involves countingaloud during item presentation, which prevents participants from rehearsing.Hence, according to Baddeley’s model of working memory, a correlation be-tween M capacity and word span is hardly to be expected.

Procedure.There were three sessions. In the first, the Figural IntersectionsTest was group-administered. In the second, Counting Span, Mr. Cucumber Test,

202 SERGIO MORRA

and Articulation Rate were individually administered in that order. The first twotests were discontinued when a child failed all items at one level.

To measure articulation rate, participants were required to repeat each wordpair five times as fast as possible. Two practice trials were carried out first, usingpairs of words from the practice set. Next, the five word pairs of each length werepresented in one of the six possible word-length orders. A voice key triggered thecomputer clock when the child started articulating, and the experimenter stoppedit by pressing a key at the end of the last repetition. This has been shown to bea very reliable procedure (e.g., Nicolson & Fawcett, 1991).

The third session included word memory span in six experimental conditions(visual vs auditory presentation of three word lengths), preceded by two practicetrials (one visual and one auditory) with another word set. Half of the participantsstarted with auditory and half with visual presentation. The six possible orderingsof word lengths were also balanced over participants.

For each modality and word length, three memory-span trials were performed.Each trial started with a list of two words, then a list of three, and so on (up toseven words), until the child failed on a list. Each trial was scored according tothe longest list correctly recalled, and a child’s average score across three trialswas his/her span score for words of a given length in a given modality.

The words appeared one at a time in the center of a screen in 8-mm capitalletters for 1500 ms each, followed by a blank screen interval of 500 ms—that is,at a presentation rate of one word every 2 s, as in the main experiment ofBaddeley et al. (1975). During visual presentation, subjects silently read thewords on the screen. For auditory presentation, the screen was turned aroundtoward the experimenter, who read out the words as they appeared.

Results and Discussion

Preliminary analyses.A 2 (age group)3 3 (word length)3 2 (presentationmodality) mixed-design ANOVA of word span scores (see Table 2) yieldedsignificant main effects of word length,F(2, 222) 5 130.73,p , .001, andmodality, F(1, 111) 5 126.48,p , .001. The main effect of age was only

TABLE 2Means (and Standard Deviations) of Word Span by Grade, Presentation Modality,

and Word Length in Experiment 1

Grade Modality

Number of syllables

2 3 4

4 Visual 4.14 (0.65) 3.80 (0.75) 3.44 (0.55)Auditory 4.53 (0.68) 4.26 (0.53) 4.06 (0.53)

5 Visual 4.41 (0.76) 3.98 (0.67) 3.55 (0.64)Auditory 4.76 (0.68) 4.50 (0.59) 4.07 (0.62)

203VERBAL STM MODEL

marginally significant,F(1, 111) 5 3.42, p , .07. The Modality3 Lengthinteraction was significant,F(2, 222)5 3.30,p , .04, and the word-length effectwas greater in visual than in auditory presentation (consistent with Watkins &Watkins, 1973). However, for each word length, performance was higher withauditory than with visual presentation (allps , .001), and conversely, withineach modality, span decreased as word length increased. Thus, the word-lengtheffect and the modality effect were replicated.

Descriptive statistics for the articulation rate are shown in Table 3. In thevisual condition, the ratio between mean span and articulation rate increased withword length, from 1.47 s for the shortest words to 2.06 s for the longest. In theauditory condition, it increased from 1.60 s for the shortest words to 2.39 s forthe longest.

In visual presentation, the regression line across six data points (two agegroups3 three word lengths) was Span5 2.47 1 0.632AR, while in auditorypresentation, it was Span5 3.29 1 0.478AR. These equations accounted for92.3% and 85.7% variance, respectively. Their intercepts (p , .001 in bothequations) and slopes (p , .002 in visual andp , .01 in auditory conditions)were significantly different from zero. The linear relationship of memory span toarticulation rate replicates the findings of Baddeley et al. (1975). However, as inthe pilot experiment, the intercepts were well above zero, and the span toarticulation rate ratio was not constant. These aspects are inconsistent with thefindings and model of Baddeley et al. (1975), although they agree with otherpublished data (e.g., Hulme et al., 1991).

With age partialled out, the Figural Intersections Test correlatedr(110)5 .30,p , .001, with the Counting Span Test andr(110)5 .34,p , .001, with the Mr.Cucumber Test. The partial correlation between Counting Span and Mr. Cucum-ber wasr(110) 5 .27, p , .002. These partial correlations among M-capacitymeasures replicate those reported by Morra (1994), which were of the order ofmagnitude of .25. Note that these three tests have very different content andresponse requirements, and that partialling out of age eliminates developmental(i.e., true) variance. Hence, the average score of these three tests was used as ameasure of M capacity.

TABLE 3Means (and Standard Deviations) of Articulation Rate in Words/s by Grade

and Word Length in Experiment 1

Grade

Number of syllables

Mean2 3 4

4 2.84 (0.38) 2.03 (0.24) 1.64 (0.19) 2.17 (0.25)5 2.98 (0.31) 2.20 (0.23) 1.76 (0.18) 2.31 (0.21)All 2.91 (0.36) 2.11 (0.24) 1.70 (0.19) 2.24 (0.24)

204 SERGIO MORRA

For the purpose of correlational analysis, each child’s articulation rate scoreswith two-, three-, and four-syllable words were averaged; so were their spanscores for visually presented words of three lengths, as well as the three spanscores for acoustically presented words.

Memory span for words was positively correlated with M capacity,r(111)5.30,p , .001, in the visual condition andr(111)5 .32,p , .001, in the auditorycondition. Memory span also correlated with articulation rate,r(111)5 .19,p ,.03, in the visual condition andr(111)5 .18,p , .04, in the auditory condition.

The correlation between span and M capacity resisted the partialling out ofboth age and articulation rate,r(109)5 .28,p , .002, in the visual condition andr(109) 5 .31, p , .001, in the auditory condition. A smaller but significantcontribution of articulation rate to memory span was also found, since thecorrelation between span and articulation rate with age and M capacity partialledout wasr(109) 5 .17, p , .04, in both visual and auditory conditions.

As in the previous experiment, correlation between M capacity and word spanwas not due to a high correlation between word span and one particular M-capacity test. With both age and articulation rate partialled out, the Mr. Cucum-ber Test correlatedr(109)5 .27,p , .01, with visual andr(109)5 .29,p , .002,with auditory word span. The Counting Span Test correlatedr(109)5 .29,p ,.002, with visual andr(109)5 .27,p , .01, with auditory word span. Only theFigural Intersections Test showed lower partial correlations,r(109) 5 .10, ns,with visual andr(109) 5 .15, p , .06, with auditory word span.

