Journal of Experimental Psychology: 1990. Vol. 16, No. 3 ...Richard Carlson, Department of Psychology, 613 Moore Building, Pennsylvania State University, University Park, Pennsylvania

Journal of Experimental Psychology:Learning, Memory, and Cognition1990. Vol. 16, No. 3, 484-496

Copyright 1990 by the American Psychological Association, Inc.0278-7393/9O/SOO.75

Practice Schedules and the Use of Component Skillsin Problem Solving

Richard A. Carlson and Robin G. YaureThe Pennsylvania State University

In motor and verbal learning, random practice schedules produce poorer acquisition performancebut superior retention relative to blocked practice. We extend this contextual interference effectto the case of learning cognitive procedural skills to be used in problem solving. Subjects in threeexperiments practiced calculation with Boolean functions. After this acquisition phase, subjectssolved problems requiring these procedures. Experiments 1 and 2 demonstrated superior transferto problem solving for skills acquired under random schedules. In Experiment 3, subjectspracticed component skills in a blocked schedule, with one of four tasks—same-differentjudgment, mental arithmetic, short-term memory, or long-term memory—intervening betweentrials. For same-different judgments and mental arithmetic, transfer performance was comparableto that found for random schedules in Experiments 1 and 2. This result suggests that thedifferences depend on processing rather than storage demands of intertrial activity. Implicationsfor theories of problem solving and part-whole transfer are discussed.

Problem solving may be characterized as a process of assem-bling an appropriate sequence of component procedures (oroperators) to accomplish a goal. Although this process maybe guided by general or domain-specific problem solvingstrategies, the specific sequence of procedures used in a par-ticular problem will typically be determined during the prob-lem-solving episode. Fluent problem solving, therefore, re-quires efficient access and use of component skills. The issueaddressed in this article is how the context in which compo-nent skills are acquired influences the ability to access andapply those skills in a problem solving context.

Practice Schedules and Component Skills

Many studies demonstrate that practice schedules can havedramatic effects on acquisition and retention when items areequated for number of practice trials (Hintzman, 1974; Shea& Zimny, 1988). For example, subjects typically show supe-rior recall for repeated verbal items when repetitions arespaced rather than massed (e.g., Proctor, 1980). A particularlyinteresting example of the influence of practice schedules isthe contextual interference effect (Battig, 1979). Increasing thesimilarity of items to be learned, or varying the processing

This research was supported in part by the Army Research Insti-tute, under Contract MDA903-86-C-0149 to Walter Schneider. Por-tions of these data were presented at the 1988 annual meeting of thePsychonomic Society in Chicago, Illinois.

We would like to thank Rondall Khoo, Lori Forlizzi, David Lundy,Walter Schneider, John Shea, and the members of the CognitiveResearch Laboratory at the Pennsylvania State University for theircomments at all stages of this research. We also thank LawrenceBarsalou, David Rosenbaum, and two anonymous reviewers for theirconstructive comments on an earlier draft.

Correspondence concerning this article should be addressed toRichard Carlson, Department of Psychology, 613 Moore Building,Pennsylvania State University, University Park, Pennsylvania 16802.

requirements from trial to trial, produces a context thatinterferes with acquisition performance but benefits retention.

Research on the contextual interference effect in motorlearning is especially relevant to understanding the effects ofcomponent practice schedules on the acquisition of cognitiveprocedures. The central experimental manipulation involvescontrasting practice schedules that do or do not require accessof different items on successive trials. The basic empiricalfinding is this: Relative to blocked practice of one movementat a time, practice of several movements appearing randomlyfrom trial to trial results in poorer performance in acquisitionbut superior retention and transfer (e.g., Shea & Morgan,1979). Furthermore, random practice leads to superior trans-fer to alternative practice schedules—subjects who learnmovements under a random practice schedule have littledifficulty with transfer to a blocked schedule, whereas subjectswho learn under a blocked schedule have great difficulty withtransfer to a random practice schedule. Many problem solvingtasks require the application of different operators at eachstep and "on-line" access of the appropriate operators, just asa random practice schedule requires the performance of adifferent movement and on-line access of the appropriatemovement on each trial. This work on motor learning (e.g.,Shea & Morgan, 1979), therefore, provides some reason tobelieve that a random practice schedule during acquisitionmight help develop the ability to efficiently access componentskills in a problem solving situation.

In previous studies of the acquisition of a procedural cog-nitive skill—making judgments about digital logic gates—wereplicated part of these results on contextual interference(Carlson, 1989; Carlson & Schneider, 1989; Carlson, Sullivan,& Schneider, 1989b). In these studies, subjects learned tocalculate Boolean logic functions. The acquisition procedureinvolved a moderate amount of blocked practice with each ofseveral rules, followed by extended practice on a randomschedule. Over large variations in the amount of blockedpractice, we found a substantial decrement in performance

484

PRACTICE SCHEDULES 485

associated with the transition to random practice. Althoughthese studies did not compare practice schedules or directlyaddress the role of component practice schedules in fluentproblem solving (but see Carlson, Sullivan, & Schneider,1989a), the results do extend previous observations of diffi-culty in transfer from blocked to random practice schedules(e.g., Shea & Morgan, 1979) to the domain of cognitiveprocedures. This suggests that the contrast between blockedand random practice may provide an important manipulationfor understanding the conditions for acquiring skill in theaccess and use of cognitive component procedures in problemsolving.

Explanations offered for the contextual interference effectand related practice schedule effects generally rely on twocategories of theoretical mechanisms. The first mechanism,emphasized by Shea and his colleagues (Shea & Morgan,1979; Shea & Zimny, 1983, 1988) focuses on the structure ofthe memory representation developed by practice. The centralidea is that random practice (high contextual interference)encourages relational, interitem processing, which results in aricher set of retrieval cues that discriminate among the set ofitems to be learned. The critical feature of random practice,according to this account, is that it allows subjects to contrastthe items to be learned—what we will call interitem or inter-trial processing. This contrast mechanism might work in twoways. First, the item presented on trial n — 1 may still bepresent in working memory on trial n, allowing subjects toform memory structures that are explicitly relational, directlyencoding similarities and differences among items to belearned. Second, the retrieval cues used to access an incorrectitem will be present in working memory along with feedbackconcerning the correct item, allowing the subject to determinewhich retrieval cues fail to discriminate among items. Thesemechanisms presumably result in memory representations ofindividual items that are elaborated with distinctive cuesappropriate for selecting the correct member of a set of itemslearned together. Anderson (1989) has offered a similar expla-nation for our partial replication of the contextual interferenceeffect (Carlson et al., 1989b). The interitem processing view,then, emphasizes the organization of long-term memory struc-tures.

The second mechanism, emphasized by Lee and Magill(1983) for motor skills and by Jacoby (1978; Cuddy & Jacoby,1982) for verbal materials, focuses on the cognitive proceduresexecuted within each practice trial—what we will call intra-item or intratrial processing. The central idea here is that oneach trial in random practice, subjects must reconstruct asolution to the problem of producing the movement (formotor tasks) or reconstruct the item to be remembered (forverbal tasks). Because the solution or memory item canremain in working memory over trials in blocked practice,this reconstruction is not necessary. For the present case—practice and transfer of procedures for calculating Booleanfunctions—we assumed that loading a procedure into workingmemory is analogous to reconstructing a movement plan orverbal item. Because most trials require loading a proceduredifferent from the one used on the previous trial, randompractice provides more practice in this aspect of componentskill. Although the development and use of distinctive re-

trieval cues—emphasized by the interitem processing view—may be best viewed as the acquisition of procedural knowledge(e.g., Shea & Zimny, 1983), this intraitem processing viewemphasizes fluency in accessing and using component skills,rather than procedures for choosing which of several skills touse. The intraitem processing view thus emphasizes the effi-ciency of processes in working memory, rather than thestructure of long-term memory representations.

