Can short duration visual cues influence students’ reasoning and eye movementsin physics problems?

Adrian Madsen,1 Amy Rouinfar,1 Adam M. Larson,2 Lester C. Loschky,3 and N. Sanjay Rebello1

1Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA2Department of Psychology, University of Findlay, Findlay, Ohio 45840, USA

3Department of Psychology, Kansas State University, Manhattan, Kansas 66506, USA(Received 10 November 2012; published 2 July 2013)

We investigate the effects of visual cueing on students’ eye movements and reasoning on introductory

physics problems with diagrams. Participants in our study were randomly assigned to either the cued or

noncued conditions, which differed by whether the participants saw conceptual physics problems overlaid

with dynamic visual cues. Students in the cued condition were shown an initial problem, and if they

answered that incorrectly, they were shown a series of problems each with selection and integration cues

overlaid on the problem diagrams. Students in the noncued condition were also provided a series of

problems, but without any visual cues. We found that significantly more participants in the cued condition

answered the problems overlaid with visual cues correctly on one of the four problem sets used and a

subsequent uncued problem (the transfer problem) on a different problem set. We also found that those in

the cued condition spent significantly less time looking at ‘‘novicelike’’ areas of the diagram in the

transfer problem on three of the four problem sets and significantly more time looking at the ‘‘expertlike’’

areas of the diagram in the transfer problem on one problem set. Thus, the use of visual cues to influence

reasoning and visual attention in physics problems is promising.

DOI: 10.1103/PhysRevSTPER.9.020104 PACS numbers: 01.40.Fk

I. INTRODUCTION

When learners attempt to solve physics problems, in ourcase those containing text and an image, various parts of thevisual information compete for the learners’ attention. Thisis because our brains can only process some of the informa-tion received by our retinas at a given time [1] and wegenerally only become aware of that part of the retinalinformation that has been attended to and entered intowork-ing memory [2–4]. There are a large number of visuallearning or assessment environments in physics, which con-tain information that is both relevant and irrelevant to thetask at hand, competing for the learner’s attention. To facili-tate learning, one can help the learner to focus their attention,and thus their cognitive resources, on relevant information ininstructional problems and to avoid focusing on irrelevantinformation. Mayer’s cognitive theory of multimedia learn-ing [5] explains that learning occurs when relevant informa-tion is successfully selected and organized into a coherentrepresentation and integrated into the existing knowledgebase. All of these processes occur in the learner’s workingmemory, which is a limited cognitive resource that can beused up by focusing on irrelevant information. To helpalleviate this problem, visual cues can help the learner attendto and notice relevant information in the problem, which

they may have previously ignored. Having attended to rele-vant information in the problem, the learner may be morelikely to retrieve relevant information from long-termmem-ory, which will then be available for problem solving pro-cesses occurring within the constraints of their workingmemory limits. Providing visual cues by no means guaran-tees that the learner will reach a correct solution and under-standing of the problem. However, such cues could at leastfacilitate correct problem solving and learning by helpingthe learner avoid ‘‘red herrings’’ based on common alternateconceptions about physics.Visual cues have been studied in a large range of con-

texts and have been found to be useful in many of thesecontexts. Grant and Spivey [6] studied how shifts in visualattention to critical diagram features can facilitate correctproblem solving. The researchers studied Duncker’s radia-tion problem1 [7] and manipulated the diagram so thateither the relevant or irrelevant area of the diagram pulsedor the diagram remained static. They found that the groupof participants who viewed the relevant area pulsing(expanding by six pixels repeatedly) spent more time

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

1Duncker’s radiation problem (adapted byGrant and Spivey [6])states, ‘‘Given a human being with an inoperable stomach tumor,and lasers which destroy organic tissue at sufficient intensity, howcan one cure the person with these lasers and, at the same time,avoid harming the healthy tissue that surrounds the tumor?’’ Thesolution is to fire several low intensity lasers at the tumor fromdifferent locations so that, although each laser is not powerfulenough to damage the tissue surrounding the tumor, the combinedpower of several laser beams is sufficient to destroy the tumor.

PHYSICAL REVIEW SPECIAL TOPICS - PHYSICS EDUCATION RESEARCH 9, 020104 (2013)

1554-9178=13=9(2)=020104(16) 020104-1 Published by the American Physical Society

looking at the relevant area and were significantly morelikely to produce a correct solution than those who saw theirrelevant area pulsing or a static diagram. They argued thatdrawing visual attention to the critical area of a diagramcan influence cognitive processing in ways that lead tocorrect problem solving. Thomas and Lleras [8] conducteda follow-up study on the work of Grant and Spivey [6] todetermine the existence and nature of an implicit connec-tion between eye movements and cognition. To do this,they overlaid visual cues on Duncker’s radiation problemdiagram for 4 sec at the end of a 26 sec free viewing period.This was repeated 20 times or until the participantanswered correctly. These visual cues moved in four differ-ent patterns. One group of participants saw a patternof random characters that mimicked the solution to theproblem.2 Participants in this ‘‘embodied solution’’ groupwere significantly more likely to solve the problem cor-rectly. They concluded that manipulating eye movementscan serve as an implicit guide to influence thinking onspatial reasoning tasks.

Thomas and Lleras conducted another study to deter-mine if the greater rate of correct problem solving by thosein the embodied solution group was a result of shifts inattention or actual eye movements [9]. The ‘‘eye-movement’’ group saw random digits appear in a patternthat embodied the solution and followed these digits withtheir eyes. The ‘‘attention-shift’’ group saw the same stringof random digits as the eye-movement group but wasinstructed to follow the digits with their attention but tokeep their eyes fixated at the center of the screen. The eye-movement and attention-shift groups were more likely thanother groups to answer the problem correctly. However, nosignificant difference was found between the eye-movement and attention-shift groups. The results of thisstudy suggest that the primary mechanism behind theincreased correct solution rates in the study by Thomasand Lleras [8] for the embodied solution group is the shiftof attention that immediately preceded the directed eyemovements. Thus, directed shifts of attention have beenfound to influence cognitive processing on spatial insightproblems and increase rates of correct solutions. Based onsuccessful problem solving presented in this previouswork, we apply visual cueing to static physics problemsto explore whether such cues serve as an implicit guide toimprove problem solving performance.

A. Theoretical background

There are two relevant theoretical frameworks whichhelp us interpret the functions and mechanisms of visualcueing. The first, representational change theory [10], is

related to the cognitive mechanisms involved in solvingproblems that require insight. The second, the cognitivetheory of multimedia learning [5], pertains to the use ofmultimodal information in learning, and more specificallyfor our current purposes, cueing.

1. Representational change theory

Representational change theory [10] provides a frame-work to understand the cognitive mechanisms involved insolving problems—particularly, problems that requireinsight, as opposed to merely algorithmic problems. Thistheory is relevant to our work on visual cues, as the prob-lems we are interested in require conceptual insight and arenot merely algorithmic in nature.Representational change theory explains that the way a

problem is represented in a solver’s mind mediates theknowledge that the solver retrieves from long-term mem-ory. The retrieval process is based on spreading activationamong concepts or pieces of knowledge in long-termmemory. An impasse or block occurs when the way aproblem is represented does not permit retrieval of neces-sary operators or possible actions. Breaking the impasserequires changing the problem representation. A new men-tal representation acts as a retrieval cue for relevant opera-tors in long-term memory, extending the informationavailable to the problem solver. Insight is achieved whenthe impasse is broken and the retrieved knowledge opera-tors are sufficient to solve the problem.According to representational change theory, there are

three mechanisms by which an impasse to solving a prob-lem is broken: (i) adding information to the problem toenrich and extend the existing representation (i.e., elabo-ration), (ii) replacing the existing representation with adifferent more productive representation (i.e., reencoding),or (iii) removing unnecessary constraints often self-imposed by the problem solver (i.e., constraint relaxation).Once the impasse is broken, the new mental representationof the problem can activate relevant concepts in long-termmemory, extending the information available to the prob-lem solver. When the relevant concept or pieces of knowl-edge are available to the solver, she can apply the conceptto answer the question correctly.