It can be seen that the overall magnitude of correlations was somewhat lowerthan in the pilot experiment. Nevertheless, their basic pattern was replicated andgeneralized to visual presentation. The correlation between M capacity and wordspan is confirmed as a robust phenomenon, while articulation rate gives asignificant but smaller contribution to children’s individual differences in span.

Goodness of fit of the model.The main aim of this experiment was to test themodel’s goodness of fit in different presentation modalities. This model assumesthat only in visual presentation must the encoding operative scheme be activatedby the M operator throughout stimuli presentation, and that the end-of-list signalalso requires M capacity.

In order to use independent observations in testing for goodness of fit, only thesecond of three memory-span trials administered to each child for each wordlength and modality was considered.

For the purpose of grouping participants by M capacity, their M-capacityscores (i.e., thek values in the formulae 1 k) were rounded up/down to thenearest unit. These scores ranged frome 1 2 to e 1 6. The probabilitydistribution (according to the model) of memory-span scores was computed foreach value ofk from 2 to 6. Of course, these probabilities were expressed asfunctions of free parameteri (see Appendix, Table 12). At this stage, theprobability distributions were weighted, according to the proportions of subjectswith an M-capacity score frome1 2 toe1 6, and then totaled in order to obtain

205VERBAL STM MODEL

a probability distribution of memory-span scores in the whole sample. Conse-quently, an expected value of the memory-span score in the whole sample(expressed as a function ofi) was obtained.

Since it was assumed thati values differ for different materials, regardless ofM capacity or presentation modality, three separatei parameter estimates weremade, one for each word length. These estimates were made by equating theexpected memory-span score value derived from the model (weighting for Mcapacity and averaging visual and auditory conditions) to the observed meanscore (averaging visual and auditory presentations) in the second trial for eachword length in the whole sample. A single estimate ofi was made across visualand auditory presentation for each set of materials, since the model posits thatpresentation modality affects M-capacity demand but not the value ofi. Theestimates thus obtained werei 5 .0127 for two-syllable,i 5 .0170 for three-syllable, andi 5 .0247 for four-syllable words. It may be noted that the valuesobtained with both two- and three-syllable words are almost identical to thosefound in the pilot experiment, while only the estimate for four-syllable words isslightly lower (by about 17%). Such findings give further credibility to themodel.

Thesei estimates were entered in the probability distributions to thus obtainpredicted memory-score distributions for each word length, presentation modal-ity, and M-capacity score. There were 26 subjects with a measured M capacityof e 1 3, 56 with a capacity ofe 1 4, and 25 with a capacity ofe 1 5. The sixsubjects whose capacity fell out of this range (one with M5 e 1 2 and five withe 1 6) were excluded from the following analyses.

Table 4 shows expected and observed means, along with the relevantt tests.Only 6 of 18 differences were significant. Moreover, 7 of 18t values were lowerthan 1 in absolute value. This suggests that the model’s goodness of fit for themeans is acceptable. On closer inspection, it can be seen that almost all signif-icant differences from expected means concern higher-than-expected means inthe children with an M capacity ofe 1 3. This may be due to some inaccuracyin M measurement (the participants in this experiment were unselected for Mcapacity), or approximation in rounding up/down to the nearest unit. In supportof the latter interpretation, it can be noted that the actual mean of M-capacity testsin this group is 3.11 (i.e., somewhat higher than 3), while it is 3.99 and 4.98 inthe other two groups (i.e., very close to 4 and 5, respectively). However, for thetwo groups of children classified as having the appropriate M capacity for theirage (i.e.,e 1 4 or e 1 5), the fit of expected to observed means is very good.

To test a model’s goodness of fit, means as well as other parameters of themeasure should be considered. Table 5 shows expected and observed variances,along with the chi-square tests for the ratios between them. The fit of expectedto observed variances in this experiment was very good, in that only 1 of 18 ratioswas significant (i.e., precisely what is expected by chance). Ten observedvariances were smaller and eight were greater than expected. Out of four

206 SERGIO MORRA

variances whose observed/expected ratio was significant or marginally signifi-cant (i.e.,p , .10), two were smaller and two greater than expected.

It might be questioned whether the range of M-capacity values considered intesting for goodness of fit (i.e., frome 1 3 to e 1 5) was too limited. Onepossible way of circumventing this problem is to pool together the auditorycondition of this experiment with the pilot experiment data (despite minordifferences in procedure and sampling). This involves using four groups ofchildren with M capacity ofe 1 2 (n 5 41), e 1 3 (n 5 65), e 1 4 (n 5 69),ande1 5 (n 5 26), excluding only three children with M5 e1 1 from the pilotexperiment, and five with M5 e 1 6 from this experiment. These results areobviously limited to auditory presentation. The obtainedi values werei 5 .0136for two-syllable, i 5 .0169 for three-syllable, andi 5 .0261 for four-syllablewords. The results are shown in Tables 6 and 7. The model’s fit also seems verygood in this larger, pooled sample. Actually, only 1 of 12t values for observedand expected means and 4 of 12 observed/expected variance ratio chi-squareswere significant. It is also remarkable that 6 of 12t values were smaller than 1.This suggests that the model predicts well not only a correlation between Mcapacity and memory span, but also, even more remarkably, the actual size ofmemory-span increase as a function of M capacity.

TABLE 4Observed and Expected Word-Memory-Span Means by Presentation Modality, Word Length,

and M-Capacity Score in Experiment 1

No. of syllables M capacity Modality

Mean span

t df pExpected Observed

2 e 1 3 Visual 3.46 3.92 2.78 24 ,.02Auditory 4.14 4.27 0.58 24 ns

e 1 4 Visual 3.96 4.11 1.04 54 nsAuditory 4.66 4.50 21.32 54 ns


3 e 1 3 Visual 3.20 3.65 3.07 24 ,.01Auditory 3.89 4.27 3.21 24 ,.004


e 1 5 Visual 4.24 4.24 20.02 23 nsAuditory 5.05 4.68 21.81 23 ,.09

4 e 1 3 Visual 2.91 3.50 3.34 24 ,.01Auditory 3.60 4.11 3.03 24 ,.01



Note.The significance values of thet tests are two-tailed.

207VERBAL STM MODEL

EXPERIMENT 2

A second experiment tested the model with supraspan five-word lists, themethod used in most studies supporting Baddeley’s model. Because there isevidence that a conventional span procedure yields different results (e.g., Morra,1990; Morra, Mazzoni, & Sava, 1993; Nicolson & Fawcett, 1991), it seemednecessary to test the current model also in a supraspan condition.

First, the model predicts that performance is positively correlated with Mcapacity. Second, the model allows calculation of the expected probability ofrecalling a whole supraspan list of a given number of words. Analyses testedthese two predictions, as well as for replication of known findings.