The present experiments were not designed to distinguishbetween the interitem and intraitem processing accounts ofthe retention and transfer benefits of high contextual interfer-ence. Our purpose was to explore some implications of theintraitem processing view. The two accounts are not mutuallyexclusive. It might be that the increased opportunity forinteritem processing provides the greatest benefit when it isdifficult to determine which component skill is appropriate—for example, when many operators might apply at a particularproblem solving step. In the present studies, we focused on asituation in which choosing the appropriate rule should notbe difficult—only a few operators are available, and perform-ance is quite accurate. In this situation, problem solvers aredistinguished by the efficiency or fluency with which theyaccess and use component skills, rather than by the accuracyor appropriateness of the components they choose. We there-fore expected differences in intraitem processing produced bydifferent practice schedules to be most important. In theGeneral Discussion, we consider the importance of the inter-item processing account and suggest that it is needed toaccount for some aspects of our results.

We addressed two major questions. Can the previouslyobserved retention benefit for random practice schedules (e.g.,Shea & Morgan, 1979) be generalized to the case of transfer-ring cognitive component skills to a problem solving situa-tion? If this transfer benefit is observed, can it be explainedby an intraitem processing account that emphasizes the effi-ciency of processes in working memory?

Experimental Task and Overview

In the present studies, we used an equation-chaining taskin which subjects calculated the value of a single variable onthe basis of a set of 3-5 equations. Each equation requiredthe application of a Boolean logic function (AND, OR,NAND, and NOR) to a pair of binary input values. Eachfunction was represented by a typographic symbol, and inputand output values were represented as 0 and 1. Subjects thusgave binary (0 or 1) responses both to individual equationsand to equation-chaining problems. Figure 1 displays thesymbols, rules, and a sample equation-chaining problem.

We conducted three experiments using this problem solvingtask. In each experiment, subjects first practiced individuallogic functions and then solved equation-chaining problems.Experiment 1 examined transfer between blocked and ran-dom practice schedules, as well as transfer to problem solving.Experiment 2 provided a replication of Experiment 1, with afiner grained examination of practice during the problemsolving phase. Experiment 3 examined transfer to problemsolving from blocked component practice in which tasksvarying in their processing requirements intervened between

486 RICHARD A. CARLSON AND ROBIN G. YAURE

AND: X wil l be 1 if and only if A AND B are 1

X - #(A,B)

OR: X wil l be 1 if and only if A OR B is 1

X • $<A,B>

NAND: X will be 0 if and only if A AND B are 1

X • -(A.B)

NOR: X will be 0 if and only if A OR B is 1

X - "(A,B)

A • #(0,1)

B - ~<A,C>

C - $(1,1)

D - *(0,1)

X - #(B,D)

Figure L Logic functions and symbols (top) and sample equation-chaining problem (bottom).

trials. We hoped to find one or more intervening tasks suffi-cient to produce a transfer benefit relative to blocked practice.The purpose of Experiment 3 was to examine our hypothesisthat differences in intratrial processing can account for thedifferences in transfer of component skills to problem solvingproduced by different component practice schedules.

Experiment 1

The major purpose of Experiment 1 was to replicate thebasic contextual interference effect—poorer acquisition per-formance but superior transfer for a random practice sched-ule—for the acquisition and transfer to problem solving ofsimple procedural cognitive skills. The acquisition phase ofthis experiment was essentially a replication of Shea andMorgan's study (1979), but with a cognitive rather than amotor task. Subjects practiced the Boolean logic functionsdescribed previously under blocked or random practice sched-ules. If the effect of practice schedules on these cognitive skillsis similar to that found for motor skills, subjects in the blockedpractice group should perform better during acquisition. After48 trials per function, half of the subjects in each conditionswitched to the alternative practice schedule. We expectedasymmetric transfer, with subjects having little difficulty inswitching from random to blocked practice but great difficultyin switching from blocked to random practice.

The second phase of the experiment examined subjects*ability to transfer skill at calculating Boolean functions to theuse of those functions in equation-chaining practices. If arandom practice schedule results in improved ability to accessand use component skills in a problem solving situation,subjects in the random-practice condition should solve equa-tion-chaining problems more fluently than subjects in theblocked-practice condition. If differences in intraitem proc-essing account for this effect, the difference should be greaterfor more difficult problems requiring the solution of moreequations and the coordination of more information in work-ing memory.

Method

Subjects. Forty-eight college students recruited from introductorypsychology classes at The Pennsylvania State University participatedin return for extra course credit. All subjects reported normal orcorrected-to-normal vision.

Design. Subjects were randomly assigned to four experimentalgroups defined by the component practice schedule. Subjects in allgroups practiced the rules for eight blocks of 48 trials. In randompractice, each block of trials included 12 trials with each of the fourrules appearing in random order within the block. Randomizationwas constrained so that the same rule could appear on no more thantwo consecutive trials. In blocked practice, each block included 48trials with a single rule. For blocked practice, the order in which rulesappeared was counterbalanced over subjects by using repeated Latinsquares.

The four experimental groups were defined as follows: Subjects inthe random-random group received eight blocks of random-scheduletrials. Subjects in the random-blocked and blocked-random groupsswitched practice schedules after four blocks of acquisition trials,receiving four blocks of random-schedule trials followed by fourblocks of blocked-schedule trials, or vice versa. Subjects in theblocked-blocked group received eight blocks of blocked-schedulepractice, with the rule sequence of the first four blocks repeated onthe second four blocks.

The problem solving transfer phase of the experiment.was identicalfor all subjects. This phase consisted of three blocks of 30 problemseach. Each block included 10 trials of each of three types of problems,as illustrated in Figure 2. No-search problems consisted of threeequations, and the target value (X) was a function of the outputvalues of the other two equations. Search problems consisted of fiveequations, and the target value was a function of the output valuesof two of the four nontarget equations. Subjects thus had to searchfor the appropriate equations before solving them. Search-plus-working-memory (search + WM) problems also consisted of fiveequations, but calculating the output value of the target equationrequired two levels of prior calculation. For example, determiningthe value of X in the problem at the bottom of Figure 2 requires priorcalculation of B and D. Determining the value of B, in turn, requiresprior calculation of A and C. Subjects thus had to search for appro-priate equations and had to hold more intermediate results in workingmemory than they did for the simpler search problems. In both no-search and search problems, subjects had to solve three equations.Because of the need for two levels of prior calculation in search +WM problems, subjects had to solve four or live equations in theseproblems. The 30 problems in each block appeared in random order.

The experimental design was thus a 4 x 3 mixed factorial. Thebetween-subjects factor was acquisition practice schedule, and thewithin-subjects factor was problem type.


No-search

A - $(0,0)

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C

D

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- "(0,1)

- #(1

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Search+WM

Figure 2. Examples of three problem types. (WM = working mem-ory.)

Procedure. Each subject participated in an individual sessionlasting approximately 90-100 min. Presentation of the experimentaltasks and collection of responses were controlled by IBM-compatiblemicrocomputers equipped with color EGA monitors and pro-grammed by using the MEL software system (Schneider, 1988).

After a brief introduction and an informed consent procedure, theexperimenter described the acquisition task. Written instructionsconcerning the Boolean functions displayed the symbols along withboth verbal rules (see Figure 1) and truth tables representing thefunctions. The instruction sheet was available throughout the acqui-sition procedure. Subjects were instructed to respond as quickly aspossible while maintaining a high level of accuracy.

