European Journal of Psychology at Education1987, Vol. I, n,> 4, 45-59© 1987, I.S.P.A.

A New Look at Learning-Disabledand Normal-Achieving Children'sWord -Pair Memorization Ability

Kees P. Van den BosUniversity of Groningen, The Netherlands

Johannes KingmaUniversity of Alberta. Canada

An l I-parameter Markov model of stages of learning, whichwas developed by Brainerd et al., will be presented. The focuswill be on parameter interpretation in terms of long-termmemory (LTM) processes.

Next the model will be used to examine the contributionof these various LTM processes to Schooltype and Age diffe­rences in a word-pair memorization experiment. Subjects were8 and ll-year-old normal-achieving (NA) children from regularelementary schools and 8 and I l-vear-old children from specialschools for learning disabled (LD) children.

One of the main conclusions is that the SchooltypexAgeinteraction which was demonstrated for traditional performan­ce measures, can be explained by LD children's little develop­mental progress in storage processes and deviations fromnormal development in aspects of the acquisition of retrievalalgorithms.

No deiiciences were, however, detected in the LD children'sretention ability early in the task, and in the so-called heuristicretrieval operations.

Introduction

45

Since learning and memory are intimately related it will hardly come as asurprise that many investigators have assumed that research into memory ormemorization task performance of learning-disabled (LD) I children would provideat least a partial answer to the question of what is wrong with these children'slearning. On the issue of memory and learning disability there exists a voluminousliterature in which LD children - as a group _ appear to perform more poorlythan normal-achieving (NA) children on a variety of memory tasks (Bauer, 1979;Ceci, 1983; Dallago & Moely, 1980; Perfetti, 1985; Torgesen, 1978-1979; Torgesen& Kail, 1980; Van den Bas, 1983). The evidence concerns performance on short­-term memory (STM) tasks, especially if one defines these tasks as those involvingbrief storage of relatively small amounts of information after a single presentation

l LD children are children of at least average intelligence who have serious difficulties withone or more elementary school subjects, usually reading and/or arithmetic. In the Netherlands thesechildren are frequently referred to special schools for learning disabilities. Children from these schoolsform our target population. Samples from this population will be compared with normal-achieving(NA) children, that is, with samples of children in regular elementary schools.

46 K. P. VAN DEN BOS & J. KINGMA

and in which immediate recall (serial or free) is required (Torgesen, 1982), as wellas performance on less frequently administered tasks, such as long-term memory(LTM) tasks in which for example, supra-span lists of words or pictures must bememorized to a criterion of 100 % correct verbal recall (Howe, Brainerd & Kingma,1985; Van den Bos & Kingma, 1985; Van den Bas, Kingma & Bakker, 1986) andstory-recall tasks (Wong, 1982). A variety of more or less traditional variables hasbeen put forward in the literature to explain the contrast between LD and NAchildren's memory task performance differences. Apart from motivation andattention (or processing effort) these variables were usually derived (Torgesen,1982) from the Atkinson & Shiffrin (1968) model in which control processes andbasic processes (structural features) are distinguished. Examples of the controlprocesses are rehearsal (labeling and repetition) and organization (grouping, ela­borative encoding). Examples of the bacic processes are duration of a memorytrace and the access speed to memory codes. The main conclusion in recentresearch reports seems to be that LD children's lower recall performance canbe attributed to difficulties in the spontaneous activation of one or more controlprocesses or «effective study techniques» (Dallago & Moely, 1980; Worden, 1983),or to reduced processing speed, or to a combination of these factors.

There are, however, important questions left. We will focus on a «big one»(Brainerd, 1985), viz., whether the LD children's problems with memory tasksconcern storage processes, retrieval processes, or both. Of course, the distinctionbetween storage and retrieval leaves open the possibility that both, or one of thetwo of these processes have a «control» or «basic» nature, depending on thetask. However, although the terms storage and retrieval are frequently used inmost of the studies mentioned above, there have been few attempts to empiricallyseparate their contributions to memorization task performance.

At the same time it must be noted that this has been a feature of mostdevelopmental studies on normally achieving children as well (Rohwer & Dempster,1977). Moreover, the separation attempts that have been reported in the litera­ture of the seventies, can be criticized because of a lack of well-defined scalingassumptions about the underlying measurement scales of the relevant processvariables (Brainerd, 1985). Recently, a solution has been offered by Brainerd et al.(see, e. g., Brainerd, Howe & Kingma, 1982; Brainerd, Howe, Kingma & Brainerd,1984) who applied a new stages-of-learning model in various experiments onchildren's memorization task performance. This model provides for a commonratio scale on the basis of which storage and retrieval processes can be quanti­tatively separated. In this study we want to apply this model to LD and NAchildren's memorization task data. Since these groups consisted of two age levels(B-year-olds and Ll-year-olds) we will have opportunities to investigate develop­mental trends in storage and retrieval processes as well.

