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Journal o f Experimental Psychology1972 , Vol. 96, No. 1, 124-129

O P T I M I Z I N G TH E LE AR NING OF A S E C OND-L AN G UAG E V O C A B U L A R YR I C H A R D C . A T K I N S O N

Stanford UniversityThe problem is to optim ize the learning of a large German-English vocabulary.Four optim ization strategies are proposed and evaluated exp erim entally . Th efirst strategy involves presenting items in a random order an d serves as a bench-mark against w hich th e others can be evaluated. The second strategy permi ts5 to determine on each trial of the exper iment which item is to be presented,thus placing instruction under "learner control." The third and four thstrategies are based on a mathematical model of the learning process; thesestrategies are computer controlled an d take account of S's response history inmaking decisions abou t which items to present next. Perform ance on a delayedtest administered 1 wk. after th e instru ction al session indicated that th elearner-controlled strategy yielded a gain of 53% when compared to the randomprocedure, whereas the best of the two computer-controlled strategies yieldeda gain of 108%. Impl icat ions of the work for a theory of ins truct ion areconsidered.

This article examines the problem ofindividualizing the instructional sequenceso that the learning of a second-languagevocabulary occurs at a m a x i m u m rate.The constraints imposed on the experi-mental task are those that typically applyto vocabulary learning in an instructionallaboratory. A large set of German-Englishi tems are to be learned during an instruc-tional session which involves a series ofdiscrete trials. On each trial, one of theGerman words is presented and S attemptsto give the English translation; the correcttranslation is then presented forabrief s tudyperiod. A prede te rmined number of trialsis allocated for the instructional session,and after some intervening period of t im ea test is administered over the entirevocabulary set. The problem is to specifya strategy for presenting items during theinstructional session so that performanceon the delayed test will be maximized. Theinstructional strategy will be referred to asan adaptive teaching system to the extentthat it takes into account S's responsehistory in deciding which items to presentfrom trial to trial.In this study four strategies for sequenc-ing the instructional material are con-sidered. One strategy (designated RO) is

1 Requests for reprints should be sent to RichardC. Atkinson, Dep a r tmen t of Psychology, StanfordUniversity, Stanford, California 94305.

to cycle through the set of items in arandom order; this strategy is not expectedto be particular ly effective, but it providesa benchmark against which to evaluateoth er procedures. A second strategy (de-signated SS) is to let 5 determine forhimself how best to sequence the material .In this mode, 5

1decides on each trial whichitem is to be tested and s tud ied ; the learnerrather than an external controller deter-mines the sequence of instruction.The th ird and fourth sequencin g schemesare based on a decision-theoretic analysis ofthe instructional task (Atkinson, 1972).A mathematical model of learning thathas provided an accurate account of vo-cabulary acquisition in other experimentsis assumed to hold in the present situation.

This model is used to compute , on a trial-by-trial basis, an individual S 's currentstate of learning. Based on these com-putations, i tems are selected for test andstudy so as to optim ize the level of learningachieved at the termination of the instruc-tional session. Two optimization strategiesderived from this type of analysis areexamined in the present experiment. Inone case, the computations for determiningan optimal strategy are carried out assum-in g that all vocab ulary items are of equ aldifficulty; this strategy is designated OE(i.e., optimal under th e assumption of equalitem difficulty). In the other case, the

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OPT IMIZ ING LEARN ING A SECOND VOCABULARY 125computations take into account variationsin difficulty level among items; this strategyis called OU (i.e., optimal under the as-sumption of unequal item difficulty). Thedetails of these two strategies are com-plicated and can be discussed moremeaningfully after the experimental pro-cedure and results have been presented.Both represent adaptive teaching strategiesin the sense defined above, because the itempresented to'S on each trial is determinedby his history of responses up to that trial.The concern of the experiment is toevaluate th e relative effectiveness of thefour instructional strategies. Of particularinterest is whether strategies derived froma theoretical analysis of the learning processcan be as effective as a procedure where 5makes his own decisions.