Participants were the same children tested in Experiment 1. The primaryreason for testing the same children was not one of convenience, but rather wasdriven by design advantage. First, these children had already practiced short-termmemory tasks and refined the rehearsal strategy, so they were likely to employit with maximum efficiency. Second, and more important, thei parameter hadalready been estimated in Experiment 1 with the same word sets. It was assumedthat thei parameter depends on the materials but not on presentation modality orspan versus supraspan lists. This meant the model could be tested in a mostrigorous way, becauseno free parameters were estimated in this experiment.

TABLE 5Observed and Expected Variances in Word Memory Span by Word Length,

Presentation Modality, and M Capacity in Experiment 1

No. of syllables M capacity Modality

Span variance

x2 df pExpected Observed

2 e 1 3 Visual 0.99 0.69 18.01 24 nsAuditory 0.89 1.20 34.92 24 ns



3 e 1 3 Visual 0.82 0.53 16.82 24 nsAuditory 0.71 0.35 12.85 24 ,.07



4 e 1 3 Visual 0.66 0.79 30.87 24 nsAuditory 0.51 0.71 36.45 24 ,.10

e 1 4 Visual 0.53 0.71 75.44 54 ,.06Auditory 0.64 0.48 41.83 54 ns


Note.The significance values of the chi-squares are two-tailed.

208 SERGIO MORRA

Method

Participants and materials.The 113 children who took part in Experiment 1were tested no more than 1 week after the prior session.

The same three sets of two-, three-, and four-syllable nouns as in the previousexperiments were used. Ten lists of five words were randomly created from eachset, with the constraints that each word appeared once in each position and thelast word in a list could not be the first in the following one. In addition, fourpractice lists of five words were created from the practice word set.

Procedure.Performance with five-word lists was measured in a single session.Values of M capacity and articulation rate were taken from Experiment 1.Following practice, children were given 10 lists, each presented for immediaterecall, in each of three experimental conditions (i.e., two-, three-, and four-syllable words). The six orderings of word lengths were balanced over subjects,as in Experiment 1. The word lists were presented only visually, both forpractical reasons of time and because five words might not be supraspan inauditory presentation (see Tables 2 and 4). As in the visual condition ofExperiment 1, the words appeared one at a time in the center of a screen at a rateof one word every 2 s.

Children were required to recall words orally in the appropriate positions,saying “niente” for those positions in which they could not recall the word.“Niente” means “nothing” and its sound is not too dissimilar from “blank,” whichis often used for this purpose in experiments with English words.

Recall of a list was scored as correct or incorrect for each single position, andalso as correct or incorrect for the whole list. Thus, each subject received 3 scores

TABLE 6Observed and Expected Means in Word Memory Span by Word Length and M Capacity:

Pooled Data of Pilot Experiment and Auditory Condition of Experiment 1

No. of syllables M capacity

Mean span


2 e 1 2 3.60 3.54 20.61 39 nse 1 3 4.08 4.32 2.26 63 ,.03e 1 4 4.60 4.55 20.42 67 nse 1 5 5.26 5.12 20.75 24 ns

3 e 1 2 3.41 3.42 0.05 39 nse 1 3 3.89 4.06 1.76 63 ,.09e 1 4 4.40 4.51 1.52 67 nse 1 5 5.06 4.65 22.01 24 ,.06

4 e 1 2 3.07 3.10 0.33 39 nse 1 3 3.56 3.62 0.53 63 nse 1 4 4.03 4.16 1.50 67 nse 1 5 4.68 4.39 21.78 24 ,.09

Note.The significance values of thet tests are two-tailed.

209VERBAL STM MODEL

for the number (out of 10) of whole lists correctly recalled for each word length,and 15 scores for the number (out of 10) of words correctly recalled in eachposition for each word length.

Results and Discussion

Preliminary analyses.Table 8 shows descriptive statistics for recall scores. A2 (age group)3 3 (word length)3 5 (position) mixed-design ANOVA of recallscores yielded significant main effects of age,F(1, 111)5 6.53,p , .02, wordlength,F(2, 222)5 117.93,p , .001, and position,F(4, 444)5 296.15,p ,.001. Two interactions were significant. One was Age3 Word Length,F(2,222) 5 3.16,p , .05, due to a larger performance decrease with four-syllablewords for the younger group. The other was Word Length3 Position, F(8,888)5 7.19,p , .001, showing a stronger position effect with longer words. Themean numbers of recalled words per list were 3.65, 3.28, and 2.80 for two- tofour-syllable words. All differences between word lengths were significant atp, .001. This pattern replicates the word-length effect often reported withsupraspan lists. The means are lower than those found in the visual condition ofExperiment 1, which also replicates thecliff beyond spanphenomenon (Drach-man & Zaks, 1967).

The effect of position was significant for each word length,F(4, 444) 5121.11,p , .001,F(4, 444)5 157.57,p , .001, andF(4, 444)5 187.01,p ,.001, for two-, three-, and four-syllable words, respectively. Bonferronit testswith p , .01 showed a decrease in recall from the first to the second, from the

TABLE 7Observed and Expected Variances in Word Memory Span for Each Word Length and M-Capacity

Score: Pooled Data of Pilot Experiment and Auditory Condition of Experiment 1

No. of syllables M capacity

Span variance

x2 df pExpected Observed

2 e 1 2 0.92 0.40 17.64 39 ,.01e 1 3 0.85 0.74 56.95 63 nse 1 4 0.98 0.80 55.97 67 nse 1 5 1.02 0.87 22.23 24 ns

3 e 1 2 0.80 0.44 22.52 39 ,.04e 1 3 0.71 0.58 52.95 63 nse 1 4 0.85 0.37 29.75 67 ,.001e 1 5 0.92 1.00 28.16 24 ns

4 e 1 2 0.61 0.23 15.81 39 ,.001e 1 3 0.49 0.64 85.15 63 nse 1 4 0.62 0.48 54.08 67 nse 1 5 0.71 0.70 25.43 24 ns

Note.The significance values of the chi-squares are two-tailed.

210 SERGIO MORRA

second to the third, and from the third to the fourth position in the list, for eachword length. Only with three-syllable words was the decrease from the fourth tothe fifth position also significant. These results broadly replicate those obtainedwith adults (Cowan et al., 1992).

The ratio between mean span and articulation rate increased from 1.25 s for theshortest words to 1.64 s for the longest. The regression line across six data points(two age groups3 three word lengths) was Recall5 1.65 1 0.712AR. Itaccounted for 75.3% variance across word lengths and age groups, and bothintercept and slope were significantly different from zero (p , .02 in each case).Once more, the linear relationship of memory span to articulation rate wasreplicated, while the intercept was clearly above zero. (As already noted, only thefirst of these two results is consistent with Baddeley’s classic model.)