2. Cognitive theory of multimedia learning

Many physics problems involve the use of informationpresented with text and diagrams. Thus, learning to solvephysics problems involves coordinating informationprovided in multiple modalities with the learner’s priorknowledge. The cognitive theory of multimedia learning[5] identifies three distinct processes—selection, organiza-tion, and integration—involved in learning from informa-tion presented in multiple modalities. Based on Mayer’scognitive theory of multimedia learning, de Koning et al.[11] proposed a framework for attention cueing whichsuggests that visual cues, if designed appropriately, can

2Participants in this embodied solution group saw randomcharacters that moved from outside the skin to inside the tumorat several locations around the diagram. This embodied thesolution of using several weak lasers incident at different angles.

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-2

facilitate all three processes involved in multimedialearning.

Mayer describes selection as the process of attending tocertain pieces of sensory information from each modality.de Koning extends selection to visual cueing and explainsthat selection cues help the learner attend to relevantinformation in a visual representation. Organization isusing the selected information in each modality to createa coherent internal representation in that modality.Organization involves structuring information to facilitatecomparison, classification, enumeration, generalization,and cause-effect relationships. Organizational cues empha-size structure and facilitate the identification and the sub-sequent representation of the material’s organization.Integration is combining internal representations from dif-ferent modalities with activated prior knowledge. Twokinds of integration processes are important for multimedialearning and problem solving: integrating elements(i) within a single representation that are widely spatiallyseparated [12] or (ii) across multiple representations ormodalities such as coordinating graphs and pictures withtext to create an operational situational mental model [13]to solve the problem. Cueing learners to relate elementswithin a single representation is especially important if theelements they need to integrate are widely spatially sepa-rated [12]. Cueing can also be useful when the problemis complex and could have more than one method forsolution and schema construction, imposing a high cogni-tive load on the learner. Cues that make implicit causal orfunctional relations between elements more explicit canpotentially improve problem solving ability. Integrationcues can be particularly helpful for learners when theymust integrate textual and graphical information to createa situation model in order to solve a math or scienceproblem [13].

The distinctions among cue types proposed byde Koning et al. [11] are useful in guiding one’s thinkingabout cues. However, in practice it seems that those cuesthat would be useful in solving a problem often involvecombinations of the three types. More specifically, virtu-ally any organization or integration cue will simulta-neously serve as a selection cue, since both must attractattention to a problem element in order to be effective.Thus, in our current study, we utilized visual cues thatserved to both select relevant information and integraterelated elements in a problem diagram. However, the cur-rent study did not investigate organization cues.

B. Research questions

In the current study, we aim to answer the followingresearch questions.

(1) Do short duration, dynamic visual integration andselection cues improve students’ problem solvingperformance on introductory conceptual physicsproblems?

(2) How do dynamic visual cues influence participants’eye movements on current cued problems and sub-sequent uncued problems?

(3) Does students’ problem solving performance on asubsequent uncued problem improve after seeingvisual cues on similar problems?

II. METHOD

A. Participants

We conducted individual sessions with 63 participantsconcurrently enrolled in either a first or second semesterintroductory physics course. These students were enrolledin either a traditional course, which included lectures, arecitation, and a lab, or a reformed course, which includedstudios [14] and lectures. There were separate instructorsfor the traditional first and second semester physics coursesas well as for the reformed first semester course. Allcourses were at the same large, Midwestern public univer-sity. Students were invited via an Email sent to all studentsenrolled in the course and were paid $10.00 for participa-tion. We collected data over the duration of two semesters,but ensured that students had covered relevant topics intheir physics course before recruiting them to volunteer inour study. We invited students from the same courses toparticipate both semesters. We also ensured that eachstudent participated only once.

B. Materials

1. Design of study problems

The materials consisted of four sets of related concep-tual introductory physics problems in which an accom-panying diagram was necessary to answer the problem.Each of these problems had been studied previously in thephysics education research literature, and found to havediagram features that students consistently used to pro-duce incorrect answers, which we refer to as ‘‘novice-like’’ areas of the diagram. The problem diagrams alsocontained areas which one needs to attend to in order toanswer the question correctly, called ‘‘expertlike’’ areas.These expert- and novicelike areas were spatially separateand the problem required a solver to make some com-parison between the areas to come to the correct answer.In the next section we point out the novicelike and expert-like areas of the diagrams for each of the four problemsets used. These were determined through interviews withnovice physics students and confirmed with previousstudies from physics education research literature thatused the same problems. A more complete descriptionof the features of these problems, details of these inter-views, and previous studies of these problems arereported in Madsen et al. [15]. Additionally, we foundsignificant differences in the time spent fixating in thesediagram areas based on the correctness of participants’answers. Those who answered incorrectly spent more

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-3

time fixating in the novicelike areas while those whoanswered correctly spent more time fixating in the expert-like areas [15]. Three of the six problems discussed in ourprevious study were on kinematics graphs. We choose to

use one of these kinematic graph questions as well as thethree other questions for a total of four problems in thecurrent study. We refer to these problems as the rollercoaster, ball, skier, and graph problems (see Fig. 1).

2. Sequence of problems

Each problem set consisted of an ‘‘initial’’ problem,four ‘‘similar’’ problems, and a ‘‘transfer’’ problem. Allproblems were open- ended and contained a diagramwhich one had to use in order to answer the problem.The similar problems in each set had the same problemstatement as the initial problem and the same surfacefeatures. The novicelike area of the diagram for eachwas manipulated in a way that would change the answerone would give if answering based on a novicelike con-ception. For example, in the similar problem set shown inFig. 2, the number and depth of bumps on the rollercoaster track and horizontal distance between carts werevaried. If a student used the features of the track todetermine the speed of the carts, their answer would bedifferent for each of these problems. The transfer problemin each problem set had different surface features buttested the same concept as the initial and similar prob-lems. For example, the roller coaster transfer problemshown in Fig. 3 contained two tracks with different startand end heights. The student needed to reason about thepotential and kinetic energy of tracks with the samedifference in height.

3. Design of and rationale for the visual cues

Participants in the ‘‘cued’’ condition were shown dy-namic visual cues overlaid on the similar problem dia-grams. The cues used in this study were designed tocombine integration and selection cues [11] and werealso designed to mimic the eye movements of thosewho answered the same problems correctly in our pre-vious study [15]. There was a large variation in eyemovements from one individual to another while viewingthe diagrams in these physics problems, so the visual cuesdid not mimic the eye movements of correct solversexactly. Instead, video playback of the correct solvers’eye movements was viewed repeatedly and special atten-tion was paid to the eye movements in and around therelevant area of interest. Similarities between participantswere observed, and visual cues were modeled after thesepatterns.Cues on all four problem sets were intended to prompt

selection and integration of expertlike elements in theproblem diagrams, and below we describe how the cuescould achieve this on each problem set. Importantly, ourcharacterization of the cues as prompting selection andintegration is from the target ‘‘expert’’ perspective (sincethe student perspective often corresponds to the ‘‘novice’’perspective). On the ‘‘roller coaster’’ problem, the expert-like area of the diagram (as determined in our previous

FIG. 1. Four ‘‘initial’’ problems taken from Madsen et al.(Ref. [15]) and used in the current study. Shown from top tobottom are the roller coaster, ball, Skier, and graph problems.

