An eye movement study of insight problem solving

Copyright 2001 Psychonomic Society Inc 1000

Memory amp Cognition2001 29 (7) 1000-1009

Although unfamiliar problems can sometimes be solvedby working through them step by step at a steady pace (egAnderson amp Lebiere 1998 Newell amp Simon 1972) solu-tions to insight problems exhibit a characteristic temporalpattern An initial period of purposeful problem solving ac-tivity is followed by an impasse a state of mind in whichthe problem solver feels that all options have been exploredand he or she cannot think of what to do next Continuedconcentration on the problem will in a proportion of casescause a new idea or option to come to mind This so-calledaha-experience is typically unanticipated by the problemsolver (Metcalfe 1986) and is followed by rapid comple-tion of the solution at least for the simple problems thatare used to study insight in the laboratory Well-known ex-amples of insight problems include the six matches prob-lem (Katona 1940) the two-string problem (Maier 1931)the candle problem (Weisberg amp Suls 1973) and the nine-dot problem (MacGregor Ormerod amp Chronicle 2001Scheerer 1963) After a pause in the decades after the

cognitive revolution in the 1950s there has been a recentresurgence of interest in insight (eg Smith Ward ampFinke 1995 Sternberg amp Davidson 1995)

The impassendashinsight sequence poses a double theoret-ical challenge (Ohlsson 1992) The first half of that chal-lenge is to understand why people become stuck on prob-lems for which they have the necessary knowledge Manyinsight problems have very short solution paths and re-quire only concepts and skills that are well within the com-petence of the average educated adult Nevertheless theimpasses produced by such problems can last for severalminutes or even hours If a person is competent to solve aproblem why does he or she experience an impasse Thesecond half of the theoretical challenge is to explain howimpasses are resolved If there is some cognitive mecha-nism or factor that prevents a person from applying his orher knowledge to a problem why is the impasse not per-manent What are the cognitive processes that allow a per-son to break out of an impasse

Theories of insight problem solving tend to emphasizeone or the other of these two challenges The functionalfixedness hypothesis claims that mental representationsof objects are associated with the common functions forthese objects If in a certain problem a familiar object hasto be used in an unfamiliar way the spontaneous retrievalof its familiar function blocks its unfamiliar usage and animpasse arises (Duncker 1945 Keane 1989) The mentalruts hypothesis (Smith 1995) claims that impasses are en-countered because the repeated exploration of an unsuc-cessful search path or the search for the same knowledgeelement adds more and more activation to this path Thisin turn decreases the probability of exploring another pathand the problem solver gets stuck (see also Simon 1966)This concept is very similar to the Einstellung concept in-troduced by Luchins and Luchins (1959) According to this

This research was supported in part by a grant of the German Aca-demic Exchange Service (HSPIIAUFE) which made it possible to carryout the study reported in this paper during a visit of the first author to theUniversity of Illinois at Chicago This research was also supported in partby a grant from the Cognitive Science Program of the Office of Naval Re-search to the second author The eye movement equipment was purchasedwith the help of a grant from the Campus Research Board of the Univer-sity of Illinois at Chicago to the third author The opinions expressed arenot necessarily those of the sponsoring agencies and no endorsementshould be inferred We thank Richard Marsh Jonathan Schooler StevenSmith Asher Koriat Sonja Stork Bas Neggers and Jochen Muumlsseler forhelpful comments and Steven Raminiak Raphael Hartmann and AndrewHalpern for their help with the data collection Correspondence concern-ing this article should be addressed to G Knoblich Max Planck Institutefor Psychological Research Amalienstr 33 80799 Munich Germany(e-mail knoblichmpipf-muenchenmpgde)

An eye movement study of insight problem solving

GUumlNTHER KNOBLICHMax Planck Institute for Psychological Research Munich Germany

and

STELLAN OHLSSON and GARY E RANEYUniversity of Illinois Chicago Illinois

The representational change theory of insight claims that insight problems cause impasses becausethey mislead problem solvers into constructing inappropriate initial representations Insight is attainedwhen the initial representation is changed In the present study (N = 24) we tested three specific impli-cations of these hypotheses against eye movements recorded while participants solved matchstick arith-metic problems The results were consistent with the predictions providing converging evidence withprior findings using solution rates and solution times Alternative theories of insight can explain individ-ual findings but only the representational change theory accounts for both the performance data andthe eye movement data The present study also suggests that eye movement recordings provide an im-portant new window into processes of insight problem solving

EYE MOVEMENTS AND INSIGHT 1001

hypothesis once a solution path has become habitual theproblem solver no longer searches the problem space foralternative and potentially more efficient solution pathsIf the habitual path is blocked in some way an impasseresults MacGregor et al (2001) have recently proposed aprinciple of satisfactory progress that says that a personis experiencing an impasse on the nine-dot problem whenhe or she cannot find a next line to draw that picks up asufficient number of dots All four of these hypothesesexplain why problem solvers enter impasses but they donot explain how impasses are resolved