M E T H O DSubjects.The 5s were 120 undergraduates en-rolled at Stanford University; 30 5s were randomlyassigned to each of the four experimental groups.None of the students had prior course work inGerman and none professed familiarity with thelanguage. The 5s were run in group s of 8, with 2 5s

in each group assigned to one of the four experi-mental conditions.Materials,The instructional material involved84 Germ an-English item s; all words were concretenouns typically taught during the first course inGerm an. Seven display lists of 12 German wordseach were formed that were judged to be of roughlyequal difficulty. A display list involved a verticalarray of German words numbered from 1 to 12;the seven lists were arranged in a round robin an dwere always cycled through in the same order.Procedure.The 5s were required to participatein tw o sessions: an instructional session that lastedapproximately 2 hr. and a much shorter test sessionadministered 1 wk. later. The test session was thesame for all 5s and involved a test over the entireset of items. The four experimental groups weredistinguished by the sequencing strategy (RO, SS ,OE, OU) employed during the instructional session.The experiment was conducted in the Computer-Based Learning Laboratory at Stanford University.The control functions were performed by programsru n on a modified PDP-1 computer (Digital Equip-ment Corp.) operating under a time-sharing system.Eight teletypewriters were housed in a soundproofroom and faced a projection screen mounted on thefront wall.The instructional session involved a series ofdiscrete trials. Each trial was initiated by project-ing one of the display lists on the front wall of theroom; the list remained on the screen throughoutth e trial. The 5s were permitted to inspect the

list for approximately 10 sec. In the RO, OE, andOU conditions this inspection period was followedby the computer typing a number from 1 to 12on each 5's teletypewriter indicating the item to betested on that trial; th e number typed on a giventeletypewriter depended on that 5's particularcontrol program. In the SS condition, 5 typed 1of 12 numbered keys during the inspection periodto indicate to the computer which item he wantedto be tested on. At the end of the inspection period,5 was required to type out the English translationfor the designated German word and then strikethe "slash" key, or if unable to provide a transla-tion to simply hit the "slash" key. After th e "slash"ke y had been activated th e computer typed out thecorrect translation and spaced down two lines inpreparation for the next trial. The trial terminatedwith th e offset of the display list and the next trialbegan immediately with the onset of the next dis-play list in the round robin of lists. A completetrial took approxim ately 20 sec. and the tim ing ofevents (with in and between trials) was synchronousfor th e eight 5s run together. The instructionalsession involved 336 trials (with a S-min. break inth e middle), which meant that each display listwas presented 48 times. In the RO condition, thisnumber of trials permitted each of the items on alist to be tested and studied an average of 4 times.The delayed-test session, conducted 7 to 8 dayslater, was precis ely the same for all 5s. All testingwas done on the teletypewriters. A trial beganwith the computer typing a German word, and 5was then required to type the English translation; 5received no feedback on the correctness of the re-sponse. The 84 German items were presented in adifferent random order for each 5. During thedelayed-test session the trial sequence was self-paced.All 5s were told at the beg inning of the experimentthat there would be a delayed-test session an d thattheir principa l goal was to achieve as high a score aspossible on that test. They were told, however,not to th ink about th e experiment or rehearse an yof the material during the intervening week; theseinstructions were emphasized at the beginning an dend of the ins truct ion al session and later reports from5s confirmed that they made no special effort torehearse the material during the week betweeninstruction and the delayed test. The instructionsemphasized that 5 should try to provide a transla-tion for every item tested during the instructionalsession; if 5 was uncertain bu t could offer a guesshe was encouraged to enter it. In the RO, OE, andOU conditions, no additional instructions weregiven. In the SS condition, 5s were told that theirtrial-to-trial selection of items should be done withthe aim of mastering the total set of vocabularyitems. They were instructed that it was best totest an d study on words they did not know ratherthan on ones already mastered.