The two-stage model and the interpretation of its parameters in termsof LTM processes

In all two-stage Markov models of the past two decades (Greeno, 1974) thataccounted for recall data in memorization experiments, three learning states andtwo learning stages are assumed. The first learning state is called U (eunlearned»}.Items in State U cannot successfully be reproduced. In any case this state appliesbefore the to-be-remembered items are presented to the S. But also after thefirst and later study trials it is possible for some items to still remain in State U.The second state is called P (from partially learned). An item is in State P whenescape from State U has been realized but in which reproduction is still unstable:sometimes the item is correctly reproduced (substate Pc) and sometimes not (subs-

MEMORIZATION PROCESSES 47

tate PE)' The third or terminal state is L (from learned). Items in this state arealways correctly reproduced and backward transitions are not possible. The twolearning stages are escape from U and entrance into L.

Now we will give the necessary details of the Markov model version whichwas recently developed by Brainerd et al.

The model assumes an experimental structure of the type Sl TIA TIB 82 r,S3 T3... Here Sl means the first study trial of a list, TIA means the first test trial,TIB means the second test before the next study trial, S2means the second study trial,T2 means the test trial following the second study trial, and so on. Note that inthis experimental structure only the first study trial is being followed by twotest trials. The 8T alternations go on until an acquisition criterion is reached, inour case two consecutive test trials of 100 % correct recall. For such experimentsBrainerd et al. (1982; 1984) wrote the following equation which consists of astarting vector (V), a transition matrix (M), and a correct response vector (C):

v = [LL2, L,PE2, LIPC2' LIU2, PEIL2, PEIPE2, Pn 1Pc2, PElUZ' PcIL2, PC1PE2, PC1PC2'

PCLU2, UIL2, U1PE2, U,PC2' U,U2]

= [a'b', 0, 0, 0, 0, a'(l - b')r(l - f) (1 - g), a'(l - b')r(l - f)g, a'(l - b')rf, 0,

a'(l - b') (l - r) (1 - f) (1 - h), a'(1 - b') (1- r) (1- f)h, a'(l - b') (l - r)f,

0, 0, 0, 1 - a'] ;

L(n + 1) PEen + 1) PcCn + 1) U(n + 1)

L(n) 1 0 0 0

PE{n) d (l - d) (l - g) (1 - d)g 0(1) M=

Pc(n) c (1 - c) (l - h) (l - c)h 0

D(n) ab a(1 - b)e a(l - b) (1 - e) I-a

1

oC=-

o

The starting vector V gives the probabilities for an item of being in variouspossible combinations of states on the first two test trials TIA and TIB (for sim­plicity, the subscripts lA and IB have been replaced in V by 1 and 2, respectively)The transition matrix M gives the probabilities of being in various possible combi­nations of states on all pairs of consecutive test trials after the first two testtrials. The correct response vector C simply gives the probability of a correct

48 K. P. VAN DEN BOS & J. KINGMA

response in each of the possible states on any test trial. It can be seen thatEq. (1) contains 11 free parameters. Seven of these parameters are called learningparameters. They measure the difficulty of the two stages of learning: escapefrom State V and entrance into State L. The remaining four parameters ar'e calledperformance parameters. They measure the variable correct response probabilitieson various types of test trials for items occupying State P. Three of the sevenlearning parameters (a', a, l-f), refer to State V: a' and a give the probability thatan item escapes from State V on the first study trial and on subsequent studytrials, respectively; the parameter 1-f measures the probability that an item,having escaped to State P, does not fall back to State V between the first andsecond test trials. For items escaped from State V, the parameters b' and bmeasure the probability that those items skip State P and go directly to thelearned State L on the first study trial and on subsequent study trials, respectively.The parameters c and d measure the probabilities that items occupying State Pescape to State J, following a test trial success or a trial error, respectively.Finally, consider the P-state performance parameters: the parameters l-r andl-e measure the probability of correct recall for items on the first State P testtrial, given that those items made the U --)0 P transition on the first study trialor on subsequent study trials, respectively. For any pair of consecutive trialsin State P, the parameters g and h measure the probabilities of an «error-success»or «success-success» sequence, respectively.

So far, the parameters of an abstract learning system were described.However, being inspired by earlier proposals of e.g., Greeno (1974) and Halff (1977)and extending the ideas of these authors, Brainerd et al. have indicated that it ispossible to interpret these parameters as measures of the difficulty or ease whichthe main LTM processes of storage and retrieval proceed. We follow Brainerd's(1985) account: Whenever certain controls for STM effects are installed in memo­rization tasks (d. our procedure section), a correct response would not seem tobe possible until a durable representation of an item has been established in LTM.