Each child’s scores with two-, three-, and four-syllable words were averagedto compute correlations between span and other variables. As mentioned above,two different scoring criteria were used (i.e., single words and whole listscorrectly recalled). The number of words correctly recalled in their positions waspositively correlated with M capacity,r(111) 5 .38, p , .001, and witharticulation rate,r(111)5 .26,p 5 .002. The number of whole lists recalled alsocorrelated with M capacity,r(111) 5 .32, p , .001, and with articulation rate,r(111) 5 .23, p , .01.

With both age and articulation rate partialled out, M capacity correlatedr(109) 5 .37, p , .001, with recalled words andr(109) 5 .34, p , .001, withrecalled lists. Conversely, with both age and M capacity partialled out, articula-tion rate correlatedr(109)5 .25,p , .01, with recalled words andr(109)5 .24,p , .01, with recalled lists. In short, correlations with M capacity were alsohigher in this experiment, but a significant contribution of articulation rate torecall of supraspan lists was found, too.

Once again, correlation between span and M capacity was not spurious due tosome specific test. With age and articulation rate partialled out, recalled lists

TABLE 8Means (and Standard Deviations) of Recall Scores by Grade, Word Length,

and Serial Position in Experiment 2

No. of syllables Grade

Serial position

1 2 3 4 5

2 4 9.00 (1.23) 8.02 (1.72) 6.55 (2.24) 5.62 (2.49) 5.83 (2.56)5 9.36 (1.01) 8.71 (1.47) 7.65 (2.21) 6.25 (2.40) 6.18 (2.62)

3 4 8.71 (1.61) 7.05 (2.07) 6.24 (2.11) 5.00 (2.51) 4.33 (2.64)5 9.24 (1.32) 7.89 (1.78) 6.87 (2.05) 5.36 (2.66) 4.96 (3.01)

4 4 7.78 (1.89) 6.31 (2.17) 4.88 (2.20) 3.22 (2.34) 3.14 (2.20)5 8.73 (1.50) 7.51 (2.13) 5.98 (2.42) 4.60 (2.58) 4.00 (2.89)

Note.Maximum possible score5 10.

211VERBAL STM MODEL

correlatedr(109) 5 .26, p , .01, with Mr. Cucumber,r(109) 5 .30, p , .001,with the Counting Span, andr(109)5 .21,p , .02, with the Figural IntersectionsTest, whereas recalled words correlatedr(109) 5 .29, p , .002, with Mr.Cucumber,r(109) 5 .34, p , .001, with the Counting Span, andr(109) 5 .22,p , .01, with the Figural Intersections Test.

Goodness of fit of the model.Expected recall probabilities for a visuallypresented five-word list are shown in the Appendix (see Table 12). The expectedrecall scores are 10 times such probabilities. As mentioned, this prediction wasput to a very strict test—parameteri was not freely estimated, but the values of.0127, .0170, and .0247, found in Experiment 1 for two-, three-, and four-syllablewords, respectively, directly substituted fori in the equations. The expected andobserved recall means are shown in Table 9, along with the goodness of fit of themodel.

The fit of the model is very good: Neither in the whole sample nor in any groupwith a specific M capacity is there a significant difference between observed andexpected means. Only 3 of 12t values were marginally significant (p , .10).Indeed, in 6 cases (i.e., half of the comparisons) there is a result oft , 1. It maybe that the model fits the data even better than in the previous experimentsbecause each child’s score was not obtained from a single trial but from 10, thusreducing random variation. In addition, participants’ previous experience withspan tasks may have improved experimental control over strategies. In any case,it can be concluded that predictive power of this model generalizes to supraspanlists presented visually—a conclusion that was reached without estimating any

TABLE 9Expected and Observed Means (and Standard Deviations) in Recall of Whole Five-Word Lists

for Each Word Length and M-Capacity Score in Experiment 2

No. of syllables Group

Mean recall


2 All 4.497 4.203 (2.771) 21.13 112 nse 1 3 3.005 3.346 (2.591) 0.67 25 nse 1 4 4.292 3.714 (2.528) 21.71 55 ,.10e 1 5 5.998 6.280 (2.542) 0.55 24 ns

3 All 3.363 2.929 (2.744) 21.68 112 ,.10e 1 3 1.851 2.077 (2.331) 0.49 25 nse 1 4 3.077 2.500 (2.435) 21.77 55 ,.09e 1 5 4.936 4.840 (2.779) 20.17 24 ns

4 All 1.943 1.770 (2.248) 20.82 112 nse 1 3 0.674 1.154 (1.736) 1.41 25 nse 1 4 1.565 1.304 (1.877) 21.04 55 nse 1 5 3.361 3.520 (2.663) 0.30 24 ns

Note.Maximum possible score5 10. The significance values of thet tests are two-tailed.

212 SERGIO MORRA

free parameter (because M capacity was independently measured andi hadpreviously been estimated in the same sample from different span tasks).

GENERAL DISCUSSION

The experiments reported in this article were designed to compare and inte-grate different lines of research and to test a new model of verbal STM.Consistent with Baddeley’s articulatory loop model were the findings that therewas a word-length effect and that there was a linear relation between groupmeans of articulation rate and short-term memory. However, inconsistent withBaddeley’s model were the findings that the intercepts of such linear functionswere well above zero and that the ratio of span to articulation rate was notconstant. Although positive correlations between individuals’ STM span andarticulation rate are consistent with the loop model, these correlations were notlarge and were not always significant after age, M capacity, or verbal ability wasstatistically removed. The estimates of the articulatory loop capacity were in-consistent. The linear function slope ranged from .48 s in the auditory conditionof Experiment 1 to .71 s in Experiment 2, while the ratio of recall to articulationrate varied from 1.25 s (Experiment 2, two-syllable words) to 2.56 s (pilotexperiment, four-syllable words).

On the one hand, these results suggest that rehearsal skill may make anindependent contribution to span. In both Experiment 1 and Experiment 2, thepartial correlations between articulation rate and short-term memory were lowbut significant.

On the other hand, the pattern of group means was inconsistent with thearticulatory loop model, at least in its standard form. Hulme et al. (1991)concluded that their results (similar to these) were incompatible with the wide-spread unitary view of short-term memory span, in which all storage is said tooccur within an articulatory loop. The inconsistent estimates of the loop capacity,reported above, seem to push this conclusion still further, raising doubts aboutthe existence of a time-limited component dedicated to articulatory storage. Theconcept of a time-limited specialized store may have been an excessive gener-alization from results obtained under specific conditions. Apart from one studyon digit span in English and Chinese (Stigler, Lee, & Stevenson, 1986), allexperiments that found a near-zero intercept shared two features: They involvedthe English language and the use of supraspan lists. Thus, the findings, which areoften interpreted as evidence for a time-limited articulatory loop, might actuallybe produced by both language and the span-assessing procedures (see alsoCheung & Kemper, 1993; Morra et al., 1993).

