Metcalfe Kornell 2005

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A Region of Proximal Learning model of studytime allocationq

Janet Metcalfe*, Nate Kornell

Department of Psychology, Columbia University in the City of New York, New York, NY 10027, USA

Received 1 September 2004; revision received 6 December 2004Available online 2 February 2005

Abstract

A Region of Proximal Learning model is proposed emphasizing two components to peoples study time allocation,controlled by different metacognitive indices. The first component is choice, which is further segmented into two stages:(1) a decision of whether to study or not and (2) the order of priority of items chosen. If the peoples Judgments ofLearning (JOLs) are sufficiently high that they believe they know the items already, they will choose to not study. Ifthey do choose to study, the order is from that which they believe is almost known to that which they believe is moredifficult (high JOL to low JOL). The second component is perseverance, with emphasis on the rule for stopping studyingonce study has begun on an item. We propose that people use a previously unexplored process-oriented metacognitivemarker: their judgments of the rate of learning (jROLs), to decide when to stop. When learning is proceeding quicklyand the jROL value is high they continue studying. When the jROL approaches zero, and their subjective assessment

indicates learning is at a standstill they stop. The extant literature bearing on this model is reviewed, and eight newexperiments, all of which support the model, are presented. 2005 Elsevier Inc. All rights reserved.

Keywords: Metacognition; Study-time allocation; JOL; jROL; Model

The manner in which our metacognitions enable usto shape and modulate our own knowledge acquisitionand impact upon the dynamics of what and how welearn is central to human cognition. At the same time

as progress continues in our understanding the condi-tions, constraints, and mechanisms underlying peoplesmetacognitions (Dunlosky & Nelson, 1992; Hertzog,Dunlosky, Robinson, & Kidder, 2003; Kimball & Met-

calfe, 2003; Koriat, 1993, 1994; Koriat & Goldsmith,1996; Koriat & Levy-Sadot, 2001; Koriat, Sheffer, &Maayan, 2002; Maki & Berry, 1984; Metcalfe, 1993a,1993b, 1998; Metcalfe, Schwartz, & Joaquim, 1993;

Metcalfe & Shimamura, 1994; Miner & Reder, 1994;Nelson & Narens, 1990, 1994; Reder, 1988; Schwartz& Metcalfe, 1992, 1994; Schwartz & Smith, 1997; Spell-man & Bjork, 1992; Thiede, 1999), we are witnessing ashift in interest towards the consequences of these meta-cognitions (Mazzoni & Cornoldi, 1993; Metcalfe, 2002;Metcalfe & Kornell, 2003; Reder & Ritter, 1992; Thiede& Dunlosky, 1999). But, although there has been anincreasing focus on how people use metacognitions toalter their study behavior and exert control over their

0749-596X/$ - see front matter 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.jml.2004.12.001

q This research was supported by National Institute ofMental Health Grant MH60637. We thank Lisa Son andBridgid Finn for their help and comments.

* Corresponding author.E-mail address: [email protected](J. Metcalfe).

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own future learning and memory, no coherent answerconcerning how metacognitions guide our study behav-ior has yet emerged. Indeed, the dominant answer, theDiscrepancy Reduction model (Dunlosky & Hertzog,1998; and see Dunlosky & Thiede, 1998; Hyland, 1988;Koriat & Goldsmith, 1996; Le Ny, Denhiere, & Le Tai-

llanter, 1972; Lord & Hanges, 1987; Nelson & Narens,1990; Powers, 1973; Thiede, Anderson, & Therriault,2003; Thiede & Dunlosky, 1999) appears to be unableaccount for recent data. We will propose an alterna-tivea Region of Proximal Learning modeland showhow it can both account for the data that gave rise to theDiscrepancy Reduction model in the first place, and alsopredict the new data. In addition, the Region of Proxi-mal Learning model is not trapped by the paradoxapparent in the Discrepancy Reduction model: if peoplestudy appropriately, as given by that model, they willspend an inordinate, perhaps an unlimited, amount of

time trying to learn items that may be unlearnable. Theyare doomed to labor in vain.

The notion that people have a region in which learn-ing can be optimized, and that they choose to studywithin it, is intuitive. It also squares with theories of hu-man learning proposed by such distinguished research-ers as Atkinson (1972), Berlyne (1978), Piaget (1952),Vygotsky (1987), and Hebb (1949). However, the heuris-tics that people use to hone in on this region have notbeen delineated. We outline, here, the underpinnings ofa metacognitively guided Region of Proximal Learningmodel, outlining some of these most important heuris-tics. First, though, we briefly summarize the alternativeDiscrepancy Reduction model.