Given that the performance measure is recall, it seems natural to interpretthe first stage of learning (escape from State V) as storage processes. Theparameters a' and a are then identified with the following different aspects ofthe overall storage difficulty: a' and a measure storage of an item representationin LTM on the first study trial or any study trial after the first one, respectively.The f-parameter is interpreted as a measure of the forgetting probability forearlier-stored representations on the second test trial.

Storing an item representation in LTM does not mean that the S will be able toretrieve it. It seems appropriate, therefore, to identify the remaining learning para­meters with retrieval. Again, different aspects of this overall process are involved.Elsewhere, it has been argued that two structural forms of retrieval can be distin­guished, viz., heuristic and algorithmic retrieval (Halff, 1977). Algorithmic retrievaloperations are procedures that invariably produce correct recall of an item represen­tation. Heuristic retrieval operations are procedures that sometimes producecorrect recall and sometimes not. We have seen that in the model only State Lallows for consistent correct recall, and that this state is realized by either adirect transition from V, or a transition from P.

With regard to the first possibility then, the parameters b' and b are identifiedwith the probability that a retrieval algorithm for an item is acquired on the samestudy trial that the storage of this item is realized, for b' and b on the first studytrial or on any later study trial, respectively. The second possibility concerns theacquisition of a retrieval algorithm in case of a P~ L transition. The para­meters c and d that are associated with this transition are identified with theprobability that a retrieval algorithm is acquired after a successful and non­-successful item reproduction in State P, respectively. These parameters are

MEMORIZATION PROCESSES 49

Table 1: LTM-process interpretations of the 11 parameters of the two-stage model

Parameter

a'

a

I-f

Interpretation

STORAGE AND RETENTION

Probability of storing an item representation on the first studytrial

Probability of storing an item representation on any study trialafter the first trial

Probability of retaining a previously stored representation bet­ween the first and second test trials

ALGORITHMIC RETRIEVAL

b' Probability of acquiring a retrieval algorithm for an item onthe first study trial, given that the item was also stored on thesame trial

b Probability of acquiring a retrieval algorithm for an item onany study trial after the first study trial, given that the itemwas also stored on the same trial(the parameters b' and b can be summarized as measuring theannex-storage algorithmic retrieval)

c Probability of acquiring a retrieval algorithm after a success inState P

d Probability of acquiring a retrieval algorithm after an errorin State P(the parameters c and d can be summarized as measuring thepost-storage algorithmic retrieval)

HEURISTIC RETRIEVAL

l-r Probability of successful heuristic retrieval on the first test trialin State P if an item was stored on the first study trial

l-e Probability of successful heuristic retrieval on the first test trialin State P if an item was stored on any study trial after thefirst study trial(because the parameters I-r and I-e concern early measures inState P they can be summarized as measuring early heuristicretrieval)

g Probability that, for any two consecutive trials in State P,unsuccessful heuristic retrieval is followed by successful heuris­tic retrieval

h Probability that, for any two consecutive trials in State P,successful heuristic retrieval is followed by successful heuristicretrieval(because the parameters g and h concern relatively late measuresin State P they can be summarized as measuring late heuristicretrieval)

Tableau 1: Interpretation des 11 parametres du modele a deux phases

50 K. P. VAN DEN BOS & J. KINGMA

therefore referred to as measuring post-storage algorithmic retrieval. By wayof contrast Brainerd (1985) used for the b' and b parameters the term pre-storageretrieval. However, since one cannot determine whether within one study trial theacquisition of a retrieval algorithm is preceded of followed by storage, it seemssafer to use the term annex-storage algorithmic retrieval instead.

Finally the interpretation of the parameters r, e, g, and h is discussed.These are the parameters that measure probabilities of correct reproduction ofitems in State P on various types of study trials. We saw that these probabilitiesvaried from 0 < p < I, and that this inconsistency was referred to as heuristicretrieval. Associated with various P-state points in time, the parameters l-r andl-e can be identified with early heuristic retrieval, and the parameters g and hwith relatively late heuristic retrieval: the parameters l-r and l-e measure theprobabilities of successful heuristic retrieval of items on the first P"state testtrial after storage, where storage took place in the first study trial or any laterstudy trial, respectively. The parameters g and h are interpreted as measuring theprobabilities of successful heuristic retrieval on a test trial after the first P-statetest trial, where on the immediately preceding test trial an error or a correctreproduction occurred, respectively.

Table 1 gives a summary of the parameters of the two-stage model in termsof the LTM processes.

The experiment

We now report the experiment in which the model will be applied in orderto deter-mine the more detailed nature (in terms of storage and retrieval aspects)of task performance differences as a function of school types and age.

Method

Subjects. Both LD children (from special schools) and NA children (fromregular elementary schools) were selected from two age ranges (92-104 monthsand 128-140 months). The four resulting groups consisted of 30 children each, andthe means and standard deviations of their chronological ages were 101 months(SD = 5.3 months) and 99 months (SD = 4.8 months) for younger LD and NAchildren, respectively, and 135 months (SD = 6.2 and 5.2 months) for older LDand NA children, respectively.