Although the present results corroborate the view that the articulatory loopmodel needs to be revised, they are not totally incompatible with some modelsderived from it (see Gathercole, 1997). Other authors report above-zero inter-cepts and suggest that they could reflect the contribution to memory span ofstorage in the central executive (Hitch, Halliday, & Littler, 1989) or in the

213VERBAL STM MODEL

phonological store (Nicolson & Fawcett, 1991), or of retrieval from long-termmemory (Hulme et al., 1991). Each of these accounts is consistent in itself andwith the data from which it originated. However, there are notable differencesamong them, and as Kuhn (1962/1969) noted, when too many versions of aparadigm are proposed, it often signals that the paradigm itself is in crisis.Moreover, some accounts may be criticized for assuming that verbal materialsare held in two separate containers, one of which is time-limited and articulatory,and the other of which holds a very small number of words (or similar chunks).Some models (e.g., Burgess & Hitch, 1992; Cowan et al., 1994; Hulme et al.,1991, 1997), however, do not make this unlikely assumption. Although they stillassume a loop that is time-limited, this does not seem to be a central feature inthem. The results presented here might therefore be compatible with thesemodels, if they were in turn modified by stating that the articulatory rehearsalprocess need not be time-limited.

Burtis’s (1982) model can account well for the correlation between STM spanand M capacity. This correlation ranged from .30 in the visual condition ofExperiment 1 to .65 in the pilot experiment. It withstood partialling out of anumber of variables, and it was significant not only with a compound M-capacityscore, but also when separate scores in different tests were considered. Never-theless, Burtis (1982) does not account for word-length and modality effects,which are often reported in the experiments and also replicated here.

The new model proposed here—a revision of Burtis’s—may offer a solutionto the shortcomings of previous models. There are four major differencesbetween the model proposed by Burtis (1982) and the present one. First, Burtis’smain experiment used very long supraspan lists and did not require strictlyordered recall. Hence, he did not need to posit a specific operative scheme forsubvocal rehearsal, and he did not need to be concerned with whether subjectsused articulatory coding. Second, in this paper I posited two different strategies,one based on subvocal rehearsal and the other one based on end-anchoring andpartial guessing of order, probably used by those subjects whose M capacity isinsufficient for using a resource-consuming rehearsal. Third, because Burtis usedonly consonants he did not posit that thei parameter would change as a functionof materials (e.g., as a function of word length). Fourth, Burtis assumed that theprobability of recalling a partially activated scheme is a function of how long ithas been decaying, whereas I assume that it is also a function of how manypartially activated schemes interfered with it.

The present model offers some hope of overcoming the limitations of othermodels because it represents (a) M capacity in the same way as Burtis’s; (b)modality effects in terms of automaticity, which yields differential M-capacitydemands; (c) rehearsal as an operative scheme with the main function of keepingorder information; and (d) word-length effects as the outcome of differentialactivation decrease per processing step. With few exceptions, this model yieldedaccurate predictions of memory-span increase as a function of M capacity

214 SERGIO MORRA

throughout a series of experiments with different age groups, presentation mo-dalities, and tasks. In addition to showing goodness of fit to the data, alsofavoring the new model was consistency across experiments ofi parameterestimates. Estimatedi value for two-syllable words was .0124 in the pilotexperiment and .0127 in Experiment 1; for three-syllable words, it was .0169 and.0170; and for four-syllable words, it was .0298 and .0247. In Experiment 2 itwas not even necessary to estimate its values, because those obtained in Exper-iment 1 from the same materials and children (but from different tasks andpresentation modalities) were used. Such consistent estimates across experimentsare perhaps more indicative of the model’s power than are any tests of goodnessof fit.

Despite success, of course, this research has its limitations. These experimentsstudied the effects of M capacity, presentation modality, word length, and spanvs supraspan tasks. Other variables, such as phonological confusion or articula-tory suppression, were not manipulated. It may be asked how far the results canbe generalized beyond the specific conditions studied here. Further researchshould tackle this issue. This would involve modifying the model so as toincorporate the constraints of other experimental conditions. To give but oneexample, articulatory suppression should force a person to choose the nonre-hearsal strategy, and also require one unit of M capacity to monitor the flow ofirrelevant utterances. In a similar way, one can derive new predictions regardingother variables, and test them.

I suggested in this article that automatic encoding in auditory presentationallows a subject to economize M capacity. This is a novel explanation for themodality effect. Although there is agreement on automatic encoding of heardspeech (e.g., Baddeley, 1986; Penney, 1989), the suggested implication abouteconomizing M capacity is new. This idea could also help to explain modalitydifferences in the suffix effect. This effect is weak in visual presentation (e.g.,Penney, 1989) possibly because encoding a visually presented suffix does notdemand more M capacity than encoding a visually presented end-of-listsignal. Instead, encoding an auditory suffix demands M capacity, whichwould not be required to encode the end-of-list signal. Furthermore, thelong-established but often-neglected finding that the auditory suffix effectextends over a number of words, regardless of word length or stimuli duration(Watkins & Watkins, 1973), is neatly suited to the role of a series of encodingoperations (one for each word) posited here. Thus, also further research onthe suffix effect is advisable.

The modality effect had been explained in various ways. The classic account,which posits a short-lived precategorical store, has met with abundant conflictingevidence (e.g., Longoni, Richardson, & Aiello, 1993; Penney, 1989; Watkins &Watkins, 1973). Others (e.g., Nairne, 1990; Penney, 1989) have posited specifictraces derived from perceptual processing. The present model does not representlower level perceptual processes. However, I do not exclude the possibility that

215VERBAL STM MODEL

they have an additional influence, nor do I suggest that economized M capacityis the only source of the modality effect. What I argue is only that this contributesimportantly to an explanation of it.

Another remaining problem is the nature of parameteri, which was defined asdecrease in probability of recalling a partially activated scheme and was assumedto be materials-specific. However, this definition tells us little about psycholog-ical mechanisms of forgetting. Decreased activation of schemes may result fromvarious causes, such as decay, output interference, input interference from newitems, and automatic interruption. The last term refers to intervention of the Ioperator, which is assumed to occur after an M operation and to reduce theactivation of schemes not boosted by the M operator (e.g., Pascual-Leone, 1987).All these causes could affect short-term forgetting. In this article I compoundedall possible causes of activation decrease in a single parameter. This is parsimo-nious, and the presence of only one free parameter makes the test of the modelstringent. One could find the model too complex and too unconstrained, if severalfree parameters were included in it for different causes of deactivation. Yet, it ispossible to distinguish experimentally various causes, and represent them byseparate parameters. Future research may establish whether the model can beimproved in this way.