In the Discrepancy Reduction model, and relatedtheoretical positions, such as the monitoring-affects-control proposal ofNelson and Leonesio (1988), peopleare thought to focus their study on those materials thateither are, or are thought to be, most difficult. It is nota-ble that this idea is similar to that used in the popularparallel distributed processing models (Rumelhart &McClelland, 1986) which attack the largest errors first.Negative correlations between choice or study timeand judged difficulty are taken to be data favoring theDiscrepancy Reduction model. According to the model,

people are thought to continue to study until they reachan internal criterion of learning. As Thiede and Dunlo-sky (1999) put it: An item will continue to be studied(either through selection or through continued alloca-tion of study time) until the persons perceived degreeof learning meets or exceeds the norm of study (p.1024). Reaching this criterion of learning takes longerthe more difficult are the to-be-learned items.

There are four implications of this model: first, it pre-dicts a negative correlation between study time alloca-tion and judgments of learning: low judgments oflearningindicating that the individual does not know

the itemshould be associated with both priority of

choice and longer study. Second, such a negative corre-lation indicates appropriate metacognitively guidedstudy time allocation, and the larger the negative corre-lation, according to this model, the better the metacog-nitively guided control. Third, like the Region ofProximal Learning model, that will be detailed shortly,

and perhaps other models as well, given that study-timeallocation is assumed to be appropriately controlled by

judgments of learning, it is essential that people be ableto make accurate JOLs. If their judgments are faulty,then they should study inappropriately, resulting in poorlearning. Fourth, insofar as the rule used to stop study-ing is attainment of an internal criterion of learning, ifpeople held to this model, and an item were unlearnable,they could, in principle, study for an unlimited amountof time (the labor in vain paradox). We next presentthe proposed alternative.

The Region of Proximal Learning model

In the Region of Proximal Learning model, there aretwo separable components to human study time alloca-tion: choice and perseverance. It is important to distin-guish between them insofar as they are guided bydifferent metacognitive markers. In the choice stage peo-ple decide which items they will study, and in which or-der. In the perseverance stage the question is: how long,once they have started studying a particular item shouldthey continue before switching to another item? Noticethat the perseverance question, as we frame it, is notwhether or not the goal has been attained, but ratherwhether study, at the present time, is having sufficientlybeneficial results. This change in perspective will allowthe model to cut through the labor-in-vain paradox.

Choice. The choice stage can be divided into twosubstages. The first is to determine which items arecandidates for study, or equivalently, which items peo-ple need not bother studying. It is proposed that ifpeople assess that they already know an item they willchoose not to study it. The second substage involvesorder determination of those items that will be studied.When determination of order is encouraged or allowed

by the experimental situation, the model proposes thatpeople will opt to study the easiest as yet unlearneditems first (items that are easy pickings), turning tomore difficult items only later. Of course, if all ofthe items must be learned and time is unlimited, peo-ple may choose all of the items, but we posit that theywill still tend to prioritize from easy to difficult if theycan.

This two-part choice heuristic is not inconsistent withnegative correlations between JOLs and choice order.However, if a negative correlation is observed, it occursentirely because of the first stagebecause people de-

cline to study those very high JOLs that they believe they

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know already. The second stage should produce a posi-tive, not a negative, correlation. The magnitude of thenegative correlation between JOL and study choice doesnot indicate goodness of metacognitive control in thismodel, as it does in the Discrepancy Reduction model.Indeed, depending on the proportion of items already

known, the correlation between JOL and appropriatestudy choice might be negative, zero, or positive, in thismodel. This is not to say that one cannot assess whetherpeople are exerting good metacognitive control: this cor-relation should behave in a principled way. It should benegative when many items are known (or thought to beknown), just because people should decline to study thealready known items, and this fact, in itself, will producea negative correlation. However, when few or no itemsare known to the participant the correlation should bepositivereflecting the fact that choice is proposed togo in the order easiest to hardest, among those items

that are not already learned.Perseverance. We propose that people base the deci-

sion to stop on the perceived rate at which learning isproceeding. When they perceive that they are learningat a rapid rate, they continue. When they perceive thatthey are no longer taking in informationthat learningis going nowherethen they stop studying a given itemand switch to another. We call this newly posited meta-cognition a judgment of the Rate of Learning (jROL),and emphasize that it refers to the monitoring of an ac-tive processthe speed of information intakeratherthan to a static state of knowledge. The jROL is thederivative of an online JOL function over time. Peoplecontinue studying when they have a high jROL (they feelthemselves on a ROL); they stop when their jROLs ap-proach zero, or some low criterion value.

