.I

.

.

Reprinted

from

JOURNAL

OF

VERBAL

LEARNING

AND VERBAL

BEHAVIOR,

Vol.

6,

No. 5,

October

1967Copyright !Zi 1967 by Academic Press Inc. Printed in

U.S.A.

JOURNAL OF VERBAL

LEARNING

AND VERBAL

BEHAVIOR

6, 780-787 (1967)

An Information-Processing Explanation of One-Trialand Incremental Learning1

Lee W. Gregg and Herbert A. Simon

Carnegie Institute of Technology, Pittsburgh, Pennsylvania 15213

This paper is concerned with identifying conditions under which verbal learningexhibits an all-or-none or an incremental character, respectively, and showing thatthe EPAM model of verbal learning predicts correctly the learning rates under anumber of these conditions. Reanalysis of data from a previous experiment removesapparent discrepancies with the theory.

The EPAM model predicts, and the data support, these generalizations: Whetherlearning will be all-or-none or incremental depends on S's learning strategy. Undernonreplacement conditions, learning will be all-or-none if S adopts a one-at-a-timestrategy. Under replacement conditions with rapid presentation, there will be littlelearning with an all-at-once strategy, but Ss who adopt one-at-a-time strategy willlearn nearly as rapidly under replacement as under nonreplacement conditions.

Determining to what extent rote verballearning is incremental, and to what extentit takes place in a single trial has been acentral problem of learning theory duringthe past decade. In the light of the accu-mulated experimental evidence, the an-swer to "Is rote learning incremental?" canonly be "Sometimes." The problem, as At-kinson, Bower and Crothers (1965, p. 118)observe, is to define the "sometimes." "Atpresent writing," they say, "a challengingtask confronting the theorist is ( 1 ) to iden-tify those experimental conditions wherethe one-element (i.e., all-or-none) modelworks, and those where it does not, and(2) to construct a more general model

1 This investigation was supported by PublicHealth Service Research grant MH 07722 fromthe National Institute of Mental Health. The au-thors are greatly indebted to Edward A. Feigen-baum, with whom they have had numerous dis-cussions of the implications of the EPAM theoryfor one-trial learning. They are grateful also toAndrew P. ChenzofT and Kenneth R. Laughery,who participated in conducting the experiment,and whose data are reanalyzed here.

which essentially reduces to the one-element model in the former cases but ac-counts for the discrepancies in the lattercases."

It is the aim of this paper to show thatan information-processing theory, EPAM(Elementary Perceiver and Memorizer ) ,makes quantitative predictions about one-trial learning, and departures from it thatare consistent with the main body of em-pirical evidence. The first version of EPAMwas constructed by Feigenbaum and Si-mon, as an explanation of the serial posi-tion effect in serial rote verbal learning,and without awareness of Rock's first ex-periments on one-trial learning and hencewithout intent to explain them.2 EPAMwas later generalized to account for arange of phenomena in serial and paired-associate learning, including some of the

2 The earliest public description of EPAM is inEdward A. Feigenbaum (1959). The predictionsof EPAM for the serial position effect are de-veloped more fully in Feigenbaum and Simon(1962).

780

781INFORMATION PROCESSING IN LEARNING

main effects of meaningfulness, familiarity,and similarity upon rate of learning.

PostulatesThe mechanisms that appear relevant to

the problem of one-trial learning are com-mon to all three versions of EPAM thathave been tested thus far. These mech-anisms are summed up in the followingpostulates (cf., Feigenbaum, 1959; Feigen-baum and Simon, 1962, pp. 310-311):

( 1 ) Serial Mechanism. The centralprocessing mechanism operates serially; sothat the total time required to memorize aset of noninteracting items is the sum ofthe times of the individual items.

(2) Chunks. The basic units on whichthe system operates are chunks, i.e., thelargest stimulus components that are fa-miliar units, either by virtue of the system'sprevious history or familiarization proce-dures.

(3) Processing Time. The fixation of anitem requires a definite amount of process-ing time per chunk. (Empirically, the timefor "normal college sophomores" appears tobe about 10 sec. per chunk, cf. Bugelsky,1962; Hovland, 1938.)

(4) Immediate Memory. An immediatememory with a capacity of a few chunks iscapable of storing information temporarily.