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-4

study [15]) was the relative heights of the roller coastercarts. The relationship between heights of the rollercoaster carts is needed to determine the potential energyof each at the beginning and end of the path and thenrelate this to the amount of kinetic energy and finally thespeed [16]. So, in this problem the cues moved betweenthe roller coaster carts to help students compare theheights of the roller coaster carts (Fig. 4). The novicelikeareas of the diagram were the roller coaster tracks, as

students who answered incorrectly cited the shape of thetracks as the reason the final speeds of the carts woulddiffer. The cues in this study helped participants to selectthe heights of the roller coaster carts and not attend to theshape of the roller coaster tracks, which is the mostcommonly used feature when giving an incorrect answer.They also aimed to help participants integrate the heightsof the roller coaster carts, which were spatially separated,so they could compare the heights of the initial and finalcarts.The expertlike areas for the ‘‘ball’’ problem were the

distances between the balls on track A and track B whenboth balls have moved the same distance in the same 1 secinterval (see Fig. 10 in the Appendix). So, for this problemthe cues aimed to help the students compare the distancesbetween balls during the same time period (integration),for example, by comparing the distance between the ballson track A and track B between 1 and 2 sec. The novicelikearea for this problem was the point when the balls are at thesame position at the same time. Here, students who answerincorrectly often explain that if the balls on tracks A and Bhave the same position at the same moment in time, theyare moving at the same speed. So, the cues were alsointended to help the students select distances betweensuccessive balls and not compare the positions of the ballsat the same time.The expertlike areas for the ‘‘skier’’ problem were the

changes in heights of each slope, as these heights are

FIG. 3. Example of a transfer problem used in the rollercoaster problem set in the study.

FIG. 2. Example of four ‘‘similar’’ problems used in the rollercoaster problem set in the study.

FIG. 4 (color online). Roller coaster similar problem used inthe study with visual cues overlaid. The blue dots are the visualcues and the numbers in italics show the sequence of animatedcues (the numbers were not seen by study participants).

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-5

directly related to the change in potential energy for eachslope (see Fig. 11 in the Appendix). So, the cues weredesigned to help the student to compare the changes inheights of each slope (integration). The novicelike areas ofthe diagram are the slopes, as students who answer incor-rectly compare the steepness of the slopes andrelate these to the relative changes in potential energy.So, the cues were also designed to help the students selectthe changes in height and ignore the steepness of eachslope.

The expertlike area for the ‘‘graph’’ problem was thepoint when the slope of the two lines was the same, as thisis when the two objects were moving with the same speed(see Fig. 12 in the Appendix). So, the cues aimed to helpthe students judge the slope of the curved line at severalpoints by tracing out an invisible tangent line at a giventime and comparing this to the slope of the straight line atthe same time (integration). The novicelike area(s) for thisproblem was (were) the point(s) where the two linescrossed. At the crossing point(s), the two objects had thesame position, but not the same speed. So, the cues wereintended to help the solvers to attend to the slopes of thelines and not the points where the line(s) crossed(selection).

C. Apparatus

Participants were presented with physics problems on acomputer screen viewed at a distance of 24 in. using achin and forehead rest to minimize participants’ extrane-ous head movements. The resolution of the computerscreen was set to 1024� 768 pixels with a refresh rateof 85 Hz. Each physics problem subtended 33:3� � 25:5�of visual angle. Eye movements were recorded with anEyeLink 1000 desktop mounted eye-tracking system(Ref. [17]), which had an accuracy of less than 0.50� ofvisual angle. An eye movement was classified as a sac-cade (i.e., in motion) if the eye’s acceleration exceeded8500�=s2 and the velocity exceeded 30�=s. Otherwise, theeye was considered to be in a fixation (i.e., stationary at aspecific spatial location). A nine-point calibration andvalidation procedure was used at the beginning of theexperiment. Participants’ verbal explanations and gestureswere recorded with a Flip video camcorder.

D. Study design and procedure

To ensure that the participants had sufficient prerequi-site knowledge of the concepts tested in the study prob-lems, each participant completed a pretest, whichconsisted of four open-ended questions designed to gaugetheir understanding of speed and potential energy. Eachparticipant took part in an individual session lastingbetween 30 and 60 min. In each session they were firstgiven an explanation of what to expect and the eye trackerwas calibrated. Next, participants were instructed to spendas much time as needed on each question and answer with

a verbal explanation of their reasoning when ready.Participants in the cued condition were told that coloredshapes may appear on some of the problems and whenthese appeared they should follow them with their eyes.No further information about the purpose of the cues wasgiven to participants.Each participant was randomly assigned to the cued

condition or the noncued condition. Equal numbers ofparticipants were assigned to each condition. The researchdesign is shown in Fig. 5. First, students answered theinitial problem to demonstrate their current level of under-standing. If they answered incorrectly, they saw a series ofsimilar problems, which contained the same problem state-ment as the initial problem, tested the same concept, andcontained a diagram with similar surface features. Whenthe student answered a similar problem correctly, theywere shown the transfer problem. This process continueduntil a maximum of four similar problems had been viewedby the participant, after which the participant was pre-sented the transfer problem regardless of whether theyanswered the similar problem correctly or incorrectly. Allparticipants viewed the four sets of problems in the sameorder.Whenever a student was ready to provide an answer

and explanation for a problem, they indicated this bypressing any key on the keyboard, at which point theproblem displayed on the computer would becomeslightly smaller in size to indicate to the student thatthey had successfully pressed a key. The participantsthen explained their answer and reasoning to the experi-menter and were able to point to areas on the computerscreen if necessary. The experimenter used a predefinedrubric to determine if the given answer and explanationwere correct or incorrect. If the answer and/or reasoningwere vague, the experimenter would ask for clarification.Once the experimenter had sufficient information to deter-mine the correctness of the answer, the experiment wouldproceed.Participants in the cued condition saw moving colored

shapes overlaid on the similar problems. Moving coloredshapes were used because color and motion have beenfound to be the most predictive of attentional selectionbecause of their high perceptual salience [18]. The cues

FIG. 5 (color online). Flow chart showing how the initialproblem, similar problems, and transfer problems were admin-istered to students in each of four problem sets.

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-6

used for the roller coaster problem are shown in Fig. 2and those for the ball, skier, and graph problems areshown in Figs. 10–12 in the Appendix. Each coloredshape appeared 4 sec after the problem was presented togive the participant time to read the problem statement(although the problem statement for each similar problemwas the same). The cues then appeared for 500 msec at 12positions in the diagram for a total cueing time of 6 sec.This 6 sec time period was chosen based on the successfulcueing work of Thomas and Lleras [8], in which visualcues were shown for 4 sec. After the cues ended, partic-ipants could spend as much time as they wanted on theproblem.