Although the jROL hypothesis may sound odd atfirst, and although there are no data (other than thosewe will present shortly) that bear on it, in other areasof studywhich share an analogous problem of deter-mining when an animal should stop doing what theyare doing and turn to something elsesimilar ideas haveemerged. For example, in foraging models, the stop ruleis to discontinue feeding in a particular location once therate of food intake at that patch declines (Stephens &

Krebs, 1986). That the perceived rate of learning con-trols whether people persist in or defer from furtherstudying is consistent with the idea that people act asinformation foragers (see, Pirolli & Card, 1999; Weber,Shafir, & Blais, 2004). Similarly, the idea of diminishingreturns is common in economic models, and is a reasonfor switching (or selling). Interestingly, Dunlosky andThiede (1998), in a paper interpreted as providing basicsupport for the discrepancy reduction view, and the stoprule therein (but which also underlined some limitationsof that view) mentioned, in the penultimate paragraph,an alternative possibility in which the stopping

rule may be a function of perceived rate of learning

(p. 54). This alternative is just like the jROL idea, pro-posed here. They further noted that this possibility pro-vides a plausible alternative to the kinds of discrepancy-reduction model that dominate theory of metacognitivecontrol (p. 55). Finally, Carver and Scheier (1990) alsopoint to the rate of discrepancy reduction as a major

determinant of peoples affect.jROLs may approach zero (or some other, partici-

pant defined, and/or situationally modifiable stoppingcriterion) for different reasons: (1) once an item islearned; insofar as no further learning is possible, the

jROL goes automatically to zero. This is an obviouscase. (2) When as much learning as can occur, immedi-ately, has already occurred, even though a subsequenttest may show that the item is not yet really learned,the jROL approaches zero. This case is interesting. Iflearning at time t has reached an asymptote such thatfurther immediate study is having no effect then the

model suggests that further immediate practice (i.e.,massed practice) is not of value and the person shouldand will stop studying. However, this does not necessar-ily mean that the person should not return to the item atsome later time, when, under new conditions, the jROLsmay be non-zero. Spaced rather than massed practice isindicated for such items. (3) A final case of close to zero

jROLs comes with very difficult materials on which theperson is making no headway. The model, through the

jROL stopping rule, provides a limit to peoples laborin vain for such items.

The JOL that should be observable when the personstops studying in (1) should be highprobably 100%.The JOLs upon stopping, in (2) might also be high,but spuriously sothese may be cases where an immedi-ate JOL would be high but a delayed JOL on the sameitem would be lower. However, JOLs might also below in this case, if the learning process is, for any reason,blocked at the current moment. The JOLs for (3) will below, often very low. Thus it is not the absolute JOL thatdetermines stopping, but rather the jROL, which neednot, itself, be correlated with the JOL.

Although the jROL is the derivative of the JOL func-tion over time, and could be computed from repeatedsampling (and comparison) of JOLs, the phenomenol-

ogy of the jROL relates more closely to feelings of inter-est and engagement (when the jROLs are high) or toboredom or stagnation (when the jROLs are low) thanto any experience of performing a computation. Thisconcept captures the frustration that people feel whenthey seem to be getting nowhere, and their discourage-ment with further study under these conditions. It alsorelates to the studies of attention to degrees of noveltythat Berlyne (1978) described in his early investigationsof curiosity and interest. He found that the visual pat-terns that provoked peoples interest and engaged theirattention (as measured by duration of gaze and by pupil-

lary dilation) were those that were more challenging

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than those they could easily understandnot perfectlysymmetric, but they were not extremely bizarre, to thepoint of being incomprehensible. We would argue thatthe challenging patterns allowed a rapid rate of learning,while the bizarre patterns did not allow learning and,therefore, did not engage peoples attention. They

shifted their gaze away from these items quickly.Factors such as the reward structures of the task, the

amount of time available, the difficulty of the materials,and the self-expectations and drives of the individual al-ter the parameter value of the stopping jROL. This valuewill be higher when people have little time than whentime is unlimited, closer to zero (lower) on tasks thatpeople care about and which they feel are central fortheir self concept, than on tasks they think are irrelevantand unimportant; higher when the alternative materialsthey could turn to rather than persisting on the presentitem are many and relatively easy, than when they are

few and difficult. Regardless of the fact that one canmanipulate the stopping jROL value, we argue thatlow jROLs are inherently aversive, and that the strongfeeling of learning that is the phenomenological accom-paniment of a high jROL is, itself, pleasurable and moti-vating for humans.