(5) Attention. The central processingmechanism fixates any part of the stimulusmaterial to which it attends (i.e., holds inimmediate memory for the requisite lengthof time). The management of attention ismodifiable by experimental instructions,attention-directing stimuli (e.g., anchorpoints), habit, and S's strategies.

In previous publications it has beenshown that these postulates lead to correctquantitative predictions of the shape ofthe serial position curve (Feigenbaum andSimon, 1962); and predict correctly thatCVC syllables of very low familiarityshould take about three times as long to

fixate as syllables of very high familiarity(Simon and Feigenbaum, 1964).

Implications ofthe PostulatesThe central issues about one-trial learn-

ing have been reviewed by Underwoodand Keppel (1962) and Postman (1963).They have pointed to chunk size (in ourterminology), length of trial, and S's strat-egy as variables likely to affect materiallywhether one-trial learning will or will notoccur. Since these variables and others areincorporated in the structure of EPAM, wecan consider whether EPAM will or willnot predict correctly their effects on thepossibility of one-trial learning. We willreview these qualitative predictions briefly,then turn to a specific analysis of someexperimental data where sharp quantita-tive predictions can be made and tested.

From the EPAM postulates, one-triallearning is more likely to occur with highlyfamiliar responses than with unfamiliarresponses, in agreement with the evidencereviewed by Postman (1963). Since in theEPAM model, the same processes accountfor both "response learning" and "associa-tive learning," and the theory predicts fromthe nature of the stimulus material howmuch is required of each, the conclusionthat one-trial learning is most compatiblewith familiar material does not requireindependent ad hoc assumptions.

Under theEPAM postulates, learning cantake place in a single trial only if the mate-rial remains in short-term memory longenough to be fixated— about 10 sec perchunk. The data of Peterson and Peterson(1959) suggest that counting backwardsfrom a three-digit number may preventeven a single syllable from remaining verylong in short-term memory. In general, aslow rate of presentation and the absenceof distracting interpolated tasks are likelyto be conducive to keeping a particular itemin immediate memory long enough to

782

GREGG

AND SIMON

.

fixate it completely. Hence, we would ex-pect one-trial learning to occur more fre-quently under such circumstances thanwith a fast rate of presentation or whenother tasks are interpolated. (The evidenceis reviewed in Gregg et al., 1963; Postman,1963; and Underwood and Keppel, 1962.)

Finally, even when the chunk and thetime unit are specified, whether one-triallearning occurs will depend on how longthe processor continues to work on anygiven item—how attention is directed.Bracket* and Battig (1963) showed thatthe differences between groups learningunder replacement and nonreplacementconditions disappeared when Ss were in-structed to learn one or a few pairs at atime.

In the next section we show again, byreanalyzing the raw data to bring new evi-dence to bear on a previously publishedexperiment of Gregg et al. ( 1963 ) , howrates of learning under replacement andnonreplacement conditions depend on themanagement of attention. The new find-ings, based on a classification of Ss by at-tention strategies, not reported in the pre-vious analysis, support the results of Brack-ett and Battig ( 1963) and resolve somepuzzling anomalies in the data in the formin which they were first analyzed.

The Experiment

Method and ResultsGregg et al. ( 1963) tested the generality of

Rock's findings on one-trial learning, using his re-placement method but more difficult tasks. Un-der all but one of the conditions (involving theeasiest of their tasks) the experiments showedsubstantial differences in performance betweenthe replacement and nonreplacement conditions,differences that are usually interpreted as anti-thetical to the one-trial hypothesis.

Their Exp. I was carried out with 20 Ss in eachof four conditions, formed from the possible com-binations of Fast (F) and Slow (S) rates of pres-entation with replacement (R) or nonreplace-

ment ( N ) of a new syllable after an erroneousresponse. We shall designate the conditions FR,

SR,

FN and

SN,

respectively. The total timesper trial in S and F conditions (including the in-tertrial interval) were 79 sec and 55 sec, respec-tively.