Materials and procedure. The children memorized a 12-item list of word pairsunder a standard cued recall condition. An item consisted of two arbitrarilyrelated concrete and familiar words. After a general introduction the child wastold that a deck of cards, each card containing two words, would be presentedand that the task was to memorize the pairs. The child was also told how lateron, after each study trial, his memory would be tested. This by asking the childto reproduce the second word of each pair after the first word would havebeen given by the experimenter (E), After this instruction the first study trialfollowed. Each word pair was shown for five seconds, The E clearly pronouncedthe words upon presentation and the child repeated them. After the first studytrial a buffer task in which the child had to circle letter pairs on a sheet wasadministered during 30 seconds. This task was meant to minimize STM effects.Then the first test trial was given, in which the E randomly presented cards- one at the time - with the first word of a pair (he also read the word aloud)and in which the child tried to recall the second word. Randomized cue presen­tation was restricted in that it was avoided to start with words that had belonged

MEMORIZATION PROCESSES 51

to the last three pairs in the study trial. The E scored the child's reponses by«zeros» in case of correct responses and by «ones» in case of incorrect or «don'tknow» responses. After the first test trial a buffer task was given and a secondtest trial followed. Hereafter, cycles of 'Study trial, buffer task, test trial, wererepeated until the child reached the criterion of two consecutive 100 % correct­recall test trials.

Results

ANOVA'S on traditional performance measures

Before considering the results of the two-stage model application we exa­mined performance patterns as reflected in two statistics which are commonlyreported in the traditional literature on memorization tasks. The first statistic,based on early performance, was the number of words correctly recalled on thefirst test trial (TIA). The second statistic, based on «total» performance, wasthe number of study trials before the criterion of two consecutive test trialswas reached. The means and standard deviations of these performance measuresare given in Table 2.

For the first statistic a 2 X 2 ANOVA showed a significant interaction ofSchool type X Age. It is clear from Table 2 that this interaction meant thatthere was no age effect for LD children, whereas ll-year-old NA children perfor­med better compared to all other groups. The 2 X 2 ANOVA on the second statisticshowed significant main effects for both School type and Age (these meant thatNA children performed better than LD children, and older children performedbetter than younger children) and a significant interaction. Post-hoc Scheffe testsindicated that this interaction meant that the developmental gains (age differen­ces) were more pronounced for NA children than for LD children.

Table 2: Means and standard deviations of two traditional recall-performancescores in the word pair memorization task

number of wordscorrectly recalledon the first test trial

number of trialsto criterion

8-yr-olds

2.57(1.41)

10.87(3.63)

LD

ll-yr-olds

2.57(1.85)

9.53(3.85)

8-yr-olds

2.47(2.21)

8.17(3.01)

NA

l l-yr-olds

3.67(2.22)

5.37(1.81)

Tableau 2: Moyennes et ecarts-types des deux scores classiques de rappel dans latache de memorisation de paires associees de mots

These results suggest that it would not only be interesting to search forthe more precise loci (in terms of storage and retrieval processes) of School typedifferences, but to include the question as to the more precise nature of develop­mental differences between the two groups as well.

52 K. P. VAN DEN BOS & J. KINGMA

Parameter estimation and goodness-of-iit tests of the two-stage model

The method of maximum likelihood (Brainerd, 1985) was used to obtainthe parameter estimates, The appropriate likelihood function and further deri­vational details are given in Brainerd et al. (1982, Eqs, (30)-(32». Just like in theexperiments of Brainerd et al. the minus two natural log transformation of thisfunction was minimized for the current data by using the simplex method ascoded in OPTISEP. Table 3 shows the estimates of the 11 parameters of Equation(1) by School type and Age level.

Table 3: Parameter estimates by School type and Age

Storage and Acquisition of a Heuristicretention retrieval algorithm retrieval

annex poststorage storage early late

a' a l-t b' b c d 1-r l-e g h

N ormal-achieving

8-year-olds .23 .48 .98 .74 .44 .36 .21 .58 .35 .58 .61ll-year-olds .35 .60 1.00 .69 .46 .38 .76 .63 .34 .49 .53

Learning-disabled

8-year-olds .23 .27 1.00 .68 .00 .51 .14 .92 .78 .50 .6211-year-olds .28 .32 l.00 .33 .10 .37 .28 .63 1.00 .51 .62

Tableau 3: Valeur des parametres par age et type d'ecoles

Before the comparisons between the estimates are reported, we must firstconsider the model's goodness of fit for the present data. Following the proce­dures which are detailed in Brainerd (1985), we conducted a necessity test and asufficiency test for each of the four experimental cells.