III. CONNECTION BETWEEN THEORETICALBACKGROUND AND CURRENT STUDY

We apply representational change theory to understandhow visual cues can help learners solve physics problems.Ohlsson [10] conceptualizes insight as ‘‘initial failure fol-lowed by eventual success.’’ He explains that insightoccurs when the problem solver is competent to solve theproblem before them, reaches an impasse in the problemsolving process, and then successfully breaks this impasse.Representational change theory is valid for problem solv-ing processes in which this impasse-insight sequenceoccurs. We claim that this sequence is likely to occur inour study since we chose problems that, by their verynature, lent themselves to impasse and insight. We usedintroductory conceptual physics problems requiring stu-dents to activate specific conceptual resources [19]. Sincethese questions are not given in any particular context, suchas the end of a chapter or during lecture, the students mustfirst recognize the appropriate concept. If they cannotrecognize an appropriate concept, they may reach animpasse, which could be resolved when they see the visualcues and focus on relevant information. Further, since thesequestions are conceptual, once a student recognizes theappropriate concept to use, the solution does not requiregoing through a long series of mental steps or calculationsbefore getting to an answer. Instead, the student applies theappropriate conceptual resource and can quickly recognizean answer.

Importantly, the problem diagrams also contain visualinformation consistent with an incorrect novicelikeanswer. In our previous study, we found that studentswho answered these problems incorrectly attended tothis novicelike visual information and activated concep-tual resources which led to the wrong answer [15]. So toanswer a problem correctly, the student must not onlyrealize the appropriate concept, but must also suppress theuse of these novicelike concepts that lead to incorrectanswers. Students may also reach an impasse when theyrepeatedly see very similar problems overlaid with visualcues but recognize that they are not answering theseproblems correctly. During this process, the visual cues

draw students’ attention to areas they had previouslyignored. The combination of being presented with similarproblems several times with their attention being redir-ected to an area they previously found irrelevant couldcause students to second-guess their previous answer. Asthey reconsider the diagram areas highlighted by visualcues, they may resolve their impasse with an insight,activate appropriate conceptual resources, and answerthe problem correctly.In order to resolve an impasse, we hypothesize that

visual cues can serve to help the student rerepresent aproblem in their mind. In line with representational changetheory, the purpose of visual cues is to help the studentreplace an existing unproductive representation with aproductive one, or add to their existing representation untilit is adequate to solve the problem. In the current study weexplore visual cues that we believe help rerepresentationoccur through elaboration and reencoding, but not con-straint removal.Elaboration is useful for a learner who has gathered

insufficient information to form a productive mental rep-resentation of the problem, and has thus reached animpasse. Integration cues can facilitate the addition ofcritical new information to the representation by helpingthe learner attend to information in a particular order and/or help the learner make comparisons between differentelements of the diagram. A learner attending to the infor-mation provided by these cues is prompted to activatepreviously dormant relevant information from long-termmemory and eventually encode a new representation forthe problems. The problems that we used containedexpertlike elements in the diagram that were spatiallyseparate and needed to be compared and integrated inorder to answer correctly. Integration cues can add infor-mation to the learner’s current mental representation byhelping them make these necessary connections. To deter-mine the most useful way to design the integration cuesfor these problems, we used the eye movements of correctsolvers on the same problems from our previous study[15], looked for patterns in the way correct solvers viewedthe expertlike elements, and modeled our visual cues onthese patterns.Reencoding, unlike elaboration, involves not just adding

new information, but instead backtracking through pre-vious layers of the problem solving process, eliminatingunproductive layers in their mental representation of theproblem and creating new productive layers. The reencod-ing process is especially important for the problems used inour study, as the diagrams for these problems each containan area consistent with the most common incorrect answer.This feature of the problems makes it more likely that thestudents will activate unproductive naıve concepts whenreasoning to an answer. In order to help them reencode theproblem representation in a scientifically accurate way,selection cues could be used. Rather than provide new

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-7

information, these cues prompt the learner to ignore irrele-vant information and attend to relevant information forsolving the problem. If the learner attends to the previouslyignored relevant information, this in turn may activatepreviously dormant relevant prior knowledge from long-termmemory, and the learner may eventually encode a newand more correct representation for the problem. In asimilar study of expert chess players solving problemswith two possible solutions, researchers found that whenthe players had found the first solution they reported look-ing for a better one, though the eye-movement recordindicated they continued to look at features of the problemrelated to the solution they had already found [20].Although they tried to seek out the better solution, theirattention was fixated on their first idea. Participants in ourprevious study who answered these problems incorrectlyspent more time looking at areas consistent with a novicethan those who answered correctly [15]. If they are similarto the chess players, they may have tried to consider othersolutions, but kept their attention fixated on areas consis-tent with their first idea. Selection cues can improve prob-lem solving by helping solvers ignore the novicelike areasof the diagram, by instead attending to the expertlike areas,and use information in those areas to create a new mentalrepresentation of the problem.

IV. ANALYSIS AND RESULTS

Participants were only included in our analysis if theycorrectly answered pretest questions demonstrating knowl-edge of the concepts tested in the study problems. Thepretests were scored as correct or incorrect by one of theresearchers. When a participant’s answer was unclear, tworesearchers discussed the answer and agreed on a conclu-sion. There were cases where a participant did not demon-strate adequate understanding of one of the concepts tested,so their data for that concept were not included in thisanalysis. Further, we only included participants with usableeye-movement data files. There were four participantswhose eye-tracking data files became corrupted and couldnot be used.

A. Improvements to problem solving performancewith visual cues

We first investigated the problem solving performanceof participants by comparing how often those in the cuedand noncued conditions who had answered the initialproblem incorrectly answered one of the similar problemscorrectly. It is necessary to look only at the subgroup ofstudents who answered the initial problem incorrectly,because we wished to test the effect of the cues only onthose who answered the initial problem incorrectly. Wecompared the aggregate number of participants in thecued and noncued conditions who gave an incorrectanswer on the initial problem and then gave a correctanswer and explanation on one of the four similar

problems. The percentages of students in each conditionwho answered a similar problem correctly are displayedin Fig. 6. Fisher’s exact test [21] was employed to test thesignificance of the difference between the cued andnoncued conditions in the proportion of students whocorrectly answered a similar problem. Fisher’s exact testis used with categorical data, which is encountered whenparticipants are classified in two different ways, and smallsample sizes. In our case, the two different ways ofclassification are as follows: (1) whether a participantbelongs to the cued or noncued condition or (2) whethera participant did or did not correctly answer a similarproblem (after answering the initial problem incorrectly).Fisher’s exact test examines whether students in onecondition are more likely to change to answer a similarproblem correctly than students in the other condition onthe same problem set. Results of Fisher’s exact test areshown in Table I. The total number of students includedfor each problem set is different and does not result in 63total participants because we included only those whoanswered the initial problem incorrectly, had satisfactorilyanswered the pretest questions, and had usable eye-movement data files.We found that a statistically greater number of partic-

ipants in the cued condition answered a roller coastersimilar problem correctly (p ¼ 0:012). This means that amere 6 sec of visual cueing for which the participants didnot know the purpose resulted in significantly more stu-dents going from the wrong understanding of the rollercoaster problem to the scientifically correct understandingon a very similar problem. It is promising to find a differ-ence using such a short intervention. We did not findsignificant differences on the ball, skier, or graph problems.Inferences on why this was the case will be reviewed inSec. VI.

FIG. 6. Comparison of percentage of participants in cued andnoncued conditions who gave the correct answer and reasoningon a similar problem. For example, 30% ¼ 6=20 students in thecued condition answering correctly on a similar roller coasterproblem.