According to Gestalt theory (Koumlhler 1924 1925 Wert-heimer 1959) thinking begins when the perceptual field isin a state of imbalance or tension A solution appears inconsciousness when the perceptual field reorganizes itselfinto a better more harmonious or balanced state (Ohls-son 1984a) Another type of explanation is the Darwinianprocess of variation and selection (Simonton 1988 1995)The variationndashselection hypothesis claims that novel solu-tions are constructed by creating more or less random vari-ants of existing solutions and then evaluating those vari-ants until one is found that solves the current problemOthers have described insight problem solving as a grad-ual transformation of past experience (Perkins 1981Weisberg 1986 Weisberg amp Alba 1981) According to thisview creative products or solutions result from gradualtransformations of past experience These three hypothe-ses explain how people can succeed in solving unfamil-iar problems However they do not explain why there areimpasses There is no clear reason why the reorganizationof the perceptual field the variationndashselection processor the gradual transformation of experience would cometo a standstill or be delayed longer on some problems thanon others

We have developed a theory of insight that addressesboth theoretical challenges (Knoblich Ohlsson Haideramp Rhenius 1999 Ohlsson 1984b 1992) Our explanationfor why people encounter impasses is that insight prob-lems have a high probability of triggering an initial men-tal representation that has a low probability of leading tothe solution The problem as initially perceived by theproblem solver interacts with his or her prior knowledge insuch a way as to activate knowledge elements (ie analo-gies concepts ideas operators principles rules schemasskills etc) that are not sufficient for solving it It mayalso lead to inhibition or suppression of knowledge ele-ments that are essential for the solution The activation ofunhelpful knowledge elements and the consequent inhi-bition of more helpful ones is the cause of impasses

The second principle of our theory says that impassesare resolved by revising the unhelpful initial representa-tion The consequence of such a change is that the distri-bution of activation over memory is altered and the prob-lem solver might access knowledge elements that have sofar remained inactive but are essential for the solution Theappearance of a crucial but previously unheeded knowl-edge element in working memory (and hence in subjectiveexperience) is the aha-experience Problem representa-

tions can be revised in multiple ways (Ohlsson 1992)for instance by constraint relaxation (ie the deactiva-tion of some knowledge element that has acted as a con-straint on the options initially considered) and chunk de-composition (ie the separation of the components of aperceptual chunk Knoblich et al 1999)

Kaplan and Simon (1990) have proposed an alterna-tive representational change theory of insight They sug-gest that people encounter impasses because their initialproblem representation is incomplete rather than mis-leading Hence the problem solver has to resolve an im-passe by noticing and encoding additional features of theproblem rather than by abandoning or deactivating un-helpful ones In particular they hypothesize that peoplesearch for and notice invariants (ie properties that re-main the same when the problem is represented in differ-ent ways) Although our notion of activation redistributionclaims that restructuring processes occur outside con-sciousness (Bowden amp Beeman 1998 Metcalfe 1986)Kaplan and Simon (1990) suggest that those processes areunder conscious control

In the past researchers have typically tested their in-sight theories against performance measuresmdashprimarilythe time it takes to find a solution and the probability offinding a solution within a given time frame Our ownpast work is no exception (Knoblich et al 1999) How-ever as argued by Newell and Simon (1972) and othersperformance measures provide only weak informationabout underlying processes and need to be supplementedwith process tracing methods Verbal protocols have beenused to study insight (Kaplan amp Simon 1990 Schooleramp Melcher 1995) but Schooler Ohlsson and Brooks(1993) have questioned whether the think-aloud method isnonreactive vis a vis insight problem solving Eye move-ments present a potentially powerful alternative There isa close connection between which display item a person islooking at and which item he or she is thinking about aswell as between fixation duration and amount of process-ing (Just amp Carpenter 1976 Knoblich amp Rhenius 1995Rayner 1978 1998) Eye movement data thus providesa temporally fine-grained record of problem solving pro-cesses In spite of the proven usefulness of eye movementrecordings there are no studies that apply this method-ology to insight problem solving In the present study wetested three predictions from our insight theory againsteye movement data recorded while the participants solvedmatch stick arithmetic problems

Eye Movements in Match Stick ArithmeticWe used matchstick arithmetic problems because each

problem consists of a small number of distinct elementsarranged in a horizontal sequence Hence we could deter-mine with precision which problem component a partici-pant was fixating at any one moment in time In matchstickarithmetic the problem solver is faced with an incorrectarithmetic statement expressed in Roman numerals con-structed out of matchsticks The goal is to correct thearithmetic statement by moving a single matchstick from

1002 KNOBLICH OHLSSON AND RANEY

one position in the statement to another Three examplesare shown in Figure 1 Problem A is solved by movingthe vertical stick on the far left to the right hand side ofthe Roman numeral V thereby creating the correct arith-metic statement VI = III + III Because all problemsused in our study are solved with a single physicallytrivial move their degree of difficulty is solely a func-tion of the probability of thinking of the right move Weinvite the reader to solve Problems B and C in Figure 1before reading further

Unlike Problem A Problem B cannot be solved bychanging the values in the equation Instead one has tochange the plus sign into a second equal sign to obtain thesolution III = III = III In prior research we have shownthat Problem B is considerably more difficult than Prob-lem A (Knoblich et al 1999 Knoblich amp Wartenberg1998) Our explanation is that matchstick arithmetic prob-lems activate the problem solverrsquos prior knowledge ofarithmetic and that this knowledge biases the initial repre-sentation in such a way that values are encoded as variableelements but operators (ie plus minus and equal signs)are encoded as constants In arithmetic there are many op-erations that change the values in an equation but few thatchange the operators In fact arbitrarily altering the oper-ators in an equation usually violates the very meaning ofthat equation Unless the constraint against altering the op-erators is relaxed Problem B cannot be solved