The necessity test asks whether some simpler model (i. e. a one-stage model;see Greeno, 1968) gives as good an account of the data as the two-stage model.The test involves a likelihood-ratio statistic (see Eq, (38) in Brainerd et al., 1982)on the basis of which the null hypothesis can be rejected if its value exceedsthe critical X2 (5) value. This was indeed the case for our data. The sufficiencytest tests the null hypothesis that the two-stage model with 11 parameters accountsfor the data as well as models with more than 11 parameters against the alternativehypothesis that the latter models do a better job (see for the appropriate teststatistic Brainerd (1985, Eq. (A24». From the results of both the necessity andsufficiency tests we concluded that the younger and older LD and NA children'sword pair memorization was a two-stage process to a statistically satisfactoryapproximation.

Comparisons between parameter values

The analyses involved a three-step sequence of standard likelihood-ratiotests. First a so-called experimentwise test was conducted to determine whetherit would make sense to continue with more detailed tests. This likelihood-ratio

MEMORIZAnON PROCESSES 53

test (see Eq. (53) in Brainerd et at, 1982) has an asymptotic "I.' distribution with- in our case - 33 degrees of freedom. The numerical result was X' (33) = 248,p < .001.

The second step was to conduct a series of conditionwise tests (see Brainerdet al., 1982, Eq. (54), one for each pair of conditions of interest, and the finalstep was to conduct the parameterwise tests (see Brainerd et al., 1982, Eq. (55)to determine the locus of parameter effects within the relevant condition pairsthat differed significantly. Conditionwise and parameterwise test results will bereported under the next two headings: School type comparisons and Age levelcomparisons.

School type comparisons. The numerical results of the two conditionwisetests used to examine differences between NA and LD children were ';('(11) = 59,p < .001 (8-y,ear-olds) and X!(l1) = 142, p < .001 (l l-year-olds), The results of theparameterwise tests which are distributed as /"(1), will be reported separatelyfor 8-year-olds and l l-year-olds,

Eight-year-olds. With regard to storage and retention (as measured by theparameters a', a and I-f) the only reliable parameterwise difference between NAand LD children was found on parameter a. This meant that it was easier for NAchildren than for LD children to store word pairs in LTM on study trials afterthe first one. This pattern also emerged for the annex storage algorithmic retrievalparameters b' and b. As can be seen in Table 3, the NA-LD difference was relativelysmall for parameter b' but quite substantial for parameter b. This meant thatit was much easier for 8-year-old NA children, compared to 8-year-oQld LD children,to acquire an annex-storage retrieval algorithm on trials after the first one.A different picture emerged, however, on the remaining algorithmic retrievalparameters (the post-storage algorithmic retrieval parameters c and d). For thec-parameter the NA-LD difference was in favor of the LD children, whereas forthe d-parameter the reverse was true. This meant that for the 8-year-old LDchildren it was 'easier to acquire a retrieval algorithm after a recall success of anitem in State P than for 8-year-old NA children, whereas for the latter childrenit was easier than for the LD group to acquire a retrieval algorithm after a recallerror or an item in State P.

Finally there were school type differences on the parameters that measurethe accuracy with which previously stored items are retrieved between the timeof storage and the time that a retrieval algorithm is acquired (the so-called heuristicretrieval parameters l-r, l-e, g and h). LD children had reliably higher values onthe early heuristic retrieval parameters l-r and I-e, whereas the NA group had areliably higher value on one of the late heuristic retrieval parameters (the para­meter g). No group difference was found on the h-parameter.

Eleven-year-olds. LD-NA differences in favor of the NA children were nowgeneralized to both storage parameters a' and a. The same was true for theannex-storage algorithmic retrieval parameters b' and b. In contrast to the post­-storage algorithmic retrieval results of the 8-year-olds, LD children were no longersuperior on the e-parameter (there was no reliable difference here between NAand LD children), and the NA children's superiority (compared to LD children)on parameter d was greatly increased.

With regard to early heuristic retrieval there was no longer superiority ofthe LD children on the l-r' parameter (LD and NA children's parameter valueswere inderrtical), whereas there still was a large difference in favor of the LDchildren on the l-e parameter. For the values of the late heuristic retrieval para-

54 K. P. VAN DEN BOS & J. KINGMA

meters the following switches (compared to the results of the 8-year-olds) wereapparant: there was no reliable NA-LD difference on the g-parameter, whereasthe value of the parameter h was realiably higher for LD children.

Age level comparisons. The numerical results of the two conditionwise testsused toexamint' differences between 8-year-old and ]1-year-old children were):2(11) = 61, p < .001 (NA children) and /.'(11) = 46, p < .001 (LD children). Theresults of the parameterwise tests will be reported separately for LD and NAchildren.