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-8

B. Changes in eye movements on similar problems

We next investigated how the visual cues influencedparticipants’ eye movements while viewing the similarproblems. Prior to the experiment, participants in thecued group were told that they might see colored shapesappear on the screen and when they saw the shapes theyshould follow them with their eyes. Participants were notinformed when they would see the shapes. The eye-movement record revealed that there were individual dif-ferences in how closely participants actually followed themoving colored shapes with their eyes. We investigated thepossibility that participants who did not follow the shapesclosely did not benefit as much from the visual cue as thosewhowatched each segment of the cue. We employed a scanpath analysis that looks at both spatial and temporal aspectsof eye movements. A scan path is the collection of fixationsand saccades one makes over time. We specifically usedScanMatch [22], which is an algorithm that compares twoscan paths at a time and computes a number which repre-sents their similarity in space and time. It is based on theNeedleman-Wunsch algorithm used to compare DNAsequences. The ScanMatch algorithm overlays a labeledgrid onto the image of interest and recodes the orderedlocations and fixation durations into a sequence of letters.Longer fixations result in repeated letters in the sequence(Fig. 7). The letter sequences of two sets of eye movementsare then compared to each other to calculate a similarityscore. Letters near each other in the grid receive a higherscore than those with greater spatial separation. The simi-larity score is normalized so that a score near one repre-sents two sequences of eye movements that are identicalspatially and temporally.

We isolated participants’ eye movements while the cueswere being shown for the first similar problem (since allcued participants saw this problem). We completed thisanalysis for participants in the cued condition and com-pared their eye movements to the scan path of the visualcues using the ScanMatch algorithm. We then comparedthe ScanMatch scores of those who had changed to acorrect answer on a similar problem to those who hadnot. This comparison revealed how the performance ofparticipants in the cued group on the similar problems

FIG. 7 (color online). Example of ScanMatch algorithm con-verting a scan path into the letter sequence which was used tocalculate the similarity score. Red circles represent fixations, redarrows represent saccades.

TABLE I. Summary of results of Fisher’s exact test comparing those who did and those who did not answer a similar problemcorrectly for the cued and noncued conditions. An asterisk indicates a significant difference at the � ¼ 0:05 level

Problem set Condition Answered similar

problem correctly

Did not answer

similar problem correctly

p

Roller coaster

Cued 6 14

0.012*Noncued 0 19

Six participants were not included because of insufficient pretest scores, four participants’

eye-movement files were unusable, and 14 answered the initial problem correctly

Ball

Cued 7 10

0.228Noncued 6 13

One participant’s eye-movement file was unusable, and 26 answered the initial problem correctly

Skier

Cued 4 6

0.142Noncued 2 12

Six participants were not included because of insufficient pretest scores, one participant’s

eye-movement file was unusable, and 32 answered the initial problem correctly

Graph

Cued 6 16

0.098Noncued 3 25

Three participants’ eye-movement files were unusable, two participants did not complete this

problem, and eight answered the initial problem correctly

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-9

varied based on how well they followed the cues with theireyes. To do the comparison, we employed the Kruskal-Wallis one-way analysis of variance in SPSS. This test isthe nonparametric method to compare two or more inde-pendent groups and is the equivalent of the one-wayANOVA. This test was appropriate for our analysis sincewe had small group sizes that did not form a normaldistribution. Average ScanMatch scores and standarderrors are reported in Table II. We found a significantdifference in ScanMatch scores between those who hadanswered a similar problem correctly and those who had

not for the roller coaster problem only [Hð3Þ ¼ 9:939,p ¼ 0:019]. We did not find statistically significant differ-ences on the ball, skier, or graph problems. This means thaton the roller coaster problem the participants whoanswered a similar problem correctly followed the visualcues more closely on similar problem 1. This suggests thaton this problem there is a connection between how wellone follows the visual cues with their eyes and if theychange from an incorrect to correct answer and verbalexplanation of their reasoning. We do not suggest a causalmechanism, but will explore this finding more in Sec. V.For the other three problems, such a relationship betweenfollowing the cues and performance on the problems wasnot found.

C. Problem solving performance on transfer problems

Showing that visual cues have the potential to helpstudents give the correct answer and reason about a prob-lem is an encouraging result, but we will only have evi-dence that some kind of learning has occurred if studentscan subsequently answer a related question with no cues.To investigate this possibility, we analyzed the correctnessof those in the cued and noncued conditions on the transferproblem for each problem set. We once again used Fisher’sexact test to test for a difference in the number of studentswho had answered the transfer problem correctly in thecued and noncued conditions. Results are shown inTable III. Figure 8 displays the percentage of students inthe cued and noncued conditions who answered each trans-fer problem correctly. We found that a statistically greaternumber of participants in the cued condition answered the

TABLE II. ScanMatch scores for cued participants who didand participants who did not answer a similar problem correctly.An asterisk indicates a significant difference at the � ¼ 0:05level

ScanMatch score (� standard error)

Problem Changed to correct

answer on similar

problem

Did not change

to correct answer on

similar problem

Roller coaster*0:588� 0:031 0:379� 0:042

(n ¼ 6) (n ¼ 14)

Ball0:552� 0:046 0:557� 0:044

(n ¼ 7) (n ¼ 10)

Skier0:700� 0:037 0:588� 0:058

(n ¼ 4) (n ¼ 6)

Graph0:652� 0:034 0:595� 0:028

(n ¼ 6) (n ¼ 16)

TABLE III. Summary of results of Fisher’s exact test comparing those who did and did not answer the transfer problem correctly forthe cued and noncued conditions. An asterisk indicates a significant difference at the � ¼ 0:05 level

Problem set Condition No. of participants

providing correct answer

No. of participants

providing incorrect answer

p

Roller coaster

Cued 3 170.263

Noncued 1 18

Six participants were not included because of insufficient pretest scores, four participants’

eye-movement files were unusable, and 14 answered the initial problem correctly

Ball Cued 8 9*0.039

Noncued 3 16

One participant’s eye-movement file was unusable and 26 answered the initial problem correctly

Skier

Cued 2 70.370

Noncued 2 12

Six participants were not included because of insufficient pretest scores, one participant’s

eye-movement file was unusable, and 32 answered the initial problem correctly

Graph Cued 7 15 0.181

Noncued 6 22

Three participants’ eye-movement files were unusable, two participants did not complete this

problem and eight answered the initial problem correctly

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-10

ball transfer problem correctly and gave the correct rea-soning (p ¼ 0:039). We also note that the raw percentagecorrect on the transfer problem was higher for those in thecued condition than the noncued condition for all fourproblem sets.

D. Changes in eye movements on transfer problems

The purpose of the visual cues was to redirect visualattention to relevant areas and help students integratedifferent important elements in a physics diagram. Itmay be that the brief visual cues did not help studentsanswer the transfer problem correctly, although it mayhave influenced their visual attention. To test this idea, wecompleted an areas of interest (AOI) analysis on the eyemovements on the transfer problem. To do this we definedtwo types of areas in each diagram, the expertlike andnovicelike areas. The definitions for the novicelike areasof interest came from the individual think-aloud inter-views and eye-tracking analysis reported in our previousstudy [15]. The expertlike areas were defined by expertraters and are also described in [15]. For example, for theroller coaster problem, we defined the expertlike AOIaround the roller coaster carts, as expert raters determinedthat the relative heights of the carts are required to judgethe final speeds of the carts on each track. We defined thenovicelike AOI around the roller coaster tracks as wefound through individual interviews and literature inves-tigating a similar problem that those who answered incor-rectly did so using features of the track. We mimicked theAOI definitions used in the previous study in the currentanalysis for each problem set. The AOIs for the rollercoaster problem are pictured in Fig. 9. The eye trackerused in this study had an average error of 0.5 deg of visualangle, so the AOIs were defined to be 0.5 deg of visualangle from the edge of the desired region or element inthe diagram.