The total number of correct responses by the20 Ss on the tenth test trial is shown in Table 1,columns ( 1 ) and ( 2 ) for each of the four experi-mental conditions. In Table 1, column (3) is

TABLE 1

Actual and Predicted Performance:Simple-Learning Model

No. correct responses"

a 4. i Simple-Actual modelCondition It N prediction

(1) (2) (3)Slow (79" per trial) 57 U6 151Fast (55" per trial) 5!) 110 105

" The entries in Columns 1 and 2 are the totalnumber of correct responses in the tenth trial of apaired-associateslearning experiment (Gregg, Chen-zoff and Laughery, 19G3). Presentation rate andReplacement (R) vs. Nonreplacement (N) of in-correct pairs were the independent variables, N =

20 for each cell. In Column (3), numbers of correctresponses are predicted on the assumption of equallearning rates per minute in the F and S conditions,the assumed rate being the average of the actualrates for the SN and FN conditions.

shown the total number of correct responses pre-dicted for the same conditions, assuming (a) thatamount of learning is simply proportional to timeavailable for learning (Postulate 3) and (b) thatreplacement causes no deficiency in learning. Itrequires no tests of significance to see from thetables that: (a) the relative amount of learningin the FN and SN conditions is consistent withPostulate 3 ( the second assumption is not involvedin these conditions); (b) much less learning thanpredicted occurs in the R condition, when theN conditions are taken as the norm; and ( c ) thedeficiency is much more severe in the S than inthe F condition. In the SR condition, Ss learnedonly about

40%,

and in the FR condition, onlyabout 55% as much as would be predicted fromthe learning rate of the Ss in the N conditions.Can we account for the deficiency in learning

783INFORMATION PROCESSING IN

LEARNING

>

i

i

under the replacement conditions, using themechanisms postulated for EPAM?

In the R condition any syllable pair not learnedin a single trial is removed from the list. If arelatively fixed processing time is required to fixateeach syllable (Postulate 3), then S could fail tolearn a pair in a single trial for any of severalreasons, among them: (a) he may be interruptedor distracted by another task before a pair islearned; or (b) he may stop processing a pairbecause he thinks, erroneously, that it has beenfixated. The extent of the former difficulty woulddepend on his attention strategy. The extent ofthe latter difficulty would depend on the feed-back available to him about how well the pairwas already learned, and his alacrity in turningto a new pair.

In the N conditions the time required, on theaverage, to learn a pair is greater than the ex-posure time per syllable per trial. In

fact,

with2-sec presentation, Ss learned, on the average,about one-half syllable per trial (eight pair pres-entations), and with 4-sec presentation, on theaverage, about two-thirds syllables per trial. Thissuggests that, unless an S attends to one or afew specific pairs on each trial, he is unlikely tolearn any syllables at all under the R conditions.

Analysis of Learning StrategiesWe now have direct evidence for this

hypothesis from raw data gathered in theexperiment but not presented or used inthe analysis of the findings in the earlierpublication. After the experiment, Ss in theR conditions were asked what strategiesthey used in learning. On the basis of theirreplies, they were classified into those whoattempted to focus on one or two syllablepairs at a time (O Strategy), vs. those whotried to learn many, or all, of the syllableson each trial (A Strategy). Of 15 S in theFR condition whose replies could be classi-fied, 10 reported that they tried to learnone or two syllables on each trial, five thatthey tried to learn all or most. On the tenthtrial, Ss in the O group made an averageof 3.4 correct responses each; those in theA group made an average of only 1.4 cor-rect responses each. Of 16 Ss in the SRcondition whose replies could be classified,

only 4 replied that they tried to learn oneor two at a time, 12 that they tried tolearn all or most. On the tenth trial, Ss inthe O group made an average of 5 correctresponses each, those in the A group anaverage of only 2.4 correct responses each.( Two A Ss account for half of these correctresponses ) .

The data confirm our conjecture thatSs who adopted a One-at-a-time (O) strat-egy under R conditions learned much morerapidly than those who adopted an All-at-once (A) strategy. Under N conditions, asexpected, there was no difference betweenlearning rates of O and A Ss. The RA Ss,indeed, with two exceptions in the S condi-tion, learned very little at all.

This result can be expressed quantita-tively. Extrapolating from the O Ss to theentire group of 20 for each condition, wewould predict 68 correct responses ( 3.4 X20) on the tenth trial for the FR Ss, and100 correct responses (5 X 20) for the SRSs (Table 2, column 2). These values arenow two-thirds as large as would be pre-dicted (105 and 151, respectively) fromthe responses of the corresponding Ngroups (Table 2, column 5), and the rela-tive learning rates of the F and S Ss are inthe predicted ratio of nearly 55 : 79.