NA-children. Parameterwise tests of differences between numerical values(see Table 3) indicated significant gains on both storage parameters (a' and a)for 11-year-old children compared to 8-year-old children. No reliable age differenceswere found on the retention parameter (l-t) and on the two annex-storage algo­rithmic retrieval parameters b' and b. With regard to the post-storage algorithmicretrieval parameters, no reliable difference was found on the c-parameter. buta very substantial age difference was found on the d-parameter. This meant thatin the present task NA children's developmental progress in the acquisition of aretrieval algorithm was restricted to post-error trials in State P. This is a signi­ficant finding to which we will return in the discussion. Finally, for heuristicretrieval aspects no reliable age differences were found on the early heuristicretrieval parameters l-r and l-e, whereas slight declines as a function of in­creasing age were found on the two late heuristic retrieval parameters g and h.

Lls-children. The values of the 8- and 11-year-old groups' storage and retentionparameters (a', a and I-f) did not differ reliably. For the retrieval parameters,however, more erratic patterns appeared, sometimes involving reliably increasedvalue as a function of age and sometimes decreased values. Significant decreaseswere found for the algorithmic retrieval parameters b' and c and for the earlyheuristic retrieval parameter 1-r. Significant increases as a function of age werefound for the algorithmic retrieval parameters band d, and for the early heuristicretrieval parameter i-e, No age differences were found for the late heuristicretrieval parameters g and h.

Discussion

Along with reviewing the main results of this study we will draw attentionto differences and parallels with results from related studies. We focus first onstorage effects and then on retrieval effects.

Concerning storage, our findings indicated a significant School type X Ageinteraction. Whereas the 8-year-old LD children had greater difficulty than their NAcounterparts in only one storage aspect (as measured by parameter a) it wouldappear that school type differences had increased for the ll-year-old groups.Eleven-year-old NA children showed substantial storage facilitation (as measuredby both a' and a) compared to both the 8-year-old NA children and the ll-year-oldLD children. Moreover, the LD children's storage values remained developmentallyinvariant.

On a global level (across tasks, and not specified into processes like storageand retrieval) it can be mentioned that similar School type or Student type X Ageinteractions have been reported in the literature. Calfee (1982, p. 161) for exam­ple, reports that the ability to define words, even when the task is completelyoral, remains relatively constant for LD children (with reading problems) fromthe second to the sixth grade,... «a time when their peers are showing conside­rable growth». Calfee does not attribute this problem to the student's inabilityto learn but sees it «as a consequence of the curricular reliance on decoding as

MEMORIZATION PROCESSES 55

the chief vehicle for vocabulary growth». Calfee's findings and interpretation arerelevant for two reasons. First, assuming that a lack of vocabulary growth alsoapplies to the LD children of the present study, this could have contributed tothe lack of developmental progress in learning word pairs. However. one wouldexpect that :if the vocabulary factor was important, LD and NA children wouldreact differently to a list with pairs consisting of concrete and familiar words(like those used in the present experiment) and a list with relatively unfamiliarwords. In a recent experiment, however, in which we included this list mani­pulation (Van den Bas et al., 1986) the Age X School type interaction (the depen­dent variable was number of study trials to criterion) was not further modifiedas a function of Word lists, and the School type X Word lists interaction was notsignificant either. This finding would seem to reduce the explanatory role of thevocabulary factor in case of word pair memorization differences.

The broader interpretational relevance of Calfee's remarks for our findingsis the following. Decoding disabilities, which so often characterize LD children,certainly constitute a barrier for the spontaneous development of vocabulary butalso of reading comprehension, inferencing and text related memorization skills(Morrison & Manis, 1982). Our hypothesis is, however, that as a result the deve­lopment of more general learning strategies (that is, in non-reading tasks like thepresently used word-pair tasks) is at risk as well. Even the remedial teachingtime that -- in case of learning disabilities - frequently is devoted to decodingproblems and not to compensatory education could be partially responsible forthis risk. We stress this point in order to make clear that it is not necessarilya structural or within-child disability that is responsible for the LD children'snon-development in certain learning areas.

Returning to more specific findings in our study, there are as yet almostno comparative developmental studies that allow a direct comparison with ourstudy. The study that comes close because of its two-stage model application andchoice of subjects, is the study by Howe et al. (1985). Although children of similarschool types and age levels were studied, the administered task was differentin that a free-recall task of word and picture lists was used. In addition, a diffe­rent School type X Age level interaction for storage values appeared in the Howeet al. study. They found that where the NA children's storage values remaineddevelopmentally invariant, LD children's values improved as a function of age,although these values still did not reach the level of the l l-year-old NA children.An explanation of the discrepancy between the storage findings in our study andthe study of Howe et al., could be based on the fact that - at least at the storageside - cued recall paired-associate tasks (like the one we used) are generallymore difficult than free recall tasks (d. Brainerd et al., 1984; p. 492). Therefore,the first mentioned type of tasks probably offers more room for developmentalimprovement at the storage side in 8-11-year·old NA children than the latter typeof tasks, in which relative «ceiling» values were reached by the NA children. LDchildren then, assuming that a developmental delay hypothesis applies, wouldshow developmental improvement on the easier task instead.