RESULTSThe results of the experiment are sum-marized in Fig. 1. On the left side of the


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126 R I C H A R D C . A T K I N S O N

OPTIMAL STRATEGY(Unequal Parameter Case )

a OPTIMAL STRATEGY( Equal Parameter Case)

1 2 3 4S U CCE S S I V E TRIAL BLOCKS( INSTRUCTIONAL SESSION )DELAYED T E S TSESS I O N

FIG. 1. Proportion of correct responses in successive trial blocks during theinstructional session and on the delayed test administered 1 wk. later.

figure, data are presented for perform anceduring the instructional session; on theright side are results from the delayedtest. The data from the instruct ionalsession are presented in four successiveblocks of 84 trials each; for the RO condi-tion this means that on the average eachitem was presented once in each of theseblocks. Note that performance dur in g theinstructional session is best for the ROcondition, next best for the OE conditionwhich is slightly better than the SS condi-tion, and poorest for the OU condition;these differences are highly significant,F (3, 116) = 21.3, p < .001. The ord erof th e experimental groups on the delayedtest is completely reversed. The OUcondition is by far best with a correctresponse probability of . 7 9 ; the SS condi-tion is next with .58; the OE conditionfollows closely at .54; and the RO conditionis poorest at .38, F (3, 116) = 18.4, p


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O P T I M I Z I N G L E A R N I N G A SECOND V O C A B U L A R Y 127DISCUSSION

At this point, we turn to an account of thetheory on which the OU and OE schemes arebased. Both schemes assume that acquisitionof a second-langu age vocab ulary can be de-scribed by a fairly simple learning model. Itis postulated t ha t a given item is in one ofthree states (P, T, and U) at any momen t intime. If the item is in State P, then it stranslation is known and this knowledge is"relatively" permanent in the sense that thelearning of other i tems will not interfere withit. If the item is in State T, then it is alsoknown but on a "temporary" basis; in State Tthe learning of other items can give rise tointerference effects that cause the item to beforgotten. In State U the i tem is not known,and 5 is unable to give a translation. Thusin States P and T a correct translation is givenwith probability one, whereas in State U theprobability is zero.When Item i is presented for test and studyth e following transition matrix describes thepossible change in state from th e onset of thetrial to its t e rmina t ion :

PP r lrlW = T * ,-u L - v i

T U .0 0I - xi 0

Rows of the matrix represent the state of Item iat the start of the trial and columns th e stateat the end of the trial. On a trial when somei tem other than I tem i is presented for testan d study (whether that i tem is a member ofItem i's display list or some other displaylist), transit ions in the learning state of Item ialso may take place. Such transitio ns canoccur only if S makes an error on the t r ia l ;in that case th e transit ion ma trix applied toItem i is as follows:

T UPrl 0 O- i , = T 0 1 - /, /,- .u L o o i J

Basically, the idea is that when some otheritem is presented to which 5 makes an error(i.e., an item in State U ), then forgett ing mayoccur for Item i if it is in State T.To sum marize , when I tem i is presented fortest and study transit ion Matrix A * is applied;when some other item is presented that elicitsan error then Matrix P,- is applied. The aboveassumptions provide a complete account of

th e learning process. For the task consideredin this article it is also assumed that Item iis either in State P (with probability gj) or inState U (with probability 1 gj) at the startof th e instructional session ; 5 either knows th ecorrect translation without having studied theitem or does not. The parameter vector< t > i = [ X i , yi, Zi, ft , gi] characterizes the learningo f a given Item i in the vocabulary set. Thefirst three parameters govern th e acquisitionprocess; the next parameter, forg ett in g; andthe last, S's knowledge prior to ente r ing theexperiment.For a more detailed accoun t of the model thereader is referred to Atkinson an d Crothers(1964) an d Calfee an d Atkinson (1965). Ithas been sh own in a series of experim ents thatthe model provides a fairly good account ofvocabulary learning and for this reason it wasselected to develop an optim al proc edu re forcontrolling instruction. We now turn to adiscussion of how the OE and OU procedureswere derived from th e model. Prior to con-duct ing the experiment reported in this article,a pilot study was run using the same wordlists and the RO procedure described above.Data from the pilot study were employed toestimate th e parameters of the model; th e esti-mates were obtained using the m in im um chi-square procedures described in Atkinson andCrothers. Two separate estimates of param-eters were made . In one case it was assume dthat the items were equally difficult, and datafrom all 84 i tems were lumped together toobtain a single estimate of the parametervector $; this estimation procedure will becalled th e equal-parameter case (E case),since all items are assumed to be of equaldifficulty. In the second case data wereseparated by i tems, and an estimate of 4 > i wasmade for each of the 84 items (i.e., 84 X S= 42 0 parameters were est imated); this pro-cedure will be called the unequal-parametercase (U case). In both the U and E cases,it was assumed that there were no differencesamong 5s; this homogeneity assumptionregarding learners will be commented uponlater. The two sets of param eter estimateswere used to generate th e optimization schemespreviously referred to as the OE and OUprocedures; the former based on estimatesfrom Case E and the latter from Case U.In order to formulate an instructionalstrategy, it is necessary to be precise about th equant i ty to be maximized. For the presentexperiment th e goal is to maximize th e totalnumber of items S correctly translates on the