However, these experiments were not intended to clarify which psychologicalmechanisms cause across-materials variation of thei parameter. Rather, theyshowed the role of M capacity, how it interacts with modality and span vssupraspan tasks, and how the word-length effect can be easily accommodatedwithin this framework. Indeed, a model with only two basic mechanisms (Mcapacity and activation decrease) generated good predictions across wordlengths. The first of these basic mechanisms modeled in quantitative terms therole of a central attentional resource. In my view, this is important because a roleof central components in verbal short-term memory has seldom been mentioned(e.g., by Hitch, Halliday, & Littler, 1989), and then only generically. Mostcurrent models seem to neglect it.

A final point to be discussed is a comparison between my model and other,recent ones. Readers may note conceptual similarities to other activation-basedmodels (Anderson & Matessa, 1997; Conway & Engle, 1994; Cowan, 1988,1993; Engle et al., 1992; Just & Carpenter, 1992). In different ways, these authorssuggested that short-term memory consists of long-term memory units, currentlyactivated either by central executive processes or by attended stimuli in thesensory input. In particular, Moscovitch and Umilta` (1991) conceive of workingmemory as “whatever processes are currently active,” and suggest that its limitsare set by the resources necessary for maintaining information and operating onit. The present model, however, takes one step further—that is, its theoreticalframework allows specification of the schemes and general-purpose mechanismsthat contribute to performance in a given short-term memory task, and this in turnallows more detailed quantitative predictions.

216 SERGIO MORRA

An important revision of the articulatory loop was advanced by Burgess andHitch (1992), whose model differs from the present one in several ways.Nevertheless, the two models are not in principle incompatible, because Burgessand Hitch do not consider time-limited capacity as a basic property, but as oneemerging from the particular connections and parameters set in their simulations.Their way of conceiving the articulatory loop, as a set of weighted connectionsamong phoneme representations, is more detailed than my view of the rehearsalprocess as an operative scheme that includes order information. Burgess andHitch (1992), however, concluded that this aspect of their model should bemodified. Consequently, how to model in detail rehearsal and order informationremains an open issue (see also Brown, 1997; Cowan, 1992; Gathercole, 1997).What Burgess and Hitch’s (1992) model still lacks is a mechanism comparableto the M operator. In addition, their model seems to exclude the possibility thata person rehearses items before the whole list has been presented, so thatrehearsal is equivalent to covertly recalling the entire list. A central attentionalcomponent such as the M operator and the assumption that people also rehearseduring stimuli presentation are two features of my model that other researchersmay choose to incorporate into their own models.

Other models, such as Brown and Hulme (1995) or Neath and Nairne (1995),are even more different. They do not include constructs like the M operator, norany role of rehearsal, and may therefore find it difficult to account for thecorrelations reported here. Their articles provide clear support for the claim thatthe word-length effect need not be explained by a time-limited rehearsal device.Nevertheless, the evidence for their models rests on estimating at least nineparameters per experiment (Hulme et al., 1997), or on making numerous, perhapsunwarranted quantitative assumptions (Neath & Nairne, 1995). Anderson andMatessa (1997) advanced a model that considers both activation and timeconstraints, but it does not consider either rehearsal or strategic allocation oflimited attentional resources. Also these authors obtained a good fit for theirmodel, but at the cost of estimating several free parameters, so that one mayquestion whether it is sufficiently constrained. In this article, as discussed above,an opposite choice was made, that is, starting to test the goodness of fit of a modelwith a single free parameter (leaving to subsequent research the task of improv-ing it).

In conclusion, while new models are flourishing in short-term memory re-search, none of them (including the present one) is likely to be fully satisfactory,as the authors themselves often recognize. However, after two decades in whichthe articulatory loop model had a status of paradigm (Kuhn, 1962/1969), it seemsthat theoretical progress is being made, and that it will probably be consolidatedin research aimed at comparing or refining models, such as those discussed here.Two main ideas have been put forward in this paper: the role of a centralattentional mechanism, whose limited capacity is divided between operative andfigurative schemes, and a decreasing recall probability only for those schemes

217VERBAL STM MODEL

which are out of the focus of central attention. In addition, it was suggested (andformally expressed in a model) that differential demands on M capacity mayaccount for differences between visual and auditory presentation and betweenspan and supraspan tasks. If the reader agrees that this paper has provided someevidence to support these ideas, but prefers classical human information pro-cessing or parallel distributed processing frameworks to a neo-Piagetian one, thechallenge is to translate the ideas advanced here into the language of one’sfavorite framework.

APPENDIX

Formal aspects of this model of verbal short-term memory can best beillustrated by means of two examples. The first involves subvocal rehearsal,while the second considers a different strategy.

An Example Involving Rehearsal

Table 10 refers to the mental processing of a subject with M capacity ofe 14 (i.e., an average 10-year-old capable of activating a task executive plus 4operative or figurative schemes), who is auditorily presented a list of five wordsand tries to remember it by rehearsing. Because a number of symbols are used,it is convenient to explain their meaning first (see also Table 1).

W1, W2, . . . ,etc., stand for the first, second,. . . , etc., word in a list. ENDstands for an end-of-list signal (which in auditory presentation might simply bethe experimenter turning to look at the subject).

TABLE 10Hypothetical Sequence of Processing Steps by a Subject with M Capacity5 e 1 4,

Auditorily Presented with a List of Five Words

Step

Schemes activated by the M operator

Output

Activation weight of the schemes Probabilityof correct

recalle k wW1 wW2 wW3 wW4 wW5

1 «Lisn [cCode] W1 wW1 12 «Lisn cReh wW1 [cCode] W2 wW2 1 13 «Lisn cReh wW1 wW2 [cCode] W3 wW3 1 1 14 «Lisn cReh wW1 wW2 [cCode] W4 wW4 1 1 1 2 i 15 «Lisn cReh wW1 wW2 [cCode] W5 wW5 1 1 1 2 3i 1 2 2i 16 «Lisn wW5 cReh wW1 wW2 [cCode END] «Rec 1 1 1 2 5i 1 2 4i 17 «Rec cRetr wW1 cReh wW2 UW1 1 1 2 8i 1 2 7i 1 2 3i 18 «Rec cRetr wW2 UW2 1 2 11i 1 2 10i 1 2 6i 19 «Rec cRetr wW3? UW3? 1 2 12i 1 2 8i 1 2 11i

10 «Rec cRetr wW4? UW4? 1 2 9i 1 2 12i11 «Rec cRetr wW5? UW5? 1 2 9i

Note.Probability of correctly recalling the list5 (1 2 11i ) (1 2 12i ) (1 2 9i ). [Square bracketspoint to the schemes activated by the F and L operators.]