Data concerning choice

Do people choose to decline study for the items that they

know they know?

A number of studies, several going back three dec-ades (Atkinson, 1972; Masur, McIntyre, & Flavell,1973), affirm peoples capability to decline study of al-ready-known items. We have conducted several demon-stration experiments focusing on this topic that will bepresented below. Masur et al. (1973) found convincingsupport for a choice strategy in which the already-known items are spurned. In their study with childrenof various ages, even very young children showed a ten-dency to choose the items they did not know for studyand to eliminate those they did, and this characteristicbecame quite marked in college students. Grade 1 chil-

dren were less likely to make this choice than were olderchildren, but that seemed to result from the difficultythey experienced in knowing what they did not know.Thus, they sometimes chose, incorrectly, to not studyitems that they did not yet knowa tendency that disap-peared by Grade 3.

In a second study bearing on this issue, Atkinson(1972) told participants that their trial-to-trial selectionof items should be done with the aim of mastering thetotal set of vocabulary items and that it was best totest and study on words they did not know rather thanon ones already mastered (Atkinson, 1972, p. 125).

Although he did not report data in terms of whether

or not the items chosen in this so-called self-selectioncondition had already been learned or not, he did com-pare the results of the self-selection condition to those inwhich a computer algorithm selected for people theitems for study based on their performance history,which allowed determination of whether items were orwere not learned. Performance in these two groupswas very similar, at every stage of learning, with onegroup showing slightly higher performance on one trialand the other group reversing this on the next trial.1

These results suggest that people were able to conformto the instructions to eliminate from further study those

items that were already known. Similarly, Cull andZechmeister (1994) explicitly told participants to selectitems for study if and only if they were unlearned. Theitems they chose to study, given these instructions ateach choice, were the lower JOLs.

In an experiment that was investigating the relationof peoples JOLs to their preferences of whether to massor space practice, Son (2004) included an option ofallowing people to decline further study entirely. Fig. 1shows the distribution of peoples JOLs conditionalupon their having chosen to study (i.e., collapsed overthe massed or spaced choices), or conditional upon their

having chosen to decline study. The data were sortedinto the JOL intervals based on the raw JOL ratings gi-ven in the original data. (We thank Son for providing

Fig. 1. The distributions of JOLs for items on which peoplechose to study and for items on which people declined furtherstudy. From Son (2004).

1 The data from these two groups, in Atkinsons (1972)experiment, were quite different from a group given a randomassignment of items (including study of already known items)which resulted in much poorer performance. They also differedfrom a group given only those items that were close to beinglearned, in which the items that were already learned as well asthose that were very far from being learned, as determined bythe computer algorithm, were eliminated. This latter condition

showed superior performance.

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her data set for this analysis.) As can be seen, when peo-ple declined further study, their JOLs were nearly alwaysvery high. In contrast, JOLs were fairly evenly distrib-uted when people chose to study.

In summary, then, although the literature on the firststage of the choice process proposed by the Region of

Proximal Learning model is clear, it is not abundant.To further elaborate on peoples choices to study ornot study, as a function of whether or not they knowthe items, we conducted several experiments.

Experiment 1

In the first experiment, with 24 Columbia Universitystudents, we used Nelson and Narens (1980) general-in-formation-question pool, pruned to eliminate thosequestions that were out of date. A typical questionwas Who was the first Prime Minister of Canada?The computer presented a random selection of such

questions, one at a time, without the answers, to partic-ipants. They were asked to choose exactly half of thequestions for further study of both the question andthe answer. They were told that your goal is to do aswell as you can on the final test. On each of the 6 trials,each consisting of a total of 32 questions, the computerdisplayed a counter, showing dynamically how many ofthe allowable choices had accumulated in the study anddont study categories. The participant decided whetheror not to study each item, one at a time, by clicking oneither study or dont study as each item was presented.When the participant had exhausted one choice option,the other option was the only possible response. Thesetrials, where the choices were constrained rather thanfree, were not included in any of the analyses that fol-low, either for this experiment, or for any of the subse-quent experiments that used a similar design. (Oneconsequence of this is that if participants select studymore often than dont study until they have exhaustedthat choice option, the proportion of study trials will begreater than .5.)