Quantitative allowance can also be madefor the second source of disadvantage ofthe R groups—that if they make an in-correct response on a pair previously re-sponded to correctly, the pair is replaced.For the entire experiment, in about onecase in ten an incorrectresponse was madeon a pair that had been responded tocorrectly on the previous trial (2189 cor-rect responses on the first ten trials for allSs, with 199 instances of "backsliding").The relative frequency of backsliding wasabout the same in R and N conditions (53instances and 669 correct responses in theformer, 146 instances and 1510 correct re-sponses in the latter).

784

GREGG

AND

SIMON

r

f

TARLE 2

Actual and Predicted Performance One-at-a-Time (O) Strategy

No. Correct Responses"

" The entries are the total number of correct responses on the tenth trial extrapolatedto an N of 20 fromreports of Ss of the R conditions who adopted the O strategy. There were 10 Ss in the FR and 5 Ss inthe

,Slt

conditions.

In the N conditions, backsliding wasoften followed by a "jump"—that is, morethan one syllable pair learned on a subse-quent trial. This seldom occurred in theR conditions. The numbers of jumps were7 for the FR, 10 for the SR, 35 for the FN,and 49 for the SN conditions, respectively.The difference largely reflects the fact thatif an S in an N condition missed a nearly-learned pair on one trial, he could recoverthat pair on a later trial with little interfer-ence with his other learning.

If we assume that the pairs for which back-sliding occurs are almost completely learned, then,to measure total amounts of learning, we shouldadd to the number of syllables learned by the Ssin the R conditions the number responded to cor-rectly at least once but lost through backsliding.We can estimate this number in several ways.Since the "efficient" O Ss exhibited less back-sliding than the others, we can take the actualrate of the former as the basis for the estimate.We will call this the "conservative" estimate. Al-ternatively, we can use the average backslidingrate for all subjects as a more "liberal" estimator.

Conservative Estimate: The ten O Ss in theFR condition backslid 10 times— a rate of 20 ad-ditional correct responses for 20 Ss ( cf . Table2 ) . The four OSs in the SR condition backslid4 times— also a rate of 201 responses for 20 Ss.Adding these numbers to the previous adjust-ments, we obtain total estimated correct responsesfor the FR and SR conditions of 88 and 120, re-

spectively, as compared with the predicted valuesfrom the N conditions, of 105 and 151, respec-tively ( Table 2, columns 3 and 5 ) . These esti-mates for the R conditions are about 80% of thevalues for the N conditions in each case.

Liberal Estimate: In the SR condition, the fourO Ss made 119 correct responses in the first 10trials, which would give an estimated 12 casesof backsliding, or 5 X 12 < 60 for a group of 20Ss. Similarly, the ten O Ss in the FR conditionmade 201 correct responses, which would cor-respond to an expected 20 cases of backsliding,or 20 X 2 < 40 for a group of 20 Ss. Adding thesenumbers to the earlier estimates based on thelearning of the O

Ss,

we obtain expected correctresponses for 20 Ss on the tenth trial of68 +40 = 108 and 100 +60 = 160 for the FRand SR groups, respectively; which are very closeto the predicted values for the FN and SN groups:105and 151 (Table 2, columns 4 and 5).

in summary, the Ss in the R conditionsperformed far less well than Ss in the Nconditions. However, those Ss in theformercondition who stated that they had fol-lowed a One-at-a-time strategy performedabout two-thirds as well as Ss in the non-replacement condition. When adjustmentis made for the fact that a single error onan almost-learned pair loses the priorlearning on that pair in the replacementcondition, the adjusted learning rates ofthe One-at-a-time Ss in the replacementcondition are approximately as high as

Same as col. 1with backsliding

adjustment

Simplemodel:Actual:

R condition(from Table 1,

Actual:"efficient"

SsN condition

(from Table 1,col. 3)Condition col. 1) (O) strategy Conservative Liberal

(057

(2)100

(3)120

(4)160

(5)151Slow

Fast 5!) 68

KS

108 105

785INFORMATION PROCESSING IN

LEARNING

.

\

.

»

the rates of Ss in the non-replacement con-dition. Comparing F and S conditions,amount of learning is also proportional to

learning time in both (efficient) replace-ment and nonreplacement conditions. Theexperiment can therefore be taken as astrong confirmation of quantitative predic-tions of the EPAM model.

