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Learning and Instruction 35 (2015) 85e93

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Learning and Instruction

journal homepage: www.elsevier .com/locate/ learninstruc

Getting the point: Tracing worked examples enhances learning

Fang-Tzu Hu, Paul Ginns*, Janette BobisThe University of Sydney, Australia

a r t i c l e i n f o

Article history:Received 9 March 2014Received in revised form24 September 2014Accepted 5 October 2014Available online

Keywords:Cognitive load theoryEmbodied cognitionWorked examplesTracing

* Corresponding author. Faculty of Education andSydney, NSW, 2006, Australia. Tel.: þ61 2 9351 2611;

E-mail address: paul.ginns@sydney.edu.au (P. Ginn

http://dx.doi.org/10.1016/j.learninstruc.2014.10.0020959-4752/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Embodied cognition and evolutionary educational psychology perspectives suggest pointing and tracinggestures may enhance learning. Across two experiments, we examine whether explicit instructions totrace out elements of geometry worked examples with the index finger enhance learning processes andoutcomes. In Experiment 1, the tracing group solved more test questions than the non-tracing group,solved them more quickly, made fewer errors, and reported lower levels of test difficulty. Experiment 2replicated and extended the findings of Experiment 1, providing evidence for a performance gradientacross conditions, such that students who traced on the paper outperformed those who traced above thepaper, who in turn outperformed those who simply studied by reading. These results are consistent withthe activation of an increasing number of working memory channels (visual, kinaesthetic and tactile) forlearning-related processing.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Cognitive load theory

Cognitive load theory (CLT; Sweller, Ayres, & Kalyuga, 2011)foregrounds the role of human cognitive architecture in predictingwhether instructional designs will support learning. The theoryholds effective problem-solving is made possible by a large, well-organised network of schemata held in long-term memory; how-ever, the construction and automation of schemata requiresconscious processing in a working memory limited in capacity andduration when information is novel. CLT researchers have tested arange of instructional redesigns targeting different hypothesisedsources of working memory load. Earlier investigations (e.g.,Cooper & Sweller, 1987; Sweller & Cooper, 1985) focused on re-designs that reduced extraneous cognitive load, i.e., workingmemory processes unrelated to schema construction and/or auto-mation. Subsequent investigations of intrinsic cognitive load (e.g.,Pollock, Chandler, & Sweller, 2002) theorised this source of load asa function of the number of interacting elements a learner mustconsciously attend to while learning. Lastly, germane cognitive loadhas been positioned as working memory capacity dedicated to theconstruction and automation of schemas (Paas & Van Gog, 2006).Recent critiques, however, have argued germane cognitive load can

Social Work, University offax: þ61 2 9351