Subjects initiated each acquisition trial by pressing the space baron the computer keyboard. After a blank delay of 500 ms, an equationappeared centered on the computer screen. The subject responded bypressing one of two adjacent keys designated 0 and 1. The computerthen displayed accuracy feedback. If the answer was correct, thelatency was also displayed. Feedback was displayed for 1 s, followedby a ready message preceding the next trial.

A brief break followed the acquisition phase. Instructions for theproblem solving phase then appeared on the computer screen, de-scribing the problem solving task and displaying a sample search +WM problem. Again, subjects received instructions to respond asquickly and accurately as possible. Subjects initiated each problemsolving trial by pressing the space bar. Following a blank delay of 500ms, the problem was displayed centered on the computer screen. Asin the acquisition procedure, subjects responded by pressing one oftwo adjacent keys designated 0 and I. The computer then displayed

accuracy and, for correct responses, latency feedback. Feedback wasdisplayed for 1 s, followed by a ready message preceding the nexttrial.

Results

Acquisition. Subjects responded quite accurately duringacquisition, as shown in Figure 3. An analysis of variance(ANOVA) on these data showed only a marginally significantdifference between practice schedules, F(3, 44) = 2.17, p <.11, MSe = 0.02245. The effects of practice block, F{1,308) = 2.49, p < .02, and the interaction of practice scheduleand block, F(2\, 308) = 2.64, p < .01, MSC = 0.0019806,were significant. As Figure 3 shows, most of this effect wasdue to the drop in accuracy when the blocked-random groupswitched to the random practice schedule beginning withBlock 5.

As expected, subjects made slower responses in the randompractice schedule, confirming the occurrence of contextualinterference. Figure 4 displays the mean latency for correctresponses during acquisition. An analysis of variance on thesedata showed significant effects of condition, F(3, 44) = 19.9,MSe = 1,786,019; block, F(7, 308) = 70.3, MS, = 95,921;and their interaction, F(21, 308) = 70.5, MS. = 95,921, allps < .001. Responses were always slower under the randompractice schedule, even after eight blocks (384 total trials) ofpractice.

The asymmetric transfer between practice schedules ob-served in previous research (Shea & Morgan, 1979) is alsoapparent in Figure 4. Subjects in the random-blocked groupexperienced little difficulty in switching from a random to ablocked practice schedule. When subjects in the blocked-random group switched from a blocked to a random schedule,however, they performed as poorly (Af - 3,247 ms) as therandom-random and random-blocked groups in the firstblock of practice (M = 3,242 ms). The performance of theblocked-random group on Blocks 5-8 (M = 2,637 ms) wasnot reliably different from the performance on Blocks 1-4 of

1.0

0.9

0.8

- # ^

- * - blocked-blocked• random-random

- K- blocked-random~$- random-blocked

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Practice Block

Figure 3. Proportion of correct responses during acquisition: Ex-periment 1.


4500

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Figure 4. Latency (ms) for correct responses as a function of con-dition during acquisition: Experiment 1.

the random-random group (M = 2,510 ms, Bonferroni t -0.86) or the random-blocked group (M = 2,539 ms, Bonfer-roni t = 0.66).

Problem solving. Overall, subjects solved 87.4% of theproblems correctly. Accuracy varied as a function of problemtype, F(2, 88) = 145.5, MSr = 0.01012, p < .001. The meanproportion of problems solved was .94 for no-search prob-lems, .93 for search problems, and .76 for search + WMproblems. No other effects in this analysis approached signif-icance, all ps > .25, except for a marginal (p = . 10) effect ofblock. Accuracy improved from .86 correct on Block 1 to .88correct on Blocks 2 and 3.

Consistent with previous research, subjects in the random-random group solved problems more quickly {M = 15.03 s)than did subjects in the blocked-blocked group (M = 17.46s). This difference was not significant, however, F{\, 22) =2.43, MS* = 131.6, p = .134. Latency varied as a function ofproblem type, F{2,44) = 202.6, p < .001, and the interactionof problem type and practice schedule, F(2, 44) = 3.1, p =.055, MSC = 195.1. As shown in Figure 5, latencies were

longest for search + WM problems. The longest latencies thuscorrespond to the lowest accuracies, indicating that speed-accuracy trade-offs are not responsible for the effects observedon latency. Subjects who learned the functions in a randompractice schedule solved all types of problems more quickly,but the difference was greatest for the most difficult, search +WM problems. Planned comparisons using Bonferroni t testsshowed that the difference between blocked and randomgroups was significant for the search + WM problems, t -3.57, p < .05, but not for search, / = 1.10, or no-search, / =1.06, problems.

Problem solving latency declined with practice, F(2, 44) =73.0, MSC = 7.972, p < .001, but practice and acquisitioncondition did not interact (F < 1). As shown in Figure 6,there was no evidence that performance for the random andblocked groups converged with problem solving practice.Problem type did interact with practice block, F(4, 88) =13.8, MSC = 5.492, p < .001. This interaction reflects the factthat the greater difficulty of the search + WM problems waslargest early in practice.

No other effects in this analysis approached significance (allps > .25). The latency analysis reported was conducted onlyon data from subjects who experienced the same practiceschedule throughout practice (the blocked-blocked and ran-dom-random groups). Means for the mixed schedule groups(blocked-random and random-blocked) were intermediate inevery case, as is consistent with previous results on motorlearning (Shea, Morgan, & Ho, 1981, cited in Shea & Zimny,1983).

Discussion

The results of Experiment 1 support our major hypotheses,extending previous findings on the contextual interferenceeffect to the domain of cognitive skill. Acquisition perform-ance was substantially faster in blocked than in randompractice schedules, and switching from a blocked to a randomschedule resulted in a large decrement in speed of perform-ance. The difference between blocked and random practice

30

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H 2 BLOCKED-BLOCKED

• 1 RANDOM-RANDOM

NO SEARCH SEARCHPROBLEM TYPE

L J L JSEARCH'WM

Figure 5. Latency (s) for correct responses during transfer as afunction of acquisition condition and problem type: Experiment I.

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a - RANDOM-RANDOM

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Figure 6. Latency (s) for correct responses during transfer as afunction of acquisition condition and practice: Experiment 1,


groups was reversed in the problem solving phase, with therandom-practice group solving problems faster than theblocked-practice group. Although the main effect of acquisi-tion condition on problem solving latency was only margin-ally significant (see Figure 5), an ANOVA using phase (acqui-sition vs. transfer) and acquisition condition (blocked vs.random) as factors verified that the crossover interaction wassignificant, F{1, 22) = 4.6, MSe = 5,940,262, p < .05.

The problem solving advantage of the random-practicegroup was greatest for the most difficult problem type, thesearch + WM problems, which required subjects to maintainand integrate large amounts of information in working mem-ory. The large difference in effect size between search + WMand other problem types (see Figure 5) makes it unlikely thatthe interaction was due simply to the larger number of equa-tions required for solution of the more difficult problems. Ifthe size of the blocked versus random difference was greaterfor search + WM problems only because those problemsrequired the solution of more equations, the size of thedifference divided by the number of equations should beequal for the three problem types. However, the actual differ-ence in problem solving latency for blocked- and random-practice groups was roughly 470 ms per equation in searchproblems but 1,004 ms per equation in search + WM prob-lems. The advantage of random practice thus seems to begreatest for problems that required coordination of multipleworking-memory representations. This result suggests that theadvantage of random practice results from reductions in theworking memory demands of executing component skills, asis consistent with the intratrial processing account.