218 SERGIO MORRA

The Greek letter« stands for a relatively simple task executive (e.g., arepresentation of the current goals). As in Burtis (1982),«Read and«Rec representthe task executives for the input and recall phases of an STM task with visualpresentation of stimuli, while«Lisn denotes a task executive for the input phasewith auditory presentation.

The letterc stands for an operative scheme. Three different operative schemesare considered in the model. The first iscCode, the word-encoding operation. Thesecond iscReh, the operation of ordered subvocal rehearsal of all the figurativeschemes currently activated by the M operator. Depending on the capacity of theM operator, these figurative schemes may represent some or all of the wordspresented to the subject. The third iscRetr, the operation of retrieving the nextword in a list.

The letterf stands for a figurative scheme. In particularfW1, fW2, . . . , etc.,stand for mental representations of the first, second,. . . , etc., word in a list. ThesymbolfEND stands for a mental representation of the end-of-list signal.

An important concept is the degree of activation of figurative schemes,particularly the loss of activation of schemes that had previously been fullyactivated. In the far right column of Table 10, full activation of a scheme isindicated by the number 1, and decrease of activation is expressed in terms ofi,the only free parameter in the model. Thus, the table contains expressions suchas 12 i, 1 2 3i, and 12 8i. Parameteri is defined as the decrease in probabilityof recall of an item per processing step and per decaying scheme. In other words,decrease of activation is proportional to both number of processing steps andnumber of partially activated schemes. Thus, if at a given point only one schemeis decaying, then it loses an amounti of activation during that step; if twoschemes are decaying,eachof them loses an amount 2i of activation during thatstep, and so on. Parameteri is assumed to be specific to each type of encodedmaterial (e.g., long or short words, confusable or nonconfusable consonants,digits, semantic–conceptual codes).

Finally, UW1, UW2, . . . , etc., represent utterances of recalled words. A questionmark in the subscript, as in UW5?, indicates that the utterance of, for example, thefifth word occurs with a specified probability smaller than 1 becausefW5 is onlypartly activated.

In the first six steps, the subject has the goal of listening to the stimuli («Lisn isactivated). In particular, in Step 1, the subject has to encode (cCode) the first word(W1). Only one of the subject’s four units of M capacity is used for this, sincearticulatory encoding of spoken words does not demand any (i.e., it is automatic).The outcome of this processing step is that a specific articulatory code (fW1) isactivated at its highest degree (i.e., 1).

Articulatory recoding of words is assumed to be effortless in the case ofauditory presentation; if the stimuli are read aloud by a human experimenter, thesame assumption is also made for understanding the end-of-list signal (i.e., anycues that cause a subject to start recalling the items). Square brackets, as in [cCode]

219VERBAL STM MODEL

in Steps 1 to 5 and [cCode END] in Step 6, are used to represent the assumptionthat these schemes do not consume any resources of the M operator to beactivated. The sources of their activation would be operators F and L due tostimulus–response compatibility and overlearning.

In Step 2, three M-capacity units are used. Two of them activate the schemes(cReh, fW1) involved in rehearsal of the previous item, and only one is allocatedto the two schemes (cCode, W2) involved in articulatory recoding of the secondword. Thus, four schemes are involved in all, but only three M-capacity units areused because activation ofcCode is automatic. At this point, bothfW1 andfW2 arefully activated. Step 3 is similar to Step 2, except that four units of M capacityare used because three schemes (i.e.,cReh, fW1, andfW2) are now involved inrehearsal. Thus,fW1, fW2, andfW3 are fully activated.

However, at Step 4 it is not possible to continue activating one more articu-latory code at its highest degree while rehearsing everything. To do so, an Mcapacity ofe 1 5 would be needed, but we are now modeling the processing ofa subject with a capacity ofe 1 4, who can use one unit of the M operator in therehearsal process (cReh), two to keep the articulatory representations of the firsttwo words activated (fW1, fW2), and the last unit in recoding the fourth word. TheschemesfW1, fW2, andfW4 are now fully activated, but activation offW3 beginsto drop. Since only one scheme is decaying at this step, its activation decreasesby an amount corresponding to free parameteri. This is the meaning of theexpression 12 i shown in Table 10, Step 4, in thefW3 activation column.

Step 5 is similar to Step 4, except that two articulatory codes,fW3 andfW4, arenow losing activation. Therefore, the activation of each of them is assumed todecrease by an amount of 2i. Thus, activation offW3 drops from 12 i to 1 2 3i,and activation offW4 drops from 1 to 12 2i.

At Step 6 the end-of-list signal is encoded, so that the subject can sethim-/herself the goal of recalling words. The two relevant schemes (cCode, END)are activated without any expenditure of M capacity. Therefore, three units of Mcapacity can be used to rehearse the first two words (cReh, fW1, andfW2), and oneunit can still be used to keepfW5 activated. Two schemes (fW3 andfW4) are nowdecaying so each of them loses an amount of activation of 2i, dropping to 125i and 12 4i, respectively.

Steps 7 to 11 represent the recall phase. In particular, at Steps 7 and 8 thefirst two words are safely recalled (with probability5 1) because they hadbeen kept fully active throughout the process. At Step 7, the four units of Mcapacity are allocated to schemescRetr, fW1, cReh, andfW2. In the meantime,schemesfW3, fW4, and fW5 continue losing activation. Activation of theseschemes decreases by an amount of 3i during Step 7 because there are threedecaying schemes, so it drops to 12 8i, 1 27 i, and 12 3i, respectively.They continue to decay during Step 8, so that their activation drops to 1211i, 1 2 10i, and 12 6i, respectively.

At Step 9, the third word is eventually recalled with probability5 1 2 11i (i.e.,

220 SERGIO MORRA

equal to the current degree of activation of its scheme). Meanwhile, schemesfW4

andfW5 continue losing activation, so that at Steps 10 and 11 the last two wordsare recalled with probabilities of 12 12i and 12 9i, respectively.

In short, the probability of correctly recalling the whole list is the product ofthe probabilities of serially recalling each of its component words. These prob-abilities are 1 for W1 and W2, 12 11i for W3, 1 2 12i for W4, and 12 9i forW5.

An Example without Rehearsal

Table 11 exemplifies the mental processing of a subject with M capacity ofe12, visually presented with a list of four words, who tries to remember themwithout rehearsing. Since it is very similar to Table 10, it is not commented onstep by step. The main differences are the following. In the input phase, thesubject’s goal is to read rather than to listen; hence, the executive«Read appears.

Articulatory recoding of words and understanding the end-of-list signal areassumed to require effort in visual presentation (i.e., to demand M capacity).Thus,cCode in Steps 1 to 5 and END in Step 5 do not appear in square bracketsbut are included among the schemes activated by the M operator.