Like Problem A Problem C is solved by changing avalue The solution is to slide the left-slanted stick thatis part of the symbol X to the left to obtain the solutionVI = III + III Roman numerals are meaningful chunks forour experimental participants Unless the relevant chunksIV and X are decomposed into their components Prob-lems A and C cannot be solved We have shown that Prob-lem C is considerably more difficult to solve than Prob-lem A (Knoblich et al 1999) Our explanation is that it ismore difficult to intellectually detach a component thathas no meaning of its own like the left-slanted stick in

X than a stick that carries its own meaning like the ldquoIrdquoin IV

If our account of insight problem solving in generaland matchstick arithmetic solutions in particular is cor-rect what regularities can we expect in the participantsrsquoeye movements We focus on three predictions

First impasses should affect the mean fixation durationDuring an impasse the problem solver is not actively ex-ploring the problem space He or she does not know whatto do next so he or she tends to stare at the problem with-out testing particular solution ideas The result should befewer eye movements per unit of time Within a fixedtime frame this translates into longer fixations Becausewe expect impasses in Problems B and C but not in Prob-lem A mean fixation duration should be greater in the firsttwo problems Furthermore because impasses only occurafter the initial exploration of the problem space meanfixation duration should increase throughout the problemsolving effort for Problems B and C as more and moreproblem solvers enter impasses but not for Problem AFinally this pattern should hold for both successful andunsuccessful problem solvers because both are hypoth-esized to experience impasses We have no reason to ex-pect impasse-driven fixations to be aimed at one prob-lem element rather than at another so this is strictly aprediction about the duration of fixations over time nota prediction about the allocation of attention

Second the initial representation of the problem shouldaffect attention allocation If the participants initially re-gard the values in the equations as the variable elementsand the operators as constants it follows that they shouldfocus on the values during the initial exploratory phase ofproblem solving Hence we predict that a larger propor-tion of the total fixation time should fall on the values (re-sults and operands) than on the operators This predictionholds only for the initial phase of problem solving beforethe constraint against altering other problem elements isrelaxed

Figure 1 Matchstick arithmetic problems


A recent study by Ballard Hayhoe Pook and Rao(1997) suggests a functional distinction between short andlong fixations A short fixation primarily serves to reen-code a problem element into working memory it does notnecessarily imply that the reencoded element is processedfurther A longer fixation is more likely to signal deeperprocessing To take this distinction into account we makeseparate predictions for short and long fixations

For short fixations no differences are expected betweendifferent problem elements because there is no reasonwhy any single element in a matchstick arithmetic prob-lem should need to be reencoded more often than an-other Because there are five elements in each problem(result equal sign operand1 plus sign operand2) weexpect that for short fixations 20 of the fixation timewill be spent on each problem element There should beno differences between problems in this respect

For long fixations the percentage of fixation time spenton the values in the expression should exceed the chancelevel of 20 and the percentage of fixation time spenton the operators should fall below that level Again thereshould be no differences between different problems be-cause the initial bias should be present whether it helpsor hinders the problem solving process To be clear weare not predicting that fixations of values are longer onaverage than fixations of operators but that a larger pro-portion of the total amount of time allotted to long fixa-tions is spent looking at the values Thus this is a pre-diction about the allocation of attention not about theduration of fixations

Of course focusing on the longer fixations poses thepotential problem that the population of relevant fixationsincludes not only those associated with deep processingbut some that are associated with impasses as well Clearlymeaningful shifts in attention can only be expected to affectthe former and not the latter A preponderance of impasse-driven long fixations will dilute the predicted effects andmake them more difficult to observe in the data For thisreason the prediction about the distribution of fixationtime holds only for the initial preimpasse phase of prob-lem solving

Third the revision of the initial problem representationthat precedes insight should also affect attention alloca-tion We make separate predictions for Problems B and CIn Problem B the initial focus on the values implies thatthe percentage of fixation time spent on the arithmetic op-erators (the plus and equal signs) should be lower than thepercentage spent on the values This holds for both suc-cessful and unsuccessful problem solvers For successfulproblem solvers this bias should become less pronouncedor should reverse when the constraint against altering theoperators is relaxed The implied increase in the per-centage of fixation time spent on the operators should onlyhappen for successful problem solvers Unsuccessful prob-lem solvers presumably fail because they never relax thatconstraint so there is no reason to expect a reversal in at-tention allocation for them The change in attention al-location should affect long fixations but not necessarilyshort ones

In Problem C the result is the crucial problem elementInitially the percentage of fixation time spent on the re-sult should be comparable to the percentage fixation timespent on other problem elements and it should be thesame for successful and unsuccessful problem solversWhen the crucial chunk X is decomposed the percent-age of fixation time spent on the result should increaseThis effect should only occur in successful problemsolvers Unsuccessful problem solvers presumably failbecause they never decompose that chunk so there is noreason to expect a change in the time spent on the resultfor them Again the change in attention allocation shouldaffect long fixations but not necessarily short ones