The benefit of random over blocked acquisition practicefor problem solving did not decline with problem solvingpractice. This surprising result has both theoretical and prac-tical implications, suggesting that component practice sched-ules have lasting effects on the usability of component skills.Experiment 2 provides a further examination of this result.

Experiment 2

Because the main effect of practice schedule on problemsolving performance in Experiment 1 was not significant andbecause the failure of the problem solving practice curves toconverge was unexpected, we conducted a second experimentto verify these effects. Experiment 2 replicated the blocked-blocked and random-random acquisition conditions of Ex-periment 1 exactly. The problem solving transfer phase wasmodified slightly. The simplest (no-search) problems were notincluded, and the remaining two problem types appeared in10 blocks of 10 trials each (5 of each problem type withineach block) in order to provide a more detailed look at theproblem-solving learning curve. Except for this difference inthe number and distribution of problem types, the transferprocedure was identical to that in Experiment 1.

Method

Subjects. Thirty-eight college students recruited from introduc-tory psychology classes at The Pennsylvania Stale University partici-pated in return for extra course credit. All subjects reported normal

or corrected-to-normal vision. Data from 5 subjects were droppedbecause of experimenter error or because their accuracy in the prob-lem solving phase did not exceed the chance level of 50%. This left17 subjects in the blocked practice condition and 16 subjects in therandom condition.

Design and procedure. Subjects were randomly assigned toblocked or random practice schedules. The acquisition phase wasidentical to that for the blocked-blocked and random-random groupsin Experiment 1. The problem solving transfer phase was similar tothat in Experiment 1, except that only search and search + WMproblems were presented. Each of 10 blocks included 5 trials each ofthe two problem types, for a total of 100 trials. In all other respects,the procedure was identical to that in Experiment I.

Results

Acquisition. As in Experiment 1, subjects responded quiteaccurately during acquisition. Subjects in the blocked-practicegroup responded somewhat more accurately (M= .96 correct)than those in the random-practice group {M = .91 correct),F(\, 31) = 12.1, M& = .01265, p < .001. No other effects onproportion correct were significant (p > .25).

As in Experiment 1 s the mean latency for correct responseswas longer for the random-practice group (M = 1,925 ms)than for the blocked-practice group (M = 642 ms), F{\,31)= 152.5, MSC = 712,227, p<. 001. There was a substantialspeedup with practice, F(l, 217) = 111.3, p < .001, and aninteraction of practice schedule with practice block, F\l,217) = 19.2, p < .001; MSe for these tests was 42,319. In thefirst practice block, mean latencies for the blocked and ran-dom-practice groups were 1,203 and 3,066 ms; in the last(eighth) practice block, the mean latencies were 483 and 1,581ms.

Problem solving. As in Experiment 1, subjects maintaineda high level of accuracy during the problem solving transferphase, solving 86.4% of problems correctly. Accuracy wasvirtually identical for the blocked (M = 86.2%) and random{M = 86.6%) practice groups (F < 1). Subjects solved searchproblems more accurately than search+WM problems (A/s =.96 and .77 correct), F([, 31) = 210.6, MSe = 0.026772, p <.001. The difference in accuracy for the two types of problemswas slightly smaller for the random-practice group, F{\,31) = 5.61, MSE = 0.026772, p < .03. No other effects onaccuracy approached significance (all ps > .25).

Subjects in the random-practice group solved problemsmore quickly than those in the blocked-practice group (Afs =13.96 s and 16.90 s. This difference was marginally significant,fU, 31) = 3.66, MSe = 389.7, p = 0.65. As in Experiment 1,an analysis of variance with phase (acquisition vs. transfer)and acquisition condition as factors verified the existence ofa crossover interaction (slower acquisition but faster problemsolving for the random-practice group), F(\, 31) = 7.94, p <.01. Problem type also affected problem solving latency, F(l,31) = 126.5, MSt = 98.32, p < .001. Mean latency was 11.13s for search problems and 19.82 s for search+WM prob-lems. This pattern of results is again inconsistent with aspeed-accuracy trade-off, with the longest latency and lowestaccuracy occurring in the same experimental condition. As inExperiment 1, the difference between problem types wasgreater for the blocked-practice group, but the interaction of


practice schedule and problem type was not significant, /*U,31) = 1.72, MS* = 98.32, p = .20.

As shown in Figure 7, problem solving latency declinedsubstantially with practice, F(9, 279) = 24.9, MSe = 15.2,p < .001. Practice and acquisition condition did not interact,F(9, 279) = 1.06, MS, = 15.2. This result suggests that theselearning curves do not converge, or at least they convergevery slowly. As a further check on this conclusion, we plottedthe learning curves in log-log coordinates and calculated theslopes for the best fitting linear functions. These slopes werevirtually identical, -4.70 for the blocked-practice group and—4.77 for the random-practice group, supporting the conclu-sion that the ability to access and use component skills is noteasily acquired in the problem solving situation.

Discussion

Experiment 2 replicates the major results of Experiment 1.Again, a random practice schedule produced poorer acquisi-tion performance but superior transfer to problem solving.Although the difference in problem solving latency betweenblocked- and random-practice groups was marginally signifi-cant in both experiments, an analysis combining data fromcomparable problem types (search and search+WM) in thetwo experiments verified that the difference between acquisi-tion conditions was significant, F(l, 55) = 5.8, MSC = 295,p = .019.

The results of Experiments 1 and 2 together demonstratethat the effect of acquisition practice schedules on the abilityto use component skills in problem solving is relatively longlasting. This conclusion underscores the theoretical and prac-tical importance of understanding the consequences of taskdemands for access and use of component skills.

The results of the two experiments are consistent with theintratrial processing account of the practice schedule effect.First, the difference between blocked- and random-practicegroups in problem solving latency was greatest for problemsplacing the greatest load on working memory, and this differ-ence could not be accounted for simply by differences in the

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number of equations to be solved. Second, the intratrialprocessing account also predicts that during random practice,performance will be faster on the second of two trials involvingthe same rule because the subject does not have to load adifferent procedure into working memory.1 A comparison oflatencies for the first and second member of such pairs oftrials, combining the random-practice conditions of Experi-ments 1 and 2, confirmed this prediction. Mean latency was2,065 ms for the first member of a pair and 1,854 ms for thesecond member, F(i, 27) = 69.1, MS* = 83,942, p < .001. Asimilar effect was present for accuracy, with a mean propor-tion correct of .895 for the first member of a pair and .911for the second member, F( 1, 27) = 6.1, p < .02, MSe = 0.13.These effects were apparent despite the possibility that somesubjects in random-practice conditions might have adopted astrategy of "dumping" the contents of working memory be-tween trials. The pattern of results in both transfer andacquisition thus implicates differences in the use of workingmemory capacity in the practice schedule effect.

Experiment 3

Experiments 1 and 2 replicate the practice-schedule effectspreviously observed in motor learning (Shea & Morgan, 1979;Lee & Magill, 1983), extending the scope of those observationsto cognitive procedures and to transfer of component skills toproblem solving. The results are also consistent with ourhypothesis that the random-practice benefit in this case canbe accounted for by differences in intraitem processing asso-ciated with the manipulation of practice schedules.

If the intraitem processing account is correct for the presentcase, it should be possible to obtain transfer benefits byintroducing practice manipulations other than a random-practice schedule. In particular, other activities that forcesubjects to load procedures into working memory on eachtrial of blocked practice should produce transfer benefits. Inthis experiment, we therefore employed an intervening-taskacquisition paradigm. Subjects in four experimental condi-tions learned the logic functions in blocked practice schedules,but with other tasks intervening between trials. Our goal wasto find one or more intervening tasks sufficient to producethe transfer benefits observed for random practice in Experi-ments 1 and 2. The intervening tasks all had content quitedissimilar to the logic functions, but they varied in the natureof the cognitive procedures required. Previous research hasdemonstrated that the similarity of to-be-remembered mate-rial (Cuddy & Jacoby, 1982) and the difficulty of interveningtasks (Proctor, 1980) influence the retention of verbal mate-rial. We hypothesized that intervening tasks requiring activeprocessing would produce transfer benefits similar to thoseproduced by random practice.