After defining the novicelike and expertlike AOIs in theproblem diagrams, we determined the amount of timeeach participant spent fixating in these areas and dividedby the total time they spent fixating on the diagram tonormalize for differences in viewing speeds. We thencompared the percentage of time participants in thecued and noncued conditions spent in the novicelikeand expertlike AOIs. If visual cues had positively influ-enced the eye movements of those in the cued condition,we would expect to see larger percentages of time in theexpertlike AOIs than those in the noncued condition.Further, we would expect to see smaller percentages oftime in the novicelike areas than those in the noncuedcondition. If cues had no influence on the eye movementsof those in the cued condition, we would expect nodifferences in the percentage of time in either the expert-like or novicelike AOIs based on condition.We compared the percentage of time spent in the

novicelike and expertlike AOIs using a one-wayANOVA with percentage of time in AOI as the dependentvariable and cued or noncued condition as the indepen-dent variable for each transfer problem. We remind thereader that we included only the eye movements of thoseparticipants who had answered the initial problem incor-rectly and thus had been shown the similar problem(s).The results are displayed in Table IV. For the rollercoaster problem, we found that participants in the cuedcondition spent a statistically higher percentage of fixa-tion time in the expertlike AOI and a smaller percentagein the novicelike AOI. We also found for the ball andskier problems participants in the cued condition spent asmaller percentage of fixation time in the novicelike

FIG. 9 (color online). Expertlike and novicelike definitions ofareas of interest (AOI) for the roller coaster transfer problem.The expertlike AOIs are around the roller coaster carts (shown inblue) while the novicelike AOIs are around the tracks (shown inred). The green boxes outline the problem statement AOI and thediagram AOI.

FIG. 8. Comparison of percentage of participants in cued andnoncued conditions who gave the correct answer and reasoningon the transfer problem for each problem set in the study. Forexample, 15% ¼ 3=20 students in the cued condition answeringcorrectly on the roller coaster transfer problem.

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-11

AOIs. This indicates that the cues helped participants inthe cued condition allocate more visual attention to theexpertlike area (on the roller coaster problem) whichcontained information needed to answer correctly andallocate less visual attention to the novicelike areas (onthe roller coaster, ball, and skier problems) which con-tained visual information consistent with scientificallyincorrect conceptions. So, seeing the visual cues influ-enced how participants viewed the transfer problems butnot how they answered them.

E. Participants’ impressions of the visual cues

Sincewe did not tell the students the purpose of the visualcues, one might wonder what they thought of the coloredshapes flashing on the screen.We present some examples ofstudents’ ideas about the cues below. All three excerptscame from transcriptions of audio-recorded conversationsthat occurred directly after the student had completed allstudy problems. Students’ names have been changed belowto numbers S1–S3 to protect their anonymity.

Interviewer: When you saw the colored shapes, what didyou think of them?

S1: Why are these moving everywhere?Interviewer: Did you have any idea what they were?S1: No, I was just following them like I was told to.

Interviewer: Did you have any thoughts about whatthose dots were for?

S2: I mean to see if they had the same mass, it was likecomparing the carts it seemed like. It would go back andforth, in the cart one at least.

S2: Did you think they were trying to get you to doanything?

S2: Oh, didn’t think about it at the time, I guess it wastrying to tell you they were at the same height. Didn’t eventhink about that . . . or the blue dots the other time.

Interviewer: What did you think of those little dots thatwere moving?S3: I actually felt like they . . . After I saw the dots then I

thought more about where my eyes were looking when Iwas looking the graph and it seemed like my eyes afterwarddid . . . I felt like I was looking at the same places that I hadjust been looking with the colored stuff . . .

We see from these examples that there was great varia-bility in students’ ideas about the cues. The cues wereinterpreted differently by individual students, which mayhave contributed to the differences in the effects of thecues. We will revisit students’ views of the cues in Sec. VI.

V. CONCLUSIONS

In this study we find some evidence that short duration,dynamic visual selection and integration cues can improvestudents’ problem solving performance on introductoryconceptual physics problems as participants were able tocorrectly answer and reason about problems they werepreviously unable to. Of the four problem sets used, wefound significantly more students changed to a correctanswer after seeing the visual cues on only the rollercoaster problem. Through the lens of representationalchange theory, this suggests that the cues may have helpedthe students overcome an impasse and mentally rerepresentthat problem so that productive concepts or pieces ofknowledge could be retrieved from long-term memoryand applied. We did not find this difference on the otherthree problem sets.

TABLE IV. Mean percentage fixation time spent (� standard error) on the transfer problems for expertlike and novicelike AOIs forparticipants in the cued and noncued conditions.

Problem set Cued Noncued ANOVA results p

Expertlike AOI

Roller coaster*18:5� 2:2 9:7� 1:7

Fð1; 38Þ ¼ 9:573 0.004(n ¼ 21) (n ¼ 19)

Ball28:4� 3:3 21:1� 3:9

Fð1; 34Þ ¼ 2:022 0.164(n ¼ 17) (n ¼ 19)

Skier0:5� 0:3 1:0� 0:6

Fð1; 21Þ ¼ 0:451 0.509(n ¼ 9) (n ¼ 14)

Graph6:3� 1:0 6:7� 1:4

Fð1; 48Þ ¼ 0:039 0.844(n ¼ 21) (n ¼ 28)

Novicelike AOI

Roller coaster*18:0� 2:1(n ¼ 21)

29:5� 3:1(n ¼ 19)

Fð1; 38Þ ¼ 9:835 0.003

Ball*4:3� 1:4 10:9� 2:4

Fð1; 34Þ ¼ 5:372 0.027(n ¼ 17) (n ¼ 19)

Skier*18:2� 2:3 49:0� 3:5

Fð1; 21Þ ¼ 42:105 <0:001(n ¼ 9) (n ¼ 14)

Graph8:0� 1:2 11:6� 1:4

Fð1; 48Þ ¼ 3:427 0.070(n ¼ 21) (n ¼ 28)

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-12

We also investigated how the dynamic visual cuesinfluenced participants’ eye movements while viewingthe cues. We looked for relationships between how welleach participant followed the visual cues with their eyesand if they changed from an incorrect answer on theinitial problem to a correct answer and reasoning on asimilar problem. To investigate this relationship we cal-culated similarity scores between their eye-movementscan path and the path of the visual cues using theScanMatch algorithm and compared these similarityscores between those who had and those who had notcorrectly answered a similar problem. We found that forthe roller coaster problem those who successfullyanswered and reasoned about a similar problem hadstatistically significantly higher similarity scores(ScanMatch scores). This means that the participantswho correctly answered and reasoned about the rollercoaster problem were following the cue more closelywith their eyes than students who did not answer orreason about the problem correctly. This suggests a linkbetween how well participants attended to the visual cuesand how helpful the cue was at implicitly influencingtheir reasoning about the problem. We did not find suchcorrespondence between how well eye movements fol-lowed the cues and problem solving improvements on theother three problems. This follows from the fact that thecues were not effective at helping students answer asimilar problem correctly; thus, there is no reason toexpect to find the above-mentioned correspondencebetween eye movements to the cues and improvementson those problems.