Considered one by one these predictions are not uniqueto our theory On the one hand the principles of func-tional fixedness mental ruts and Einstellung all predictimpasses and hence the elongation of fixation times afterthe exploratory phase However because they do not pre-dict changes in problem representation they do not gen-erate specific predictions about changes in attention al-location On the other hand principles like variation andselection and gradual transformation of past experiencedo not predict impasses In addition they are very generaland lack any conceptual mechanism for relating them tothe details of either tasks or behaviors so it is difficult toderive precise predictions about attention allocation fromthem The conjunction of our three predictions dependsessentially on our analysis of exactly why people en-counter impasses in matchstick arithmetic and exactlyhow their problem representations change when they re-solve those impasses

METHOD

ParticipantsTwenty-four undergraduates from the University of Illinois at

Chicago 10 of them male participated in the study for coursecredit They ranged in age from 18 to 29 years We selected onlyparticipants who were familiar with Roman numerals The partici-pants were seen individually Because of restrictions presented bythe eye movement monitor the participants could not wear glassesduring the experiment but were permitted to wear contact lenses Theparticipants reported no eye abnormalities (eg lazy eyes)

ApparatusA Dr Bouis Monocular Oculometer was used to track eye move-

ments Eye position was sampled at a rate of 1000 Hz The initiationof a fixation was defined as the point when five consecutive sampleseach differed from the sample taken 5 msec earlier by less than 19of a visual degree The initiation of a saccade was defined as the pointwhen three consecutive samples each differed from the previous sam-ple by more than 19 Problems were displayed on a VGA monitor po-sitioned 72 cm from the participant The visual angle subtended bythe problems was 12ordm horizontal and 2ordm vertical

Procedure Materials and Design The participants f irst went through a training phase to speed up

the recognition of Roman numerals Then the participants weregiven a description of the eye tracking apparatus Afterwards theexperimenter prepared a bite bar that served to increase the preci-sion of the measurement by stabilizing the participants rsquo heads Fi-nally the participants received instructions about the rules of match-stick arithmetic and the experimental procedure Before presenting


the first problem a calibration procedure was conducted to adjustthe eye tracker

The participants solved three matchstick problems (Problems AB and C) that were presented in random order They pushed a but-ton as soon as they thought that they had found the solution to aproblem removed their teeth from the bite bar and said the solutionout loud If the solution was correct the next problem was pre-sented If not they continued to work on the same problem untilthey found another solution or until they reached the time limit of5 min If the participants did not solve a problem within 5 min theywere told the solution

A short recalibration was done (1) before presenting a new task(2) after an incorrect solution had been proposed and (3) when aparticipant had worked on a problem continuously for 1 min with-out proposing a solution The recalibration took between 3 and10 sec

RESULTS

The dependent variables were the frequency of solutionduring a 5-min interval the solution time for problemssolved and the position and the duration of each fixa-tion on the display

Solution Frequencies and Solution TimesThe performance results confirmed the predicted dif-

ferences in task difficulty Figure 2 shows the cumulativefrequency of solutions across 1-min intervals for Prob-lems A B and C

As Figure 2 shows the differences between problemshold at each interval Single chi-square tests were com-

puted to test whether frequency of solution within a 5-mintime limit differed significantly between two problemsProblem B which requires that the operator be changedwas solved significantly less often (9 out of 24 solved) thanwas Problem A which requires that the value of the resultbe changed (23 out of 24 solved) [c2(1 N = 24) = 1838p lt 001] Problem C which requires decomposition of atight chunk was solved significantly less often (18 out of24 solved) than was Problem A which requires decompo-sition of a loose chunk [c2(1 N = 24) = 418 p lt 05]Moreover Problem B was solved significantly less oftenthan Problem C [c2(1 N = 24) = 478 p lt 05]

Solution times for Problems A B and C were analyzednext For problems that were not solved solution timeswere replaced with the upper time limit of 5 min Becausethe distribution of solution times was highly skewed wereport median and quartiles and use ordinal tests to as-sess statistical significance Table 1 shows median andlower and upper quartiles for Problems A B and C

The medians as well as the lower and upper quartilesare consistent with the expected rank ordering of task dif-ficulty (Problem B gt Problem A Problem C gt Problem A)Single Wilcoxon tests were computed to assess the statis-tical significance of the differences Problem A was solvedsignificantly faster than Problem B (n = 24 T = 1 p lt001) and Problem A was solved significantly faster thanProblem C (n = 24 T = 22 p lt 001) In addition Prob-lem C was solved significantly faster than Problem B (n =24 T = 36 p lt 05)

Figure 2 Cumulative solution rates for Problems A B and C


The observed differences in solution frequency and so-lution times are indistinguishable from those obtained inearlier experiments (Knoblich et al 1999) during whichno eye movements were recorded and subjects were notinterrupted by recalibration procedures In short the eyemovement recording procedure was not highly reactive inthis situation

Eye Movement DataOnly fixations that lasted longer than 100 msec were

included in the data analysis Before computing the pro-portion fixation time spent on each problem element amedian split was used to categorize the fixations into shortand long To trace changes in eye movements over timethe problem solving process was divided into three inter-vals of equal duration for each problem solver and eachtask Because the total solution time varied so did the ab-solute duration of the intervals The relevant dependentmeasures were aggregated across participants for each in-terval

Fixation duration Figure 3 shows the results of theanalysis of mean fixation duration across the three in-tervals