The transfer benefit of random practice might depend notjust on an intervening activity that clears each procedure fromworking memory between repetitions but also on the similar-ity of the intervening activity to the procedures being learned.In the random-practice conditions of Experiments 1 and 2,

Figure 7. Latency (s) for correct responses during transfer as afunction of acquisition condition and practice: Experiment 2. 1 We are grateful to Lawrence Barsalou for suggesting this analysis.


for example, the activity intervening between repetitions of asingle-logic function was calculation by using other logicfunctions. One condition in Experiment 3 therefore includedan intervening task requiring processing—calculation of arith-metic functions—similar to that required by the logic-func-tion task. If processing similarity from trial to trial is a criticalcharacteristic of random practice in these experiments, thenonly this condition should produce a transfer benefit.

Because recent research on working memory (e.g., Baddeley& Hitch, 1974; Daneman & Carpenter, 1980; Klapp, Marsh-burn, & Lester, 1983) demonstrates that storage and process-ing capacities are separable aspects of working memory, weincluded tasks that involved primarily storage, as well as tasksrequiring active processing. Our hypothesis that the criticalfeature of intraitem processing produced by random practiceis the loading of procedures into working memory on eachtrial, together with the theoretical assumption that storageand processing involve separate aspects of working memorycapacity, led us to the prediction that active processing, butnot storage tasks, would produce a transfer benefit. In addi-tion, the storage tasks were expected to provide a control forthe increased temporal spacing of logic-function trials pro-duced by more active intervening tasks.

Method

Subjects. Fifty-four college students recruited from introductorypsychology classes at The Pennsylvania State University participatedin return for extra course credit. All subjects reported normal orcorrected-to-nonnal vision. Data from 6 subjects were eliminatedbecause of experimenter error or because accuracy in the problemsolving phase did not exceed the chance level of §0%. This left 12subjects in each of four experimental groups.

Acquisition tasks and experimental design. All subjects in thisexperiment received blocked-schedule practice of the Boolean rules,with a secondary task intervening between trials. Four experimentalgroups were defined by the nature of the intervening task: same-different judgment, math verification, short-term memory (STM)task, and long-term memory task (LTM). Figure 8 summarizes thesequence of events on each trial for each of these tasks. Twelvesubjects were randomly assigned to each of these groups. Each trialof each intervening task was designed to require approximately 7.5 s,including time for displaying stimuli, collecting responses, and pro-viding accuracy and latency feedback.

The same-different task required subjects to judge whether twoletters were the same or different On each trial, the pair of letterswas drawn randomly from the possible pairs defined by upper- andlowercase A and B. Subjects were instructed to respond on the basisof a name match; that is, to respond "yes" if the two letters had thesame name, regardless of case. Each display included one upper- andone lowercase letter to ensure that responses were always based onname matches. Over trials, equal numbers of positive and negativepairs appeared. Three same-different trials appeared between eachpair of logic-function trials. This task requires controlled retrieval ofletter names from long-term memory and comparison of perceptualand memory representations. These processing demands should besufficient to clear procedures from working memory between trials,so that a transfer benefit will be produced only if the random-practiceadvantage depends primarily on intratrial processing. If, however,that advantage depends on the similarity of the intervening processesto those required by the logic-function task, then there should be noadvantage.

same-diff

ACQUISITION CONDITION

math stm(begin trial]

Itm

(yes/no}

B b[yes/not

(yes/no)

A A

T

M

K

R

farm

bird

{yes/noi X - #{1,1)

[respond 0 or 1}lend of block

only]

TMRK farm

{yes/nol {yes/no]

Figure 8. Intratrial sequence of events during acquisition: Experi-ment 3. (Time runs from top to bottom, and the four columnsrepresent the four intervening tasks. The Boolean equation displaywas identical for all groups. Diff = different; stm = short-termmemory; Itm - long-term memory.)

The math task required subjects to evaluate the answer to a three-digit addition problem. The addends were selected randomly, withthe constraint that carrying was required for at least one column. Onhalf of the trials, a correct sum was displayed. On the other half oftrials, the displayed sum differed by plus or minus one in one column.A single addition problem was presented between each pair of trials.The processing demands of this task should be similar to those of thesame-different task, with the addition of calculation procedures(arithmetic rules) similar to those needed for the logic-function task.If the random-practice advantage depends on the similarity of pro-cedures used on successive trials, then this condition might producea transfer benefit not present in the same-different condition.

In the STM task, a memory set consisting of four consonants wasdisplayed. The letters in the memory set appeared sequentially, at arate of 1 per s. After each logic-function trial, memory for the previousmemory set was tested. A string consisting of the four letters fromthe memory set appeared, and the subject pressed one of two keys toindicate that the sequence matched or did not match the order inwhich the memory set was presented. On half of the trials a correctsequence was presented, and on half of the trials the sequence wasrandomized. Accuracy and (for correct responses) latency feedbackwas displayed for 1 s. The subject then initiated the display of thenext memory set. Although it is obviously not correct to regard thistask as requiring only storage and no active processing, it is similarto the standard tasks shown to be separable from active processingcapacity (Baddeley & Hitch, 1974; Daneman & Carpenter, 1980;Klapp et al., 1983), This task therefore ought to produce a transferbenefit only if the random-practice advantage depends primarily onthe storage demands of intervening trials.

In the LTM task, two common four- or five-letter words to beremembered for a later recognition test appeared on each trial. Each


word was displayed for approximately 2 s, preceded by a 500-msblank delay. A 1-s blank delay followed the second word, for a total7.5-s interval between logic-function trials. During each block of 48logic-function trials, a total of 32 words was presented. Each wordtherefore appeared three times during the block. Subjects made noresponses to this task during the logic-function blocks, but theyreceived a 10-trial recognition test at the end of each block. On eachtrial of the recognition test, a single word appeared, and the subjectpressed a key to indicate whether the word had appeared as a studyitem or not. Half of the words had appeared, and half had not. Thistask was not expected to produce a transfer advantage because thetwo items appearing on each trial do not approach the limits ofworking memory and do not require substantial active processing.However, if the temporal spacing of practice trials is the critical factorin producing the random-practice advantage, this condition shouldbe equivalent to the other conditions (and superior to blocked practicein Experiments 1 and 2).

Procedure. Each subject participated in an individual sessionlasting approximately 2 hr. After a brief introduction and an informedconsent procedure, the experimenter described the acquisition andintervening tasks. Instructions stressed the importance of respondingquickly and accurately to both logic-function and intervening tasks.The acquisition procedure was similar to that in the blocked-practiceconditions of Experiments 1 and 2, except that the acquisition phasebegan with eight trials of practice on the intervening task alone. Asin Experiments 1 and 2, each subject received eight blocks of practice,with 48 trials in each block. The arrangement of practice blocks wasidentical to that in Experiments 1 and 2, with the order of rulescounterbalanced over subjects and the rule sequence of the first fourblocks repeated on the second four blocks. The problem solvingtransfer phase was identical in all respects to that in Experiment 1.