Let us now turn to the retrieval effects and first consider heuristic retrieval.The results make clear that on both age levels the LD children's average heuristicretrieval value is higher than for NA children.

From this it can be safely concluded that LD children's retrieval accuracybetween the time of storage and the time of acquisition of a retrieval algorithm,is definitely not deficient. A similar conclusion is drawn by Howe et al. (1985).Also at a more local level there are striking correspondences between patternsof heuristic retrieval data in the present study and those for word lists in theHowe et al. study. Although, in contrast to our study, significant (but relativelymoderate) developmental effects were found by Howe et al. for LD as well as

56 K. P. VAN DEN BOS & J. KINGMA

for NA children's early heuristic retrieval performance (average values of theparameters l-r and T-e), none of the two studies indicated a differential develop­mental effect for LD compared to NA children on early (average parameter values)and late (average parameter values) heuristic retrieval. Furthermore, in bothstudies LD children showed a higher average value for early heuristic retrievalthan NA children, whereas the average LD-NA difference for late heuristic retrievalwas small.

An explanation of this result can be derived from a mixture of reflectionson item difficulty and the relationship between aspects of heuristic retrieval andalgorithmic retrieval. With regard to the item difficulty effect, Brainerd (1985)notes that the early heuristic retrieval parameters I-r and l-e are based on allitems that enter State P, while the late heuristic retrieval parameters g and hare based on a subset of items that remain in Sate P for two or more trials (i. e.,more difficult items). We have seen that LD and NA children's heuristic retrievaldid not differ for these more difficult items, but that the difference between thegroups was restricted to the retrieval accuracy of items that had just enteredState P. It is not unlikely that this diference is related to another difference, viz.,that LD and NA children differed in which items they transferred to the P-stateat all. To make this clearer, it is necessary to refer to the annex-storage algorithmicretrieval parameters. Remember that the parameters b' and b measure the P-stateskipping acquisition of a retrieval algorithm. The average b' and b values weremuch higher for NA compared to LD children. This means that NA childrentransferred less items to State P, because these items were already perfectlyretrievable for them, than LD children. Probably, annex-storage retrieval algo­rithms were acquired by the NA children for the relatively easy items, whereasthe remaining (more difficult items) were still to be refined in their retrievability.LD children on the other hand, failed, relatively spoken, in the acquisition ofannex-storage retrieval algorithms, and transferred almost all stored items (easyand difficult) to State P. This raised for LD children (compared to NA children)the probability of retrieval accuracy for items in the early P-state, whereas NAchildren's lower values of the early P-state operations were probably the effectof an efficient «trade-off» with annex-storage algorithmic retrieval operations.

Let us finally consider the remaining results, i.e. the patterns of probabilitiesof post-storage algorithmic retrieval. In contrast to heuristic retrieval and annex­-storage algorithmic retrieval, where School type differences were not develop­mentally modified, the post-storage algorithmic retrieval results can be summa­rized in terms of a significant School type X Age interaction. To a certain extent,the interaction was caused by the different c-parameter values, but a much largercontribution undoubtedly came from the d-parameter values. LD children showeda «negative» development as a function of age on the c-parameter, thereby approa­ching NA children's values which did not show variation as a function of age.The second result was that, as function of age, the increment on the d-parameterwas much larger for NA children than for LD children. Aside from NA-LD diffe­rences, the values on the c and d parameters are parallel to results reported inother studies (Brainerd et al., 1984; Kingma & Van den Bas, 1986) and they canbe interpreted as an advance in the direction of patterns reported for adults.Halff (1977), for example, showed that learning-progress in adults is restricted tostudy trials after arrors, and that study trials after successes are psychologicallyineffective.

Summarizing: in its application of the two-stage model our research hasmade it possible to draw some rather new conclusions about NA and LD children'sword pair memorization processes. LD children's problems tended to be tied tospecific components of the acquisition process. Not affected were retention abilityearly in the task, and heuristic retrieval. Storage processes on the other hand,

MEMORIZATION PROCESSES 57

improved only minimally as a function of age, in contrast to NA children'sstorage. Furthermore, annex-storage algorithmic retrieval was very difficult forLD children compared to NA children, and LD children's poststorage algorithmicretrieval operations followed a different developmental course.

A final remark seems relevant in this context. Our study was not designedto answer questions beyond the localization issue of LD children's problems inthe present task. This is not to 'say, however, that its results could not form a basisfor (special-) educationally relevant research. Now that we have a model at hand,which allows a simultaneous evaluation of several storage and retrieval aspectswithin one task, we can revisit proposals in chapters in the traditional literature,like that by Rohwer and Dempster (1977).