From an educational standpoint, it is not sufficient thatvisual cues help students answer problems containingthose cues. Instead, the educational value of visual cueingwould be more apparent if after seeing visual cues repeatedon several similar problems, students could then success-fully answer and reason about related but different prob-lems without cues, which we have called transfer problemsin the current study. We compared the correctness ofanswers and reasoning on the transfer problems associatedwith each of the four problem sets between those who hadseen visual cues and those who had not. We found asignificant difference in transfer problem correctnessbetween conditions for the ball problem only, with agreater number of participants in the cued conditionanswering this problem correctly. Thus, we find someevidence that repeatedly showing novices visual cues onrelated problems may help them form a productive mentalrepresentation on similar future problems viewed withoutcues. Nevertheless, no such relationship was found for theother three problem sets.

We also investigated how seeing the dynamic visual cueson similar problems may have influenced participants’visual attention on the transfer problems. We comparedthe percentage of fixation time spent in novicelike and

expertlike areas of interest between those in the cued andnoncued conditions on the transfer problems associatedwith all four problem sets. We found that on the rollercoaster problem participants in the cued condition spent asignificantly greater percentage of time looking in theexpertlike AOI and a significantly smaller percentage oftime in the novicelike AOI than those in the noncuedcondition. We also found for the ball and skier problemsthose in the cued condition spent a significantly smallerpercentage of fixation time looking in the novicelike AOI.This result suggests that seeing the cues on this problemhad an influence on participants’ visual attention on sub-sequent uncued problems and helped them to pay moreattention to the expertlike elements (in one of four problemsets used) and less attention to the novicelike elements (inthree of the four problem sets used). This result is prom-ising, as we know from previous work that participantswho answer a problem correctly spend more time lookingat the expertlike areas of the problem and those whoanswer incorrectly spend more time looking at the novice-like areas. Helping participants look at relevant areas andignore distracting areas when no visual cues are presentcould be a first step to helping them reason correctly aboutthe problem.This work adds to the building body of research in

physics education on the importance of visual attentionin physics problem solving [23–26]. As educators andresearchers, we often overlook the way our students viewvisual representations in physics. This study provides someevidence that where a student looks in a visual representa-tion can influence their reasoning about it, especially whenthe representation contains relevant and irrelevant ele-ments. This research suggests that computer-assistedinstruction may benefit from the use of visual cues to guidelearners’ attention to relevant areas of figures, especiallyfor those in which novices often attend to the wronginformation.

VI. LIMITATIONS AND FUTURE WORK

We find some evidence that visual cues overlaid onstatic problems can help a student answer similar prob-lems correctly, a transfer problem correctly, and caneven influence visual attention on the transfer problemso that participants spend more time looking at relevantareas and ignoring irrelevant areas. But we find this to betrue for only some of the problem sets used in this study.This finding also raises the question, why did we not seethe same positive results on the other problem sets?Possible answers to this question motivate our futurework.First, we speculate on why the cues on the roller coaster

problem were effective at helping students answer thesimilar problems correctly, but not the cues on the ball,skier, or graph problems. Upon examining the cues, wenoticed that the roller coaster cues were especially simple.

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-13

The simple back and forth motion highlighting the rollercoaster carts was repeated several times. On the other hand,the visual cues used in the ball, skier, and graph problemsmoved in a more complex pattern. For example, in the ballproblem, the cue moved between balls in track A at a giventime period, then moved between balls on track B at thesame time period, and were then repeated with a differentset of balls. This pattern was shown only once for 6 sec andit is likely that the pattern was simply too complicated todraw significant meaning from it in such a short time.Further, we designed the cues to mimic the patterns thatcorrect solvers used when viewing the problem diagrams.When helping someone who does not know how to solve aproblem, showing them what an expert does may not behelpful, as an expert’s problem solving process is likelystreamlined and condensed and based on deep knowledgeof why this section of the diagram is important. There arealso many types of visual cues that could be applied to agiven problem, and we tried only one type, namely, flash-ing colored shapes that helped the participants select andintegrate important diagram elements. In future research, itwould be better to use very simple cues that are easilyencoded and understood by students. To ensure that thecues are ‘‘student friendly’’ one should first test variousversions of visual cues on a given problem with introduc-tory physics students in individual interviews. During suchinterviews, it would help to observe the problem solvingprocess of an introductory student (as opposed to anexpert) and offer different types of cues starting with themost implicit moving to the most explicit and illustrative.For example, on the roller coaster problem, one could startby highlighting the carts and dimming the tracks, and thenwe could try highlighting the carts in a temporal order (aswe did in this study). If one found that this was unhelpfulfor a student, one could add even more information to theproblem by overlaying lines under each cart representingthe vertical height of each cart. Researchers could also varyhow long the cues were shown. This process should becontinued with different cues, cueing times, and studentsuntil we find the ideal cues.

Additionally, there may only be certain types of prob-lems that lend themselves to improvement through visualcueing. In the successful cueing study of Thomas andLleras, the problem they used did not require any speci-alized content knowledge. In our work, students mustpossess certain physics content knowledge to be able toprovide a correct answer and explanation. It may be thatimplicit cueing is less effective with problems that requirecontent knowledge. Further, we have explored only fourproblems in this study. A multitude of problems couldpotentially be tested in future studies. It could also bethat the order in which the problems are presented influ-ences the usefulness of the cue. The roller coaster problemwas presented first each time and was the only problem thecues were found to influence. In future studies, the order of

cue problems should be randomized to balance out anyorder effects.In this study, similar to the work of Thomas and Lleras

[8], we did not tell students the purpose of the cues. Wehoped that the cues would implicitly influence students torerepresent a problem and overcome an impasse. Whilewe found evidence that the cues were helpful on theroller coaster problem, they were not helpful on the otherthree problem tests. We asked a subset of participantswhat they thought of the visual cues and found greatvariability in students’ ideas about the cues. It may bethat students’ impressions of the cues influenced howuseful the cues were at helping the students. In a futuresimilar study, one could carefully probe students’ impres-sions of the cues at the end of the session and conduct adetailed analysis of the relationship between their viewsof the cues and their problem solving success. It may beeven more beneficial to tell students that the cues arehelpful and draw their attention to relevant diagramelements. We are currently conducting a study investigat-ing the benefit of these types of visual cues when stu-dents know their purpose.Further, in this study we found, on one of the four

problems tested, a difference in the similarity scores(ScanMatch) between those who did answer a similarproblem correctly and those who did not. This meansthat there was a difference in how well the participantsfollowed the cues with their eyes and this difference wasrelated to their success on this similar problem. We predictthat participants will follow the cues more closely andpurposefully if they know they are helpful (as opposed tojust being random flashing shapes), and the cues are morelikely to facilitate correct problem solving since the stu-dents are actually looking at them. Additionally, in futurestudies researchers could include a training session wherestudents gain experience following practice cues with theireyes. This will familiarize students with the task beforethey see the actual cues, and we predict their ability tofollow the cues closely will increase.We also found differences between the cued and

noncued groups on only one of the four transfer problemstested. It appears that the three transfer problems thatshowed no difference were too difficult for this level ofstudent, as very few students in either group answeredthese problems correctly. It is also possible that, althoughwe viewed the transfer problems as closely related to thesimilar problems, the students did not view them this way,and thus were unable to apply what they gained from thecues to the transfer problems. It also may be that thestudents did not gain anything from the cues that couldbe applied to solve the transfer problems, thus producingthe lack of differences between the cued and noncuedgroups. Based on the current study, we cannot determinethe precise reason for finding differences between the cuedand noncued groups on only one of four transfer problems.

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-14

In future studies, it would be profitable to first test thetransfer problems with students in individual or groupinterviews to gain insight into how the students view thetransfer problems and the connections they see between thesimilar and transfer problems. Once one is confident thatthe level of the transfer problems is appropriate and thatstudents clearly interpret the problems as being similar tothe initial problems, stronger conclusions about the effec-tiveness of the cues could be drawn.