Overall fixation duration was higher in Problems B andC than in Problem A Mean fixation duration increasedmonotonously across intervals in Problems B and C butremained constant after the second interval in Problem AWe computed a 3 acute 3 analysis of variance (ANOVA) withproblem (A B C) and interval (first second third) aswithin-subjects factors to assess the statistical signifi-cance of these differences There was a significant maineffect for problem [F(244) = 349 p lt 05] Post hoccomparisons showed that fixation duration for ProblemsB and C were significantly greater than for Problem A(both ps lt 05) These results are consistent with the hy-pothesis that problem solvers encountered more impassesin Problems B and C Furthermore there was a signifi-cant main effect of interval [F(244) = 858 p lt001]Mean fixation duration was longer in later intervals Therewas no significant interaction between the two factors[F(488) = 154 p = 20] Further analyses showed thatthere were also no significant differences in mean fixa-tion duration between successful and unsuccessful prob-lem solvers

Fixation time on single elements during the initialphase To determine whether there was a preference forcertain problem elements in the initial phase of problemsolving we computed the proportion of f ixation timespent on different problem elements during the first in-terval of problem solving This measure was computedseparately for fixations that were below and above themedian of the mean fixation duration (ie for short andlong fixations) If fixations were equally distributed acrossdifferent elements of the display one would expect that

Table 1 Solution Times (in Seconds) For Problems A B and C

Problem Mdn Lower Q Upper Q

A 22 14 31B 300 112 300C 136 42 300

Figure 3 Mean fixation duration across intervals in Problems A B and C


20 of the overall fixation time was spent on each ele-ment Figure 4 shows the results (for the two operandsthe arithmetic mean of the two percentages is reported)

For short fixations (see Panel A in Figure 4) the per-centage of fixation time spent on the result was lower thanthe percentage time spent on all other elements Conse-quently the percentage fixation time was lower than theexpected 20 for the result and slightly higher than that forthe other problem elements Accordingly a 4 acute 3 ANOVAwith element (result operands plus sign equal sign) andproblem (A B C) as within-subjects factors resulted ina significant main effect for element [F(363) = 282 p lt05] There was no significant main effect for problem( p = 42) and no significant interaction ( p = 26)

For long fixations (see Panel B in Figure 4) the per-centage of fixation time spent on the result was higherthan the percentage time spent on the operands which inturn was higher than the percentage time spent on the plusand the equal signs The percentage of time spent on theplus and equal signs was clearly lower than the 20 that

would be expected if fixations were equally distributedacross elements Again a 4 acute 3 ANOVA with element (re-sult operands plus sign equal sign) and problem (A B C)as within-subjects factors revealed a significant main ef-fect for element [F(363) = 2402 p lt 001] but no sig-nificant main effect for problem (p = 42) There was amarginally significant interaction [F(6126) = 206 p =06] that was due to the fact that the percentage of timespent on the plus sign was especially low in Problem APost hoc tests were conducted to confirm that the differ-ences between the different conditions of the element fac-tor were significant This was true for the difference be-tween the result and the operands conditions (p lt 01) andthe difference between the operands and the plus andequal sign conditions (both ps lt 001) In short there wasa bias towards values for long fixations and no such biasfor short fixations

Fixation time on crucial elements across intervalsThe next question is whether successful and unsuccessfulproblem solvers differed in the percentage of time spent

Figure 4 Percentage of fixation time spent on different problem elements during theinitial phase of problem solving for short (A) and long (B) fixations


on the crucial element across successive intervals We firstpresent the results from Problem B in which the plus signand the equal sign were the crucial problem elements

For short fixations (left panel of Figure 5) the percent-age of time spent on the operators was higher for success-ful problem solvers during the first two intervals For un-successful problem solvers the rate never deviated fromthe chance level of 20 A 2 acute 3 ANOVA with success(successful unsuccessful) and interval (first second third)as within-subjects factors revealed no significant maineffects or interactions However a contrast analysis con-firms that the difference between successful and unsuc-

cessful problem solvers during the first two intervals wassignificant [F(122) = 709 p lt 05]

For long fixations (right panel of Figure 5) the per-centage of fixation time spent on the operators increasedacross intervals for successful problem solvers but not forunsuccessful problem solvers Moreover the percentageremained below chance level for unsuccessful problemsolvers but was above chance level in the third interval forsuccessful problem solvers A 2 acute 3 ANOVA with success(successful unsuccessful) and interval (first second third)as within-subjects factors revealed a significant main ef-fect of interval [F(244) = 1235 p lt 001] and a signif-icant interaction between success and interval [F(122) =791 p lt 01] There was no significant main effect of suc-cess ( p = 28)

In Problem C the result was the crucial problem elementFigure 6 shows the percentage of fixation time spent on theresult by successful and unsuccessful problem solversacross intervals For short fixations this percentage wasconsistently higher for unsuccessful problem solvers thanfor successful problem solvers Moreover it was alwaysclose to chance level for unsuccessful problem solvers butconsistently below chance level for successful problemsolvers However a 2 acute 3 ANOVA with success (success-ful unsuccessful) and interval (f irst second third) aswithin-subjects factors revealed only a marginally signifi-cant main effect of success [F(121) = 309 p = 09] Therewas no significant main effect of interval (p = 78) and nosignificant interaction of success and interval (p = 87)

For long fixations the percentage of fixation time spenton the result was consistently above chance level in suc-cessful and unsuccessful problem solvers There was nodifference between the two groups during the first two in-tervals However during the third interval the percentagefixation time increased dramatically for successful prob-lem solvers and not at all for unsuccessful problem solversA 2 acute 3 ANOVA with success (successful unsuccessful)and interval (first second third) as within-subjects fac-tors revealed a significant main effect for interval [F(242) =531 p lt 01] and a significant interaction between suc-cess and interval [F(242) = 508 p lt 05] but no signifi-cant main effect for success (p = 33)