Results and Discussion

Logic-function acquisition. Overall, subjects respondedcorrectly on 95.0% of logic-function acquisition trials. Accu-racy varied as a function of condition, F(3, 44) = 5.04,MSt - 0.008802, p < .01. Mean proportion correct was .92for the same-different group, .97 for the LTM group, .94 forthe math group, and .96 for the STM group. No other effectson proportion correct approached significance (all ps > .25).

Latency for correct responses was almost identical for allconditions, F(3, 44) = 0.81, as shown in Figure 9. Latencydeclined substantially with practice, F(7, 308) = 109.3,MSe = 42,420, p < .001, but practice did not interact withacquisition condition, F(21, 308) = 1.35,;? = . 14. The overallmean latency, 941 ms, was much closer to the mean forblocked practice in Experiments 1 and 2, 692 ms, than to themean for random practice in those experiments, 1,771 ms.

Intervening task performance. Subjects in all groups main-tained high levels of accuracy in the intervening tasks, asshown in Figure 10. There was little variability in intervening-task accuracy as a function of practice, and latency for correctresponses declined slightly with practice for each task. Theproportion of decline in latency ranged from .14 for the same-different task to .34 for the STM task. As expected, the longestlatency was observed for the math task.

For the LTM task, which required subjects to respond tothe secondary task only between blocks, the interval betweenlogic-function trials was fixed at 7.5 s. For the remainingtasks, this interval depended on the latency of subjects' re-

2000

1500

1000

500

INTERVENING TASK

-*" SAME-DIFF

-Q- STM

X MATH

- £ - LTM

1 2 3 4 5 6 7 8PRACTICE BLOCK

Figure 9. Latency (ms) for correct responses as a function of con-dition during acquisition: Experiment 3.

sponses to the intervening tasks, and in pilot work we at-tempted to develop tasks that would approximately matchthe fixed interval of the LTM task. The observed meanintervals were 8,189 ms for the STM task, 7,573 ms for thesame-different task, and 4,667 ms for the math task. Theinterval between logic-function trials was thus approximatelyequal for three of the experimental conditions but was some-what shorter for the math condition because the subjects inthis study performed the math task substantially faster thandid our pilot subjects.

Problem solving transfer. Once again, problem solving wasquite accurate. Overall, subjects gave correct answers to 88.6%of problems. Accuracy did vary as a function of acquisitioncondition, F(3, 44) = 3.61, MSe = 0.017630, p < .03. Meanproportion correct was .85 for the same-different condition,

l_ATENCY

-

MS

500046004000350030002500200015001000500

0

1

0.8

0.6

0.4

0.2

2 3 4 5 6PRACTICE BLOCK

- * - S-D RT

- * - S-D p(c)

INTERVENING TASKQ MATH RT * STM RT -*

- * - MATH p(ct*~ STM p(c)^

*- LTM RT

t- LTM p(c>

Figure 10. Latency (ms) for correct responses to intervening tasks:Experiment 3. (Latencies for the same-different task are means forindividual responses, averaged over the three responses required oneach trial. S = same; D = different; RT = reaction time; p(c) =percent correct; STM = short-term memory; LTM = long-termmemory.)


.88 for the STM condition, .89 for the math condition, and

.91 for the LTM condition. Newman-Keuls tests revealed thatthis effect was due to the same-different group respondingwith somewhat lower accuracy than the other three groups(p < .05), which did not differ significantly from one another.Accuracy also varied as a function of problem type, F(2,88) = 122.1, MS. = 0.01356, p < .001. Mean proportioncorrect was .95 for no-search and search problems and .76 forsearch+WM problems. No other effects on problem solvingaccuracy approached significance (p > .25).

Acquisition condition had a significant effect on problemsolving latency, F(3,44) = 5.18, MSC = 103.0, p < .01. Latencydeclined substantially with practice, F\2, 88) = 102.3, MSC ~16.02,/? < .001, but practice did not interact with acquisitioncondition, F(6, 88) = 1.53, MS. = 16.02, /J = .18. Theseeffects are displayed in Figure 11. Subjects in the same-different and math conditions solved problems faster thansubjects in the STM or LTM conditions. Newman-Keuls testsconfirmed that latencies for the same-different and mathconditions differed significantly (p < .05) from those for theSTM and LTM conditions and that tasks within these pairsof conditions did not differ from one another.

The blocked-blocked condition from Experiment 1 pro-vides a comparison group for assessing the effects of interven-ing tasks. Subjects in that condition received practice identicalin amount and distribution to that presented in Experiment3, but without intervening tasks between logic-function trials.The number and distribution of transfer problems were alsoidentical in the two experiments. Figure 12 illustrates thiscomparison. Bonferroni / tests verified that the same-different(r = 3.48, p < .05) and math (t = 4.95, p < .05) groups solvedproblems significantly faster than the blocked-practice groupfrom Experiment 1. However, mean problem solving latenciesfor the STM (t = 2.04, p > .05) and LTM (t = 0.12, p > .05)groups did not differ significantly from that for the blocked-practice group from Experiment i. As Figure 12 shows, theSTM group was slower than the blocked-practice group,though not significantly so. Figure 12 also provides a com-parison with the mean latency for the random-random group

30

25

LA

I »NC

10

ACQUISITION

- * - SAME-DIFF

•a S T M

* MATH

- $ - LTM

PRACTICE BLOCK

Figure 11. Latency (s) for correct responses during transfer as afunction of acquisition condition and practice: Experiment 3. (DifT= different; STM = short-term memory; LTM = long-term memory.)

20

15LATENC 10Y

• • ]

I ] i !

i

!

] j 1 t 1

BLOCKED RANDOM

EXPERIMENT 1

SAME-DIFF STM MATH

EXPERIMENT 3

.....l I

LTM

Figure 12. Latency (s) for correct responses during transfer as afunction of acquisition condition, Experiment 3, compared withblocked practice acquisition, Experiment 1. (Diff = different; STM= short-term memory; LTM = long-term memory.)

from Experiment 1. Bonferroni t tests showed that the prob-lem solving latencies for the same-different (t = 0.37, p >.05) and math (t = 0.95, p > .05) groups did not differ fromthose of the random-practice group, whereas the STM (t -5.35, p < .05) and LTM (f = 3.40, p < .05) groups weresignificantly slower.

The present data thus demonstrate that two of the interven-ing tasks (same-different and math) were sufficient to producea transfer benefit relative to a standard blocked practiceschedule. Other intervening tasks (STM and LTM) that re-sulted in similar temporal spacing between logic-functiontrials were not sufficient to produce a transfer benefit. Thisconclusion must be qualified by noting that some of thetransfer benefit observed for the same-different group mightbe due to a speed-accuracy trade-off; as noted above, thesame-different group answered problems with somewhatlower accuracy than the other groups.

Problem type again had a substantial effect on problemsolving latency, F\2, 88) = 199.6, MSC = 319.5, p < .001.This effect interacted with acquisition condition, F\6, 88) =2.55, MSC = 319.5, p < .03. The differences between acquisi-tion conditions were greater for the more difficult problems,as shown in Figure 13. Bonferroni t tests showed that theacquisition conditions did not differ significantly (p > .05)for no-search problems, and only the fastest (math) andslowest (STM) groups differed {p < .05) for search problems.For search+WM problems, however, the math and same-different groups differed significantly (p < .05) from the STMand LTM groups, whereas the two members of each pair ofgroups did not differ (p > .05). Thus, the transfer benefit ofsame-different or math tasks intervening between logic-func-tion transfer trials was apparent primarily for problems thatinvolved a substantial working memory load. This result isimportant because it demonstrates that the problem solvingadvantage is qualitatively similar to that observed in Experi-ment 1. As in Experiments 1 and 2, the lowest accuracy andlongest latency (for search+WM problems) corresponded, a


35

30

k 25

N 2 °CY 15

10

PROBLEM TYPE

; i NO SEARCH

• 1 SEARCH

l'~] SEARCH»WM

SAME-DIFF STM MATH

INTERVENING TASKLTM

Figure 13. Latency (s) for correct responses during transfer as afunction of acquisition condition and problem type: Experiment 3.(Diff = different; STM = short-term memory; LTM = long-termmemory; WM = working memory.)

finding that argues against an explanation in terms of a speed-accuracy trade-off.