Further, the cued group showed superior performance onthe roller coaster similar problem, but not on the rollercoaster transfer, as one would expect. Instead, it was theball transfer problem on which the cued group outper-formed the noncued group, though there were no differ-ences in performance between groups’ similar problemsfor the ball problem set. There is no clear reason for whythis occurred. Using the improvements suggested in thissection, we will need to see if such a result is replicable,and if so, what it means.

Students’ level of prior physics knowledge may alsoinfluence the effectiveness of the visual cues. In the currentstudy, we used a simple pretest to ensure that the partic-ipants had the minimum level of conceptual knowledge toanswer the questions. In future studies, researchers couldcontrol for prior knowledge more closely with a thoroughpretest and students’ current and previous semester physicsgrades to use as covariates in the analyses. Further, the timebetween the relevant material being covered in the stu-dent’s physics course and the time of the visual cueingsession may be important in determining how useful thecues are for the students. In the current study, studentsparticipated in the study throughout the course of a semes-ter, though this was after they had covered the relevantmaterial in their physics course. In the future, visual cueingsessions could be condensed to a given week in the semes-ter so that all students have approximately the same timebetween exposure to the material in class and participationin the study.

In conclusion, there is much work to be done to under-stand the factors that lead to effective visual cues in physicsproblem solving. This study suggests that cueing canpotentially serve as effective conceptual scaffolding fornovice physics students, but much further work will benecessary to develop both a sound theory of cueing that isapplicable to a wide array of physics problems and meth-ods of cueing that are more reliably effective in facilitatinglearning of physics concepts.

ACKNOWLEDGMENTS

This material is based upon work supported by theNational Science Foundation under Grant No. 1138697.We would like to thank Allison Coy for her assistance withcollecting data. We are also grateful to two anonymousreviewers for their detailed and thoughtful commentswhich have greatly improved our manuscript.

APPENDIX

Problems used in study with visual cues overlaid(Figs. 10–12). The colored shapes in each problem arethe visual cues and the numbers in italics show sequenceof animated cues (the numbers were not seen by studyparticipants). Each colored shape was seen by participantsfor 0.5 sec.

FIG. 10 (color online). Ball problem overlaid with visual cues.

FIG. 11 (color online). Skier problem overlaid with visualcues.

FIG. 12 (color online). Graph problem overlaid with visualcues.

CAN SHORT DURATION VISUAL CUES . . . PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-15

[1] R. Desimone and J. Duncan, Neural mechanisms of se-lective visual attention, Annu. Rev. Neurosci. 18, 193(1995).

[2] A.M. Treisman and G. Gelade, A feature-integrationtheory of attention, Cogn. Psychol. 12, 97 (1980).

[3] D. E. Irwin and R.D. Gordon, Eye movements, attentionand trans-saccadic memory, Vis. Cognit. 5, 127 (1998).

[4] D. J. Simons and C. F. Chabris, Gorillas in our midst:Sustained inattentional blindness for dynamic events,Perception 28, 1059 (1999).

[5] E.M. Richard and R. E. Mayer, Multimedia Learning(Cambridge University Press, Cambridge, England, 2001).

[6] E. R. Grant and M. J. Spivey, Eye movements and problemsolving: Guiding attention guides thought, Psychol. Sci.14, 462 (2003).

[7] K. Duncker and L. S. Lees, On problem-solving, Psychol.Monogr. 58, I (1945).

[8] L. E. Thomas and A. Lleras, Moving eyes and movingthought: On the spatial compatibility between eye move-ments and cognition, Psychonomic Bull. Rev. 14, 663(2007).

[9] L. E. Thomas and A. Lleras, Swinging into thought:Directed movement guides insight in problem solving,Psychonomic Bull. Rev. 16, 719 (2009).

[10] S. Ohlsson, in Advances in the Psychology of Thinking,edited by M. T. Keane and K. J. Gilhooley (Harvester-Wheatsheaf, London, 1992), p. 1.

[11] B. B. de Koning, H.K. Tabbers, R.M. J. P. Rikers, and F.Paas, Towards a framework for attention cueing in instruc-tional animations: Guidelines for research and design,Educ. Psychol. 21, 113 (2009).

[12] R. K. Lowe, Search strategies and inference in the explo-ration of scientific diagrams, Educ. Psychol. 9, 27 (1989).

[13] P. N. Johnson-Laird, Mental Models: Towards a CognitiveScience of Language, Inference, and Consciousness(Harvard University Press, Cambridge, MA, 1983), Vol. 6.

[14] C.M. Sorensen, A. D. Churukian, S. Maleki, and D.A.Zollman, The New Studio format for instruction of intro-ductory physics , Am. J. Phys. 74, 1077 (2006).

[15] A.M. Madsen, A.M. Larson, L. C. Loschky, and N. S.Rebello, Differences in visual attention between thosewho correctly and incorrectly answer physics problems,Phys. Rev. ST Phys. Educ. Res. 8, 010122 (2012).

[16] We recognize that the ‘‘similar’’ roller coaster problemsstate that the coaster starts from rest, but between the cart’s

initial and final positions a section of track extends slightlyabove the initial height of the cart. In this case the cartcould not reach the intended final position. We learned ofthis mistake after the study was complete. We did askstudents to explain out loud their answer and reasoning foreach of these problems. For the roller coaster similarproblems, we did not have any participants explain thatthe height of the final incline slightly exceeded the initialheight, so we do not believe that the students noticed andresponded to this error. Students who answered incorrectlyalways cited the shape of the middle section of the tracks(where there were no cases of a hill exceeding the initialheight), the horizontal distance between carts, or thenumber of ‘‘bumps’’ as the reason the final speeds weredifferent.

[17] http://www.sr-research.com[18] R. Carmi and L. Itti, Visual causes versus correlates of

attentional selection in dynamic scenes, Vision Res. 46,4333 (2006).

[19] D. Hammer, Student resources for learning introductoryphysics, Am. J. Phys. 68, S52 (2000).

[20] M. Bilalic, P. McLeod, and F. Gobet, Why good thoughtsblock better ones: The mechanism of the perniciousEinstellung (set) effect, Cognition 108, 652 (2008).

[21] R. A. Fisher, On the interpretation of �2 from contingencytables, and the calculation of P, J. R. Stat. Soc. 85, 87(1922).

[22] F. Cristino, S. Mathot, J. Theeuwes, and I. D. Gilchrist,ScanMatch: A novel method for comparing fixation se-quences, Behav. Res. Meth. Instrum. Comput. 42, 692(2010).

[23] D. Rosengrant, C. Thomson, and T. Mzoughi, Comparingexperts and novices in solving electrical circuit problemswith the help of eyetracking, AIP Conf. Proc. 1179, 249(2009).

[24] A. Feil and J. P. Mestre, Change blindness as a means ofstudying expertise in physics, J. Learn. Sci. 19, 480(2010).

[25] A. D. Smith, J. P. Mestre, and B.H. Ross, Eye-gaze pat-terns as students study worked-out examples in mechan-ics, Phys. Rev. ST Phys. Educ. Res. 6, 020118 (2010).

[26] R. H. Tai, J. F. Loehr, and F. J. Brigham, An exploration ofthe use of eyegaze tracking to study problemsolving onstandardized science assessments, Int. J. Res. Meth. Educ.29, 185 (2006).

MADSEN et al. PHYS. REV. ST PHYS. EDUC. RES. 9, 020104 (2013)

020104-16