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12 8 RICHARD C. ATKINSONdelayed test.2 To do this , we need to specifythe theoretical relationship between the stateof learning at the end of the instructionalsession and performance on the delayed test.The assumption made here is that only thoseitems in State P at the end of the instruc tionalsession will be translated correctly on thedelayed test; an item in State T is presumedto be forgot ten dur in g the interve ning week.Thus , th e problem of maximizing delayed-testperformance involves, at least in theory ,maximizing the number of i tems in State P atth e termination of the instructional session.Having numerical values for parametersand knowing 5 's response history, it is possibleto estimate his current state of learning.3Stated more precisely, the lear nin g mode l canbe used to derive equations and, in tu rn ,compute the probabilities of being in States P,T, and U for each item at the start of Trial, conditionalized on 5's response history upto and including Trial.w 1. Given numericalestimates of these probabilities, a strategy fo roptimizing perfo rman ce is to select that i temfo r presentation (from the current displaylist) that has the greatest probabili ty of mov-ing into State P if it is tested and studied on thetrial. This strategy has been termed the one-stage optimization procedure because i t looksahead only one trial in m ak ing decisions. Th etrue optimal policy (i.e., an JV-stage procedure)would consider al l possible item-response

2 Other measures can be used to assess the benefitsof an instructional strategy; e.g., in this case weightscould be assigned to items measuring their relativeimportance. Also costs may be associated with th evarious actions taken during an instructional session.Thus, for the general case, th e optimization probleminvolves assessing costs an d benefits and findinga strategy that maximizes an appropriate functiondefined on them. For a discussion of this issue seeAtkinson and Paulson (197 2), Dear, Silberman,Estavan, and Atkinson (1967), and Smallwood(1971).3 The 5's response history is a record fo r each trialof the vocabulary item presented and the responsethat occurred. It can be shown that there exists asufficient history that contains only th e informat ionnecessary to estimate 5"s current state of learning;the sufficient history is always a function of thecomplete history and the assumed learning model(Groen & Atkinson, 1966). For the model con-sidered in this paper th e sufficient history is fairlysimple. It is specified in terms of individualvocabulary items fo r each S; we need to knowthe ordered sequence of correct and incorrect re -sponses to a given item plus the number of errors(to other items) that intervene between eachpresentation of the item.

sequences for the remaining tr ials and selectthe next i tem so as to m aximize the nu m ber ofitems in State P at the termination of theinstructional session. Unfortunately, for thepresent case the TV-stage policy cannot beapplied because the necessary computationsare too time c on sum ing even for a large-scalecomputer. A series of Monte Carlo studiesindicates that th e one-stage policy is a goodapproximation to the optimal strategy for avariety of Markov learning models; it was forthis reason, as well as the relative ease ofcomputing, that the one-stage procedure wasemployed. For a discussion of one-stage and./V-stage policies and Monte Carlo studiescomparing them see Groen and Atkinson(1966), Calfee (1970), and Laubsch (1970).