General Discussion

The present results replicate the effect of practice schedule(blocked vs. random) previously observed for the acquisitionof motor skills (e.g., Shea & Morgan, 1979). Random practicewith Boolean logic functions produced poorer acquisitionperformance than did blocked practice, but problem solvingwith those functions was faster for subjects who receivedrandom practice during acquisition. These results extend thefindings of previous research in two ways. First, they dem-onstrate the effect of practice schedule on a procedural cog-nitive skill, calculation of logic functions. Second, they dem-onstrate that the superior transfer produced by random prac-tice occurs in the transfer of component skills to a problemsolving situation. Experiment 3 demonstated that two inter-vening tasks—same-different judgments and math—inblocked practice were sufficient to produce a benefit in thetransfer of component skills to problem solving that was bothquantitatively and qualitatively similar to the benefit pro-duced by random practice. This result is consistent with theintraitem processing account of the practice schedule effect inthis situation and with our suggestion that loading proceduresinto working memory is an important aspect of this process-ing.

Random Practice and Transfer to Problem Solving

It is perhaps unsurprising that a practice schedule requiringthe use of component skills in random order produces supe-rior transfer to a problem solving situation that requires accessand use of those skills in varying sequences. However, it doesappear paradoxical that superior transfer occurs even thoughacquisition performance is much poorer in a random practiceschedule (Battig, 1979). Also puzzling is the very slow con-vergence of problem solving practice curves (Figures 6, 7, and

11) for different acquisition conditions. The problem solvingtask should provide component practice similar to the randomacquisition schedule (because each problem requires the useof several different rules), and the total number of equationsneeded to solve the problems (300 in Experiments 1 and 3,350 in Experiment 2) is a substantial fraction of the practiceprovided in the acquisition phase (384 total trials). Becauserandom practice following initial blocked practice does seemto be effective in producing retention and transfer benefits(Shea & Zimny, 1988), this result suggests that other demandsof problem solving somehow prevented subjects from achiev-ing the full benefits of this additional practice.

The transfer advantage of random practice (and of thesame-different and math intervening-task conditions in Ex-periment 3) was greatest for the most difficult problems. Thiseffect is not due simply to the larger number of equationsrequired in the most difficult problems because the random-practice advantage was more than doubled for thesearch+WM problems, even when calculated in terms of timeper equation. This result suggests an interpretation of thepractice-schedule effect in terms of the ability to coordinaterepresentations and procedures in working memory (Carlsonet al., 1989a; Logan, 1985). The hypothesis that the need toload procedures into working memory- on each trial is animportant aspect of the processing evoked in random practiceis supported by the observation that when functions wererepeated on consecutive trials in random practice, perform-ance was significantly faster and more accurate on the secondrepetition.

Processing Demands and Part- Whole Transfer

The results of Experiment 3 provide support for the viewthat differences in intratrial processing are responsible for thepractice-schedule effects observed in Experiments 1 and 2.Two of the intervening tasks used in blocked practice—same-different judgments about letter names and verification ofaddition problems—produced transfer benefits (relative toblocked practice without intervening tasks). These tasks re-quired subjects to retrieve information from long-term mem-ory and to coordinate it with displayed information in orderto make judgments, presumably as did the processing requiredfor logic-function trials. If close similarity of processing wascritical to this effect, however, then only the math task—which, like the logic-function task, required calculation—should have produced a transfer benefit. The fact that bothtasks produced transfer benefits suggests that clearing thelogic-function procedure from working memory, thus requir-ing that it be reloaded for the next trial, was the importantaspect of the same-different and math tasks. Two otherintervening tasks—holding a short-term memory load duringa logic-function trial and studying information for a later testof long-term memory—produced transfer performance simi-lar to blocked-practice schedules in Experiments 1 and 2. Thisresult is important for two reasons: First, it supports our viewthat active manipulation of representations in working mem-ory, rather than more passive storage or retrieval factors, isthe critical factor in the random-practice advantage. Second,it provides evidence that the temporal spacing of trials with


the same function is not the cause of the random-practiceadvantage because the interval between logic-function trialswas comparable for intervening tasks that did and did notproduce transfer benefits.

These considerations suggest that the correct explanationfor the present transfer results should rely more on the intra-item processing mechanism emphasized by Jacoby (1978) andLee and Magill (1983) than on the relational interitem proc-essing mechanism emphasized by Shea and Zimny (1983,1988). That is, a feature of random practice sufficient forproducing the transfer advantage observed here is that theprocedure for applying a particular rule is cleared from work-ing memory by intervening trials with other rules. Withineach trial, then, subjects must reload into working memorythe appropriate procedure for the logic function presented onthat trial.

We would suggest, however, that both intraitem and inter-item processing mechanisms are needed to account for theentire pattern of results observed in acquisition and transfer.The intervening-task paradigm used in Experiment 3 pro-duced (for same-different and math intervening tasks) sub-stantial transfer benefits without producing the large decre-ment in acquisition performance produced by random prac-tice. It therefore seems unlikely that the same explanation canaccount for both the slower performance during random-practice acquisition and the transfer benefit of random prac-tice. We see two possible explanations for this pattern ofresults. First, differences in interitem processing might ac-count for the slower acquisition performance by random-practice groups, whereas differences in intraitem processingmight account for the observed transfer benefit. In a problemsolving situation that places a greater premium on choosingwhich rule to use at each step—perhaps problems in which awider range of operators might apply—our intervening-taskprocedure might not be sufficient to produce a transfer benefitcomparable to that produced by random practice. A secondpossibility is that we have observed transfer benefits due totwo sources: (a) differences relative to blocked practice ininteritem processing in Experiments 1 and 2, and (b) differ-ences relative to blocked practice in intraitem processing inExperiment 3. Both explanations, however, depend on theassumption that differences in intraitem processing are suffi-cient to produce transfer benefits. These differences in intrai-tem processing appear to involve differences in the use ofworking memory. The main point of our theoretical argu-ment, then, is that one locus of the contextual interferenceeffect is the ability to efficiently load procedures into workingmemory.

The present results also contribute to the large literature ontransfer of learning (Cormier & Hagman, 1987), particularlywith respect to the issue of part-whole transfer (Wightman &Lintern, 1985). Although much of the research on part-wholetransfer has been concerned with perceptual-motor skills andhas been applied rather than theoretical in focus (Wightman& Lintern, 1985), recent work on cognitive skills providessome basis for predictions about transfer. In production-system models like Anderson's (1987) ACT*, transfer dependson the ability to use identical productions in acquisition andtransfer settings. In this view, part-whole transfer depends

largely on the similarity of information in working memorywhen productions are to be executed in acquisition and intransfer, so that the conditions of appropriate productionscan be matched in both cases. Anderson (1989) explained thepoorer performance during random practice by noting thatrandom practice—unlike blocked practice—requires produc-tions with conditions that discriminate among rules. Thisexplanation is consistent with the relational interitem proc-essing hypothesis, but it is not clear that this hypothesis couldaccount for the benefit of same-different and math (but notSTM or LTM) intervening tasks in blocked practice. Clearingworking memory with an intervening task might require thatrules be retrieved from long-term memory (which may requiremore discriminative cues).2 But the STM task also ought tointerfere with storage of the declarative information used tomatch the conditions of productions. Thus it seems thatcurrent production-system accounts of transfer should besupplemented by something like the intratrial processingmechanism described above.