Predictions by SimulationThe predictions we have just made can be

checked in a more precise way by using theEPAM program to simulate the exact conditionsof the Gregg et al. (1963) experiment. Exceptfor the modifications to be listed in a moment,the same version of EPAM was used in the pres-ent simulation as in the simulations reported bySimon and Feigenbaum (1964). Eight conditionsare to be simulated, deriving from the two dichot-omous variables manipulated by the Es (rate ofpresentation and replacement), and the strategydeterminedby S.

Rate of Presentation: Slow ( S ) or Fast ( F ).This variable was manipulated directly by chang-ing the drum-speed parameter in EPAM. Thetotal time per trial in the S condition was 79 : 55the time per trial in theF condition.

Syllable Replacement: Replacement (R) orNon-replacement (N). After each test of a syl-lable pair, the program checked the correctnessof the response. In the R condition, if no responsewas made, or theresponse was wrong, the syllablepair was replaced by another pair stored in thecomputer memory. The syllables employed in thesimulation were drawn from the same populationas that used by Gregg et al. ( 1963 ) .

Subject Strategy: One-at-a-time (O) or All-at-once (A). A particular subroutine in the EPAMprogram determines when S will replace the syl-lable pair he is holding in immediate memorywith a new pair read from the memory drum.In the O conditions, on each learning trial pres-entation, EPAM checked whether it could makea correct response to the stimulus already heldin immediate memory; if so, thepair in immediatememory was replaced by the pair in the memorydrum window; if not, learning continued withthe part already in immediate memory, and thepair currently in the memory-drum window wasignored. In the A condition, each time the mem-ory drum turned during a learning trial, EPAMreplaced the syllable pair in immediate memorywith the pair in the memory-drum window. This

was the only difference in the EPAM programsfor the two strategies.

In analyzing the data from Gregg et al.(1963), we have used number of correct

responses on the tenth trial as the measureof learning rate. In the simulation, learn-ing was morerapid than for the average ofthe human Ss in all conditions. (The simu-lated syllable exposure times proved to belonger than the corresponding times in thehuman experiment). Hence, EPAMlearned the lists in less than 10 trials in allconditions except one, and a differentmeasure of learning rate had to be used.Since both numbers of errors to criterionand number of trials to criterion vary in-versely with learning rate, the reciprocalsof these quantities were used to measurelearning speed. In order to adjust for thedifference in average learning speed in thesimulation and the human data, all learn-ing rates are expressed as ratios to theaverage of the rates for the SNO and SNAconditions. One df is lost in this adjust-ment, and 7 df remain. In the presenta-tion of the data, since there was no differ-ence in learning rates between NO andNA Ss, the average rates are used for thecombined groups in the FN and SN con-ditions.

Table 3 compares the two measures oflearning rates in the eight conditions ofthe simulation with the actual rates for theSs. The product-moment coefficient of cor-relation between the EPAM (errors) andhuman learning rate indexes was .87; thecoefficient between the EPAM ( trials ) andhuman indexes was .93. Both coefficientsare significant at the .05 level. It will beobserved that in the FRA conditions,EPAM did not succeed in learning the listby the time all replacement syllables hadbeen exhausted after 11 trials. Fifty-six er-rors had been made, and only five pairslearned. Thus, the learning in this condi-tion was about half as fast as in the FRO

786

GREGG

AND

SIMON

i

/

,'

*

" Entries in the EPAM rows are thereciprocals of the numbers of errors and numbers of trials, while theentries in the last row are numbers of correct responses on the tenth trial, both expressed as ratios to tlie

average

of the SNO and SN.A. conditions. (.See text.)b List not learned in 11 trials. See textfor method of estimating learning rate.c In the N conditions, there was no difference in the learning rates of O and A Ss. The rates used here

are those for the entire

group

of 20 Ss in each condition.

condition, where the entire list was learnedin nine trials with 24 errors.

The EPAM simulation also gave excel-lent quantitative predictions of the rate ofbacksliding. We have noted that, whilemaking 2189 correct responses, the humanSs "backslid" 199 times, a rate of .087 syl-lables lost per correct re.sponse. For EPAM,the corresponding figures were 232 re-sponses and 18 losses, for a backsliding rateof .078. As with the human Ss, there werein the EPAM runs nobig differences in thebacksliding rates for different conditions,but the samples were not large enough todetect small differences reliably.