Some schemes begin to show activation decrease at Step 3, when the two unitsof the M operator are fully engaged in keeping active the encoding operativescheme (cCode) and processing the third word (W3). The final probability ofrecalling each of the single words in this list is 12 10i, 1 2 12i, 1 2 12i, and1 2 10i, respectively.

TABLE 11Hypothetical Sequence of Processing Steps by a Subject with M Capacity5 e 1 2,

Visually Presented with a List of Four Words

Step

Schemesactivated by the

M operator

Output

Activation weight of the schemes Probabilityof correct

recalle k fW1 fW2 fW3 fW4

1 «Read cCode W1 wW1 12 «Read cCode W2 wW2 1 2 i 13 «Read cCode W3 wW3 1 2 3i 1 2 2i 14 «Read cCode W4 wW4 1 2 6i 1 2 5i 1 2 3i 15 «Read cCode END «Rec 1 2 10i 1 2 9i 1 2 7i 1 2 4i6 «Rec cRetr wW1? UW1? 1 2 12i 1 2 10i 1 2 7i 1 2 10i7 «Rec cRetr wW2? UW2? 1 2 12i 1 2 9i (1 2 12i )/28 «Rec cRetr wW3? UW3? 1 2 10i 1 2 12i9 «Rec cRetr wW4? UW4? 1 2 10i

Note.Probability of correctly recalling the list5 (1 2 10i ) 2 (1 2 12i ) 2/ 2.

221VERBAL STM MODEL

TABLE 12Equations Expressing Probability of Recall of a List of a Given Length as a Function

of M Capacity, Presentation Modality, and the Free Parameteri

M capacityModality ofpresentation

Listlength Probability of recall

e 1 1 Auditory 2 (1 2 i )(1 2 2i )3 (1 2 3i )(1 2 5i )(1 2 6i )4 (1 2 6i )(1 2 9i )(1 2 11i ) 2/25 (1 2 10i )(1 2 14i )(1 2 17i ) 2(1 2 18i )/66 (1 2 14i )(1 2 20i )(1 2 24i ) 2(1 2 26i ) 2/247 (1 2 21i )(1 2 27i )(1 2 32i ) 2(1 2 35i ) 2(1 2 36i )/120

e 1 2 Auditory 2 1 2 i3 (1 2 3i )(1 2 4i )4 (1 2 6i )(1 2 8i )(1 2 11i ) 2

5 (1 2 10i )(1 2 13i )(1 2 17i ) 2(1 2 18i )6 (1 2 15i )(1 2 20i )(1 2 24i ) 2(1 2 26i ) 2

7 (1 2 21i )(1 2 26i )(1 2 32i ) 2(1 2 35i ) 2(1 2 36i )Visual 2 1 2 3i

3 (1 2 6i ) 2(1 2 7i )4 (1 2 10i ) 2(1 2 12i ) 2/25 (1 2 15i ) 2(1 2 18i ) 2(1 2 19i )/66 (1 2 21i ) 2(1 2 25i ) 2(1 2 27i ) 2/247 (1 2 28i ) 2(1 2 33i ) 2(1 2 36i ) 2(1 2 37i )/120

e 1 3 Auditory 2 13 1 2 i4 (1 2 6i )(1 2 8i )(1 2 9i )5 (1 2 10i )(1 2 13i )(1 2 15i ) 2

6 (1 2 15i )(1 2 19i )(1 2 22i ) 2(1 2 23i )7 (1 2 21i )(1 2 26i )(1 2 30i ) 2(1 2 32i ) 2

Visual 2 1 2 2i3 (1 2 5i ) 2

4 (1 2 9i )(1 2 10i )(1 2 12i ) 2

5 (1 2 14i )(1 2 15i )(1 2 18i ) 2(1 2 19i )6 (1 2 20i )(1 2 21i )(1 2 25i ) 2(1 2 27i ) 2

7 (1 2 27i )(1 2 28i )(1 2 33i ) 2(1 2 36i ) 2(1 2 37i )e 1 4 Auditory 2 1

3 14 (1 2 5i )(1 2 6i )5 (1 2 9i )(1 2 11i )(1 2 12i )6 (1 2 14i )(1 2 17i )(1 2 19i ) 2

7 (1 2 20i )(1 2 24i )(1 2 27i ) 2(1 2 28i )Visual 2 1

3 1 2 3i4 (1 2 9i ) 2(1 2 10i )5 (1 2 14i ) 2(1 2 16i ) 2

6 (1 2 20i ) 2(1 2 23i ) 2(1 2 24i )7 (1 2 27i ) 2(1 2 31i ) 2(1 2 33i ) 2

222 SERGIO MORRA

However (and this is the main difference between Tables 10 and 11), itcannot be taken for granted that the ordering of items is correct. Withoutrehearsal to ensure serial-order encoding, if W2 and W3 are retrieved, thenthe probability of their being reported in the correct order is 1/2. For thisreason, the probability of correctly recalling a visually presented four-wordlist by a subject with an M capacity ofe 1 2 is given as (12 10i)2 (1 212i)2/2.

In a conventional memory-span procedure, the probability that a subject has aspan ofat least nitems is, of course, equal to the product of the probabilities ofcorrectly recalling the lists ranging from the shortest to the one includingn items.Table 12 shows the equations expressing the probability that a list of a givenlength is correctly recalled. Of course, a subject can obtain a span score of, say,at least four words only if the lists of two words and three words have alreadybeen recalled. Thus, the probability of span$ 4 is equal to the product of theprobabilities of recalling the lists of two, three, and four words. In turn, theprobability that a subject’s span score isexactly four words is equal to thedifferencep(span$ 4) 2 p(span$ 5).

TABLE 12—Continued

M capacityModality ofpresentation

Listlength Probability of recall

e 1 5 Auditory 2 13 14 1 2 3i5 (1 2 7i )(1 2 8i )6 (1 2 12i )(1 2 14i )(1 2 15i )7 (1 2 18i )(1 2 21i )(1 2 23i ) 2

Visual 2 13 14 (1 2 7i ) 2

5 (1 2 12i ) 2(1 2 13i )6 (1 2 18i ) 2(1 2 20i ) 2

7 (1 2 25i ) 2(1 2 28i ) 2(1 2 29i )e 1 6 Auditory 2 1

3 14 15 1 2 4i6 (1 2 9i )(1 2 10i )7 (1 2 15i )(1 2 17i )(1 2 18i ) 2

Visual 2 13 14 (1 2 4i )5 (1 2 9i ) 2

6 (1 2 15i ) 2(1 2 16i )7 (1 2 22i ) 2(1 2 24i ) 2

223VERBAL STM MODEL

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Received October 10, 1997; revised September 14, 1999

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A New Model of Verbal Short-Term Memory

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