The present results suggest an emphasis on the proceduresused to load and apply procedures in working memory, ratherthan on the content of working memory. This emphasis isconsistent with other recent work on woiking memory andon the conditions for transfer. Daneman and Carpenter (1980,1983), for example, have demonstrated that performance ona complex task—reading comprehension—can be predictedfrom performance on a working memory task involving bothprocessing and storage but cannot be predicted from short-term memory tasks involving only storage. Similarly, Klappet al. (1983) have demonstrated that short-term storage andprocessing capacity can be experimentally separated. In the-oretical work on transfer, Schneider and Detweiler (1988)have argued that single-task practice is often ineffective inproducing transfer to dual-task situations because compensa-tory activities are needed to manage and coordinate the work-ing memory demands of dual-task performance. These com-pensatory activities include efficient loading of proceduresinto working memory. Although the problem solving tasks inthese experiments did not require concurrent processing ofmultiple rules, a similar analysis might be applied. Randompractice or appropriate intervening tasks may benefit transferby providing practice at loading procedures into workingmemory.

Cognitive and Motor Skills

One striking aspect of the present results is the similarity ofthe effects of practice schedules on the acquisition of motorskills (e.g., Lee & Magill, 1983; Shea & Morgan, 1979; Shea& Zimny, 1983, 1988) and the cognitive procedural skillsstudied here. This consistency across domains fits well withthe emphasis on cognitive factors in explaining contextualinterference effects in the acquisition of motor skills (e.g.,

1 This possibility was suggested to us by Lawrence Barsalou.


Shea & Zimny, 1988). Perhaps more important, the presentfindings contribute to the growing evidence that skill acqui-sition and skilled performance in perceptual, cognitive, andmotor domains share underlying mechanisms (e.g., MacKay,1987; Rosenbaum, 1987). A general theory of human learningand skill may follow from research informed by findings that,like the present ones, generalize across domains.

Conclusion

The present study demonstrates that the processing contextin which cognitive component skills are acquired is importantin determining the ability to transfer those skills to problemsolving situations. Our interpretation of these results has ledus to focus on the ability to access and use component skillsfluently, rather than on the more often studied ability tochoose appropriate operators (e.g., Lewis & Anderson, 1985).Understanding the acquisition of problem solving skill willrequire understanding both of these aspects of cognitive skill.

References

Anderson, J. R. (1987). Skill acquisition: Compilation of weak-method problem solutions. Psychological Review, 94, 192-210.

Anderson, J. R. (1989). Practice, working memory, and the ACT*theory of skill acquisition: A comment on Carlson, Sullivan, andSchneider (1989). Journal of Experimental Psychology: Learning,Memory, and Cognition, 15, 527-530.

Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H.Bower (Ed.), The psychology of learning and motivation (Vol. 8,pp, 47-89). New York: Academic Press.

Battig, W. F. (1979). The flexibility of human memory. In L. S.Cermak & F. I. M. Craik (Eds.), Levels of processing in humanmemory (pp. 23-44). Hillsdale, NJ: Erlbaum.

Carlson, R. A. (1989). Processing nonlinguistic negation. AmericanJournal of Psychology, 102, 211-224.

Carlson, R. A., & Schneider, W. (1989). Acquisition context and theuse of causal rules. Memory & Cognition, 17, 240-248.

Carlson, R. A., Sullivan, M. A., & Schneider, W. (1989a). Componentfluency in a problem solving context. Human Factors, 31, 1-14.

Carlson, R. A., Sullivan, M. A., & Schneider, W. (1989b). Practiceand working memory effects in building procedural skill. Journalof Experimental Psychology: Learning, Memory, and Cognition,15, 517-526.

Cormier, S. M, & Hagman, J. D. (Eds.). (1987). Transfer of learning:Contemporary research and applications. San Diego: AcademicPress.

Cuddy, L. J.,&Jacoby, L. L. (1982). When forgetting helps memory:An analysis of repetition effects. Journal of Verbal Learning andVerbal Behavior, 2J, 451-467.

Daneman, M., & Carpenter, P. A. (1980). Individual differences inworking memory and reading. Journal of Verbal Learning andVerbal Behavior, 19, 450-466.

Daneman, M, & Carpenter, P. A. (1983). Individual differences inintegrating information between and within sentences. Journal ofExperimental Psychology: Learning, Memory, and Cognition, 9,561-584.

Hintzman, D. L. (1974). Theoretical implications of the spacingeffect. In R. L. Solso (Ed.), Theories in cognitive psychology: TheLoyola symposium (pp. 77-99). Potomac, MD: Erlbaum.

Jacoby, L. L. (1978). On interpreting the effects of repetition: Solvinga problem versus remembering a solution. Journal of Verbal Learn-ing and Verbal Behavior, 17, 649-667.

Klapp, S. T., Marshburn, E. A., & Lester, P. T. (1983). Short-termmemory does not involve the "working memory" of informationprocessing: The demise of a common assumption. Journal ofExperimental Psychology: General, 112, 240-264.

Lee, T. D., & Magill, R. A. (1983). The locus of contextual interfer-ence in motor-skill acquisition. Journal of Experimental Psychol-ogy: Learning. Memory, and Cognition., 9, 730-746.

Lewis, M. W., & Anderson, J. R. (1985). Discrimination of operatorschemata in problem solving: Learning from examples. CognitivePsychology, 17,26-65.

Logan, G. D. (1985). Skill and automaticity: Relations, implications,and future directions. Canadian Journal of Psychology, 39, 367-386.

MacKay, D. G. (1987). The organization of perception and action.New York: Springer-Verlag.

Proctor, R. W, (1980). The influence of intervening tasks on thespacing effect for frequency judgments. Journal of ExperimentalPsychology: Human Learning and Memory, 6, 254-266.

Rosenbaum, D. A. (1987). Successive approximations to a model ofhuman motor programming. In G. H. Bower (Ed.), The psychologyof learning and motivation (Vol. 21, pp. 153-182). San Diego:Academic Press.

Schneider, W. (1988). Micro Experimental Laboratory: An integratedsystem for IBM PC compatibles. Behavior Research Methods,Instruments. & Computers, 20, 206-217.

Schneider, W., & Delwciler, M. (1988). The role of practice in dual-task performance: Toward workload modeling in a connectionist/control architecture. Human Factors, 30, 539-566.

Shea, J. B., & Morgan, R. L. (1979). Contextual interference effectson acquisition, retention, and transfer of a motor skill. Journal ofExperimental Psychology: Human Learning and Memory, 5, 179-187.

Shea, J. B., & Zimny, S. T. (1983). Context effects in memory andlearning movement information. In R. A. Magill (Ed.), Memoryand control of action (pp. 345-366). Amsterdam: North-Holland.

Shea. J. B,, & Zimny, S. T. (1988). Knowledge incorporation inmotor representation. In O. G. Meijer & K. Roth (Eds.), Complexmovement behavior: 'The' motor-action controversy (pp. 289-314).Amsterdam: North-Holland.

Wightman, D. C, & Lintern, G. (1985). Part-task training for track-ing and manual control. Human Factors, 27, 267-283.

Received June 26, 1989Revision received October 19, 1989

Accepted October 30, 1989 •

Documents

Journal of Experimental Psychology: 1990. Vol. 16, No. 3 ...Richard Carlson, Department of Psychology, 613 Moore Building, Pennsylvania State University, University Park, Pennsylvania