ConclusionThis paper has sought to meet the chal-

lenge of Atkinson et al. quoted earlier"(1) to identify the experimental condi-tions where the . . . all-or-none . . . modelworks. . . and (2) to construct a moregeneral model . . . [that] accounts for thediscrepancies." The EPAM model predicts,and the data support, these generalizations:

(a) Whether learning will be all-or-noneor incremental depends not only on theexperimental conditions but also on thelearning (i.e., attention ) strategies that Sscan, or do, adopt. The E can establish nec-essary, but not sufficient, conditions forall-or-none learning when he sets the pa-rameters of the experiment. These condi-tions, in turn, may influence the strategyS adopts.

(b) Under nonreplacement conditions,learning will be all-or-none if S adopts aone-at-a-time strategy. It may be incremen-tal otherwise.

(c) Under replacement conditions, if Sfollows a one-at-a-time strategy, learningwill be all-or-none provided that the totaltime per trial (for all the syllables) isabout as long as, or longer than, the timerequired for fixating a syllable pair. Forshorter exposure times, and for Ss who fol-low an all-at-once strategy, little or nolearning will occur.

(d) For Ss who follow a one-at-a-timestrategy, the speed of learning under re-

TABLE 3Comparison op EPAM Learning Rates wrTH Human Rates

Experimental Conditions

One-at-a-time All-at-once

Past Slow Past SlowHates N R N I! N 1! N R

EPAM" ( j\errors/43 39 116 71 49 .06 84 44

EPAM" (—-—)\ trials/

50 38 114 Ii!) 69 196 86 50

Human Ss" 69c 45 100' (i? 69' 19 100c 32

787

information

processing in learning

]

.

.

-i

placement conditions will fall short of thespeed under nonreplacement conditionsonly by an amount that can be attributedto backsliding. Under both conditions, fixa-tion will occur at a rate of about 10 secper chunk, where the number of chunks ina syllable pair can be derived from thefamiliarity (to these Ss) of the syllables.

(c) Severe experimental conditions,e.g., replacement with short exposuretimes, may induce more Ss to follow a one-at-a-time strategy than easier conditions,hence increasing average learning rates un-der the former relative to the latter condi-tions.

References

Atkinson, R.

C.,

Bower, G. H., and

Crothers,

E. J. An introduction to mathematical learningtheory. New York: Wiley, 1965.

Brackett, H. R., and Battig, W. F. Method ofpretraining and knowledge of results in paired-associate learning under conditions of repeti-tion and non-repetition. Amer. J. Psychol,1963, 76, 66-73.

Bugelski, B. R. Presentation time, total time, andmediation in paired-associate learning. J. exp.Psychol, 1962, 63, 409-412.

Feigenb.aum, E. A. An information-processingtheory of verbal learning. Unpublished doc-

toral dissertation. Pittsburgh: Carnegie Insti-tute of Technology, 1959.

Feigenbaum, E. A., and

Simon,

H. A. A theoryof the serial position effect. British J. Psychol.,1962, 53, 307-320.

Gregg, L. W.,

Chenzoff,

A. P., and Laughehy,K. R. The effect of rate of presentation, sub-stitution, and mode of response in paired-associate learning. Amer. ]. Psychol., 1963, 76,110-115.

Hovland, C. I. Experimental studies in rotelearning theory; 111. Distribution of practicewith varying speeds of syllable presentation./. exp. Psychol, 1938, 23, 172-190.

Peterson, L. R., and Peterson, Margaret J.Short-term retention of individual verbalitems. /. exp. Psychol, 1959, 58, 193-198.

Postman, L. One-trial learning. In C. N. Coferand Barbara S. Musgrave (Eds.), Verbal be-havior and learning. New York:

McGraw-Hill,

1963. Pp. 295-321.

Simon,

H. A., and Feigenbaum, E. A. An in-formation-processing theory of some effects ofsimilarity,

familiarization,

and meaningfulnessin verbal learning. /. verb.

Learn,

verb.Behav., 1964, 3, 385-396.

Underwood, B. J., and Keppel, G. One-triallearning? }. verb. Learn, verb. Behav., 1962,1, 1-13.

( Received February 21, 1966)