Departing from the distinction between storage and retrieval (but withouthaving a model with quantitative power) Rohwer & Dempster (1977) thoroughlydiscuss the educational research perspectives and relevance of this distinction. Typi­cally but understandably, their discussion of research on processes and conditions ofstorage is more extensive than the discussion on processes and conditions ofretrieval. With regard to the «unknowns» that they mention for the latter area,our results at least suggest that the feedback condition in memorization taskswould be important to manipulate further. This could be done in several ways.For example, the technique of «selective reminding» may be used (Buschke, 1974).Alternatively, the child may be instructed to explicitly ask himself (sself-caecking»routines) in a study trial whether a given item has been correctly recalled in aprevious test trial. According to the «win-stay/lose-shift» principle (Halff, 1977),incorrectly recalled items would then require extra or new processing activity.

The relevance of such future research follows directly from this study, aswell as from other studies (Howe et al., 1985; Kingma & Van den Bos, 1986), whichindicated that the d-parameter was a consistent discriminator between school typesand age levels

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Brainerd, C. J., Howe, M. L., Kingma, J. & Brainerd, S. H. (1984). On the measurement of storageand retrieval contributions to memory development. Journal of Experimental Child Psychology, 37,478-499.

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Ceci, C. J ..(1983). An inve~tigation of the semantic processing characteristics of normal and language!/Iearning-disablsd children (L/LDS). Developmental Psychology, 19, 427.439.

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Kingma, J. & Van den Bos, K. P. (1986). A stages-of-learning analysis of MIldly Mentally Retardedchildren's memorization task performance, Psychologica Belgica, 26, 43-60.

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Nouvelles perspectives sur la memorisation de couplesde mots chez des enfants avec ou sans

difficultes d'apprentissage

Cet article presente le modele developpe par Brainerd etal. qui decrit les phases de la memorisation au rnoyen de 11parametres. L'accent est mis sur l'interpretation. des parame­tres en termes de stockage et de recuperation. Puis le modeleest employe pour etudier le role de ces processus au coursde la memorisation de paires de mots en [onction de l'tige etdes capacites d'apprentissage scolaire. Les sujets sont deseniants ages de 8 et 11 ans provenant de classes primairesnormales et de classes pour enfants presentant des dijiicultesd'apprentissage specifiques. L'interaction entre l'dg« et lescapacites d'appreniissage donne lieu a des differences statis­tiquernent significatives. Une des conclusions principales estque ces differences peuvent etre expliquees par le developpe­ment limite des processus de stockage et des algorithrnes derecuperation chez les eniants qui ont des diiiicultes d'appren­tissage. Aucune anomalie n'a pourtant ite detectee dans leurcapacite de retention au cours des deux premiers cycles derappel et dans la mise en oeuvre des heuristiques de recupe­ration.

MEMORIZATION PROCESSES 59

Key words: Mathematical model of long-term memory, Storage and retrievalprocesses, Learning disabilities, Memorization, Cued recall.

Received: June 1986Revision received: September 1986

Kees P. Van den Bos. Department of Special Education, University of Groningen, Oude Boteringes­traat 1, 9712 GA Groningen, The Netherlands.

Current theme of research:

Cognitive development.

Most relevant publications in the field of Educational Psychology:

Van den Bas, K. P. (1980). Cognitive abilities and learning disabilities. Bulletin of The Orton Society.30, 94-111

Van den Bos, X. P. & Bloksma, Y. B. M. (1984). Information processing aspects of spatial skillsin children in a technical training course. Psychologica Belgica, 24, 63·81.

Van den Bas, K. P. (1985). Learning to read and learning to think. In W. A. Van de Grind &K. J. P. Van Wouwe (Eds.), Teaching thinking (pp. 23-26). Leiden (The Netherlands): ForumHumanum The Netherlands.

Kingma. J. & Van den Bos, K. P. (1986). A stages-of-learning analysis of mildly mentally retardedchildren's memorization task nerformance, Psychologica Belgica, 26, 43-60.

Johannes KinP.'ma. Department of Psychology, University of Alberta, Edmonton, Alberta, CanadaT6G 2E9

Current theme of research:

Cognitive development.

Most relevant publications in the field of Educational Psychology:

Kingma. J. (19B). Seriation, Correspondence, and Transitivity. Journal of Educational Psychology,75, 763-771.

Kingma, J. & Koops, W. (1983). Piagetian tasks. traditional intelligence and achievement tests. BritishJournal of Educational Psychology, 53, 278-290.

Kingma, J. & Koops, W. (1984). Consequences of task variations in cardination research. GeneticPsychology Monographs, J09, 77·94.

Kingma. J. & Van den Bos, K. P. (1986). A stages-of-learning analysis of mildly mentally retardedchildren's memorization task performance, Psychologica Belgica, 26, 43-60.