In a survey at the end of the experiment, 20 of 24 par-ticipants reported selecting for study the items to whichthey did not know the answers. None reported selectingknown items. The items that were selected for study

were more difficult (180.90) than were those not selected(138.64), based on Nelson and Narens (1980) norms,t(23) = 7.88, p < .0001, Effect Size = .73. This patternheld for 22 of the 24 participants. People, apparently,had selected the items they did not know, both accord-ing to self report, and to the normative data.

It appears, then, with semantic memory generalinformation questions on which it is known, from theconsiderable past research on this particular item pool,that people have very good metacognitive accuracy, peo-ple choose to study those items that they know they donot know, and will decline to study those that they do.

Items in semantic memory, such as the general informa-

tion questions in this first experiment, might be expectedto be easy to monitor. In the experiments we report be-low, we sought to determine whether such a clear pat-tern also emerged with new learning. We conductedthree new-learning experiments in which in the firstphase participants were allowed to study only half of

the to-be-learned materials (so that the other half wasnecessarily unlearned). Following study, participantswere given the cues for all of the pairs and asked to se-lect half of the items for (re)study. They were then al-lowed to (re)study, and were tested.

Experiment 2

In this experiment, participants were 24 ColumbiaUniversity students who participated for either coursecredit or for pay. They studied highly associated pairsof words with cue-to-target associability scores withinthe .050.054 range, based on norms published by Nel-

son, McEvoy, and Schreiber (1998). These were pairssuch as well-done, which were easy to learn quickly,but which had only a low probability of being correctlyproduced without any exposure, that is, by guessing. Weused these pairs because we thought that a single rela-tively brief observation of the target would be sufficientto allow full learningmaking it highly likely that peo-ple would know that they knew these items.

Each participant was tested on four lists each ofwhich consisted of 24 item-pairs. Participants were onlypresented with half of the pairs in each list during thestudy phase, however. On two of the lists, the pairs thatwere presented were shown six times, each for 2.5 s in aspaced manner. On the other two lists the presentedpairs were shown only once for 2.5 s. Order of the repe-tition condition (6 or 1) was counterbalanced across par-ticipants. The item-pairs were presented for study, withonly one pair showing at a time, on Macintosh comput-ers. Participants were informed that although they onlywould be shown half of the to-be-remembered items inthe initial study phase, they would be shown all of thetest cues, in the choice phase, and that they would betested on the entire set of 24.

The participants were then presented with each of the24 cues (12 of which were new), one at a time, in a ran-

dom order, and asked to choose whether they did or didnot want to study that cue-target pair for an upcomingtest in which they would be asked the responses to allcues. They were told: You will only be allowed to selecthalf of the pairs for additional study. This makes it veryimportant that you make your selections carefullykeep in mind that you will be tested on all of the pairs,not just the ones you select, and your goal is to do aswell as you can on the final test. As in Experiment 1,a counter kept track, dynamically, for them, onscreen,of how many had already been chosen in the studyand dont study categories. Data were analyzed, as

before, only up until the point that one of these two

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categories was filled, since once that happened the par-ticipants no longer had a choice.

The answer to the question of whether people se-lected for study the items to which they had not been ex-posed (and that they therefore had not learned) waspositive. As is illustrated in the left panel of Fig. 2, peo-

ple were much more likely to choose the unpresentedpairs than the pairs presented once or six times,F(2,23) = 34.72, p < .0001, MSE= .09, Effect Size =.60. TukeyKramer post hoc tests (which were usedfor all post-hocs throughout this article) showed signifi-cant differences between 0 and 1 presentation, and 0 and6 presentations, though not between 1 and 6 presenta-tions. This case, which we had intentionally made asclear cut as possible, indicated that people declinedstudy of the known items under conditions of newlearning.

Because the materials were so easy to learn in a single

brief exposure, we had expected little or no difference be-tween the 6- and the 1-presentation conditions. How-ever, in situations in which it would take more timeand effort for learning to occur, we expected to find adifference between these two conditions. In the experi-ment that follows, we used more difficult materials,expecting to find a difference in choice as a function ofthe degree of learning in these two conditions.

Experiment 3

In this experiment, the only change from Experiment 2was that the materials we used were unrelated pairs ofitems such as footwear-acrobat. These pairs were moredifficult to learn than the very high associates of the previ-ous experiment. Participants were 24 Columbia Univer-sity students who participated for course credit or for pay.

As the center panel of Fig. 2 illustrates, participantschose to study the unpresented items more than the

items presented once, which were chosen more thanthe items presented six times, F(2,23) = 32.46, p

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Metcalfe Kornell 2005