The optimization procedure described abovewas implemented on the computer and per-mitted decisions to be made on-line for each 5on a trial-by-trial basis. For 5s in the OEgroup, the computations were carried outusing the five parameter values estimatedunder the assumption of homogeneous i tems(E-case) ; for 5s in the O U group the computa-tions were based on the 42 0 param eter valuesestimated under th e assumption of hetero-geneous items (U-case).The OU procedure is sensitive to in ter i temdifferences and consequently generates a moreeffective optimization strategy than the OEprocedure. The OE procedure, however, isalmost as effective as having 5 make his owninstructional decisions and far superior to arandom presentation scheme. If ind iv idua ldifferences among 5s also are taken into ac-count , then fur ther improvements in delayed-test performance should be possible; this issueand methods for dealing with individualdifferences are discussed in Atkinson andPaulson (1972).The study reported here illustrates oneapproach that can contribute to the develop-me nt of a theory of instructio n (Hilgard , 1964).This is not to suggest that the OU procedurerepresents a final solution to the problemof optimal item selection. The model uponwhich this strategy is based ignores severalimportant factors, such as interi tem relation-ships, motivation, and short-term memoryeffects (Atkinson & Shiffrin, 1968, p. 190).Undoubtedly, strategies based on learningmodels that take these variables into accountwould yield superior procedures.Although th e task considered in this articledeals with a l imited form of instruction, thereare at least tw o practical reasons for s tudying


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O P T I M I Z I N G L E A R N I N G A S EC O ND V O C A BU L A RY 129it. First, this type of task occurs in numerouslearning situations; no matter what the peda-gogical orientation, any initial reading programor foreign- language course involves some formof list learning. In this regard it should benoted that a modified version of the OUstrategy has been used successfully in theStanford computer-assisted instruction pro-gram in initial reading (Atkinson & Fletcher,1972) . Second, the study of simple tasks thatcan be understood in detail provides proto-types for analyzing more complex optimiza-tion problems. At present, analyses compar-able to those reported here cannot be made formany instructional procedures of central in-terest to educators, but examples of this sorthelp to clarify the steps involved in devisingand testing optimal strategies.4

4 For a review of work on optimizing learning andreferences to the literature see Atkinson (1972).REFERENCES

ATKINSON, R. C. Ingredients for a theory of instruc-tion. American Psychologist, 1972, 27, 921-931.ATKINSON, R. C., & CROTHERS, E. J. A comparisonof paired-associate learning models having dif-ferent acquisitions an d retention axioms. Journalo f Mathematical Psychology, 1964, 2, 285-315.ATKINSON, R. C., & FLETCHER, J. D. Teachingchildren to read with a computer. The ReadingTeacher, 1972, 25 , 319-327.ATKINSON, R. C., & PAULSON, J. A. An approach

to the psychology of instruction. PsychologicalBulletin, 1972, 78, 49-61.ATKINSON, R. C., & SHIFFRIN, R. M. Hu ma nmemory: A proposed system and its controlprocesses. In K. W. Spence & J. T. Spence (Eds.),The psychology of learning an d motivation: Ad -vances in research an d theory. Vol. 2. New York:Academic Press, 1968.CALFEE, R, C. The role of mathematical models inoptimizing instruction. Scientia: Revue Inter-nationale de Sy nthese Scientifique, 1970, 105, 1-25.CALFEE, R, C., & ATKINSON, R. C. Paired-as-sociate models and the effect of list length.Journal of Mathematical Psychology, 1965, 2,255-267.DEAR, R. E., SILBERMAN, H. F., ESTAVAN, D. P,, &ATKINSON, R. C. An optimal strategy for thepresentation of paired-associate items. BehavioralScience, 1967, 12 , 1-13.

GROEN, G. J., & ATKINSON, R. C. Models foroptimizing th e learning process. PsychologicalBulletin, 1966, 66, 309-320.H I L G A R D , E. R. (Ed.) Theories of learning an dinstruction: The sixty-third yearbook of the Na-tional Society for the Study of Education. Chicago:University of Chicago Press, 1964.LAUBSCH, J. H. Op tim al item allocation in com-puter-assisted instruction. IA G Journal, 1970,3, 295-311.S M A L L W O O D , R. D. The analysis of economicteaching strategies for a simple learning model.Journal of Mathematical Psychology, 1971, 8,285-301.

(Received February 4, 1972)

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