DISCUSSION

The experiment tested three predictions about eyemovements derived from our theory of insight The firstprediction follows from the principle that insight prob-lems produce impasses During an impasse people tendto sit and stare at the problem so there should be fewereye movements (ie longer fixation times) This effectshould gradually increase throughout the problem solv-ing process as more and more of the problems solvers inthe sample enter impasses We found this pattern for thetwo difficult problems B and C but not for the simplerproblem A (see Figure 3)

The second prediction follows from the principle thatimpasses are caused by inappropriate initial representa-tions In matchstick arithmetic prior knowledge of arith-

Figure 5 Percentage of fixation time spent on the operators inProblem B across intervals for successful and unsuccessful prob-lem solvers and for short (A) and long (B) fixations


metic ought to bias people toward seeing values but not op-erators as variable problem elements Hence attentionshould be differentially allocated to the values during theinitial phase of problem solving This is the pattern wefound (see Figure 4 Panel B)

The third prediction follows from the principle that im-passes are resolved by relaxing inappropriate constraintsand decomposing unhelpful perceptual chunks Such revi-sions of the problem representation ought to result in shiftsin attention allocation In Problem B we expected problemsolvers to succeed because they finally relaxed the constraint

against manipulating the operators which implies an in-creased attention to the operators toward the end of prob-lem solving This is what we found for successful problemsolvers but not for unsuccessful ones (see Figure 5 Panel B)In Problem C we expected problem solvers to succeed bydecomposing the chunk X into its component matchstickswhich should have led to increased attention to that symboltoward the end of problem solving but only for successfulproblem solvers This is what we found (see Figure 6Panel B)

The conjunction of these three regularities is not pre-dicted by other theories of insight There are several prin-ciples that explain impasses including functional fixed-ness mental ruts Einstellung and insufficient progress(MacGregor et al 2001) These principles all share theprediction that fixation time should increase throughoutproblem solving However because they do not explainhow impasses are resolved they cannot predict in detailhow attention allocation will change at the moment ofinsight

The principles of Gestalt restructuring the variationndashselection hypothesis and gradual transformation of pastexperience all predict at a general level that attentionshould shift throughout a solution attempt However theydo not predict any particular regularities in attention al-location For example the variationndashselection hypothesiscannot explain why our experimental participants initiallyfocused on the values in Problem B but later shifted theirfocus of attention to the operators nor why this shift oc-curred only in successful problem solvers Similarly thegradual transformation principle cannot explain why at-tention shifted to the symbol X specifically toward theend of the successful solutions for Problem C

Taken together the three regularities we observed sup-port our analysis of what happens when people solvearithmetic matchstick problems The arithmetic formatautomatically activates prior knowledge about arithmeticwhich brings with it mental habits and dispositions thatare not useful for solving such problems primarily thehabit of regarding the values of the numbers as the vari-able elements of the problem and the operators and theequal sign as constant elements and the disposition to seecomplex Roman numerals as indivisible entities Thesehabits and dispositions lead to impasses When they areabandoned or overcome attention allocation and henceprocessing shifts the impasse is broken and the solutionis quickly found This analysis successfully accounts forboth traditional performance measures (Knoblich et al1999) and the patterns in the eye movement recordings

The success of the task specific analysis lends credenceto the general representational change theory of insightfrom which it was derived People encounter impasses onsimple problems that they are competent to solve becausethe presentation of the problem triggers the retrieval or ac-tivation of prior knowledge that blocks the solutionChanges in the inappropriate initial representation allowpreviously unheeded possibilities to come to mind this isthe moment of insight However there is still room for dis-

Figure 6 Percentage of fixation time spent on the result inProblem C across intervals for successful and unsuccessful prob-lem solvers and for short (A) and long (B) fixations


agreement about the exact nature of the processes of rep-resentational change Kaplan and Simon (1990) empha-size the incompleteness of the initial representation and theimportance of invariant properties This hypothesis has ahigh degree of face validity with respect to their experi-mental task the mutilated checkerboard problem How-ever it is not clear which invariant properties there are inour matchstick problems nor in the classical insightproblems such as the two-string problem or the nine-dotproblem We prefer the hypothesis that initial representa-tions are inappropriate or misleading rather than incom-plete and thus have to be deactivated or inhibited ratherthan extended or elaborated but the available data leavethe issue open

The present study demonstrates the power of eye move-ment recordings Traditional performance measures likesolution time and solution rate could not have revealedthe structure of the participantsrsquo attention allocation innearly the same amount of detail We expect that extensiveuse of eye movement recordings will enable insight re-searchers to empirically differentiate between alternativemechanisms of representational change

REFERENCES

Anderson J R amp Lebiere C (1998) The atomic components ofthought Mahwah NJ Erlbaum

Ballard D H Hayhoe M M Pook P K amp Rao R P N (1997) De-ictic codes for the embodiment of cognition Behavioral amp Brain Sci-ences 20 723-767

Bowden E M amp Beeman M J (1998) Getting the right idea Seman-tic activation in the right hemisphere may help solve insight problemsPsychological Science 9 435-440

Duncker K (1945) On problem-solving Psychological Monographs68 (Whole No 270)

Just M A amp Carpenter P A (1976) Eye fixations and cognitiveprocesses Cognitive Psychology 8 441-480

Kaplan C A amp Simon H A (1990) In search of insight CognitivePsychology 22 374-419

Katona G (1940) Organizing and memorizing Studies in the psychologyof learning and teaching New York Columbia University

Keane M (1989) Modelling problem solving in Gestalt ldquoinsightrdquo prob-lems Irish Journal of Psychology 10 201-215

Knoblich G Ohlsson S Haider H amp Rhenius D (1999) Con-straint relaxation and chunk decomposition in insight problem solvingJournal of Experimental Psychology Learning Memory amp Cognition25 1534-1556

Knoblich G amp Rhenius D (1995) Zur Reaktivitaumlt Lauten Denkensbeim komplexen Problemloumlsen [The reactivity of thinking aloud dur-ing complex problem-solving] Zeitschrift fuumlr Experimentelle Psy-chologie 42 419-454

Knoblich G amp Wartenberg F (1998) Unbemerkte Loumlsungshinweisebeguumlnstigen Veraumlnderungen der Problemrepraumlsentation [Unnoticedhints facilitate representational change in problem solving] Zeit-schrift fuumlr Psychologie 206 207-234

Koumlhler W (1924) Die physischen Gestalten in Ruhe und im stationaumlrenZustand [The physical shapes in rest and stationary state] ErlangenGermany Verlag der philosophischen Akademie

Koumlhler W (1925) The mentality of apes New York LivewrightLuchins A S amp Luchins E H (1959) Rigidity of behavior A vari-

ational approach to the effect of Einstellung Eugene University ofOregon Press

MacGregor J N Ormerod T C amp Chronicle E P (2001)Information-processing and insight A process model of perfor-mance on the nine-dot and related problems Journal of Experimen-tal Psychology Learning Memory amp Cognition 27 176-201

Maier N R F (1931) Reasoning in humans II The solution of a prob-lem and its appearance in consciousness Journal of Comparative Psy-chology 12 181-194

Metcalfe J (1986) Feeling of knowing in memory and problem solv-ing Journal of Experimental Psychology Learning Memory amp Cog-nition 12 288-294

Newell A amp Simon H A (1972) Human problem solving EnglewoodCliffs NJ Prentice-Hall

Ohlsson S (1984a) Restructuring revisited I Summary and critique ofthe Gestalt theory of problem solving Scandinavian Journal of Psy-chology 25 65-78

Ohlsson S (1984b) Restructuring revisited II An information pro-cessing theory of restructuring and insight Scandinavian Journal ofPsychology 25 117-129

Ohlsson S (1992) Information-processing explanations of insight andrelated phenomena In K J Gilhooley (Ed) Advances in the psy-chology of thinking (pp 1-44) London Harvester-Wheatsheaf

Perkins D (1981) The mindrsquos best work Cambridge MA Harvard Uni-versity Press

Rayner K (1978) Eye movements in reading and information process-ing Psychological Bulletin 85 618-660

Rayner K (1998) Eye movements in reading and information process-ing 20 years of research Psychological Bulletin 124 372-422

Scheerer M (1963) Problem-solving Scientific American 208 118-128

Schooler J W amp Melcher J (1995) The ineffability of insight InS M Smith T B Ward amp R A Finke (Eds) The creative cognitionapproach (pp 97-133) Cambridge MA MIT Press

Schooler J W Ohlsson S amp Brooks K (1993) Thoughts beyondwords When language overshadows insight Journal of Experimen-tal Psychology General 122 166-183

Simon H A (1966) Scientific discovery and the psychology of problemsolving In R Colodny (Ed) Mind and cosmos (pp 22-40) Pitts-burgh University of Pittsburgh Press

Simonton D K (1988) Scientific genius A psychology of scienceNew York Cambridge University Press

Simonton D K (1995) Foresight in insight A Darwinian answer InR J Sternberg amp J E Davidson (Eds) The nature of insight (pp 465-494) Cambridge MA MIT Press

Smith S M (1995) Getting into and out of mental ruts A theory of fix-ation incubation and insight In R J Sternberg amp J E Davidson (Eds)The nature of insight (pp 229-251) Cambridge MA MIT Press

Smith S M Ward T B amp Finke R A (Eds) (1995) The creativecognition approach Cambridge MA MIT Press

Sternberg R J amp Davidson J E (Eds) (1995) The nature of insightCambridge MA MIT Press

Weisberg R W (1986) Creativity Genius and other myths NewYork W H Freeman

Weisberg R W amp Alba J W (1981) An examination of the allegedrole of ldquofixationrdquo in the solution of several ldquoinsightrdquo problems Journalof Experimental Psychology General 110 169-192

Weisberg R W amp Suls J M (1973) An information-processingmodel of Dunckerrsquos Candle Problem Cognitive Psychology 4 255-276

Wertheimer M (1959) Productive thinking New York Harper

(Manuscript received December 7 1999 revision accepted for publication June 9 2001)


hypothesis once a solution path has become habitual theproblem solver no longer searches the problem space foralternative and potentially more efficient solution pathsIf the habitual path is blocked in some way an impasseresults MacGregor et al (2001) have recently proposed aprinciple of satisfactory progress that says that a personis experiencing an impasse on the nine-dot problem whenhe or she cannot find a next line to draw that picks up asufficient number of dots All four of these hypothesesexplain why problem solvers enter impasses but they donot explain how impasses are resolved

According to Gestalt theory (Koumlhler 1924 1925 Wert-heimer 1959) thinking begins when the perceptual field isin a state of imbalance or tension A solution appears inconsciousness when the perceptual field reorganizes itselfinto a better more harmonious or balanced state (Ohls-son 1984a) Another type of explanation is the Darwinianprocess of variation and selection (Simonton 1988 1995)The variationndashselection hypothesis claims that novel solu-tions are constructed by creating more or less random vari-ants of existing solutions and then evaluating those vari-ants until one is found that solves the current problemOthers have described insight problem solving as a grad-ual transformation of past experience (Perkins 1981Weisberg 1986 Weisberg amp Alba 1981) According to thisview creative products or solutions result from gradualtransformations of past experience These three hypothe-ses explain how people can succeed in solving unfamil-iar problems However they do not explain why there areimpasses There is no clear reason why the reorganizationof the perceptual field the variationndashselection processor the gradual transformation of experience would cometo a standstill or be delayed longer on some problems thanon others

We have developed a theory of insight that addressesboth theoretical challenges (Knoblich Ohlsson Haideramp Rhenius 1999 Ohlsson 1984b 1992) Our explanationfor why people encounter impasses is that insight prob-lems have a high probability of triggering an initial men-tal representation that has a low probability of leading tothe solution The problem as initially perceived by theproblem solver interacts with his or her prior knowledge insuch a way as to activate knowledge elements (ie analo-gies concepts ideas operators principles rules schemasskills etc) that are not sufficient for solving it It mayalso lead to inhibition or suppression of knowledge ele-ments that are essential for the solution The activation ofunhelpful knowledge elements and the consequent inhi-bition of more helpful ones is the cause of impasses

The second principle of our theory says that impassesare resolved by revising the unhelpful initial representa-tion The consequence of such a change is that the distri-bution of activation over memory is altered and the prob-lem solver might access knowledge elements that have sofar remained inactive but are essential for the solution Theappearance of a crucial but previously unheeded knowl-edge element in working memory (and hence in subjectiveexperience) is the aha-experience Problem representa-

tions can be revised in multiple ways (Ohlsson 1992)for instance by constraint relaxation (ie the deactiva-tion of some knowledge element that has acted as a con-straint on the options initially considered) and chunk de-composition (ie the separation of the components of aperceptual chunk Knoblich et al 1999)

Kaplan and Simon (1990) have proposed an alterna-tive representational change theory of insight They sug-gest that people encounter impasses because their initialproblem representation is incomplete rather than mis-leading Hence the problem solver has to resolve an im-passe by noticing and encoding additional features of theproblem rather than by abandoning or deactivating un-helpful ones In particular they hypothesize that peoplesearch for and notice invariants (ie properties that re-main the same when the problem is represented in differ-ent ways) Although our notion of activation redistributionclaims that restructuring processes occur outside con-sciousness (Bowden amp Beeman 1998 Metcalfe 1986)Kaplan and Simon (1990) suggest that those processes areunder conscious control

In the past researchers have typically tested their in-sight theories against performance measuresmdashprimarilythe time it takes to find a solution and the probability offinding a solution within a given time frame Our ownpast work is no exception (Knoblich et al 1999) How-ever as argued by Newell and Simon (1972) and othersperformance measures provide only weak informationabout underlying processes and need to be supplementedwith process tracing methods Verbal protocols have beenused to study insight (Kaplan amp Simon 1990 Schooleramp Melcher 1995) but Schooler Ohlsson and Brooks(1993) have questioned whether the think-aloud method isnonreactive vis a vis insight problem solving Eye move-ments present a potentially powerful alternative There isa close connection between which display item a person islooking at and which item he or she is thinking about aswell as between fixation duration and amount of process-ing (Just amp Carpenter 1976 Knoblich amp Rhenius 1995Rayner 1978 1998) Eye movement data thus providesa temporally fine-grained record of problem solving pro-cesses In spite of the proven usefulness of eye movementrecordings there are no studies that apply this method-ology to insight problem solving In the present study wetested three predictions from our insight theory againsteye movement data recorded while the participants solvedmatch stick arithmetic problems

Eye Movements in Match Stick ArithmeticWe used matchstick arithmetic problems because each

problem consists of a small number of distinct elementsarranged in a horizontal sequence Hence we could deter-mine with precision which problem component a partici-pant was fixating at any one moment in time In matchstickarithmetic the problem solver is faced with an incorrectarithmetic statement expressed in Roman numerals con-structed out of matchsticks The goal is to correct thearithmetic statement by moving a single matchstick from


















METHOD











RESULTS


















A 22 14 31B 300 112 300C 136 42 300
















DISCUSSION
















REFERENCES
























































METHOD











RESULTS


















A 22 14 31B 300 112 300C 136 42 300
















DISCUSSION
















REFERENCES











































RESULTS


















A 22 14 31B 300 112 300C 136 42 300
















DISCUSSION
















REFERENCES
















































A 22 14 31B 300 112 300C 136 42 300
















DISCUSSION
















REFERENCES





















































DISCUSSION
















REFERENCES



















































REFERENCES







































An eye movement study of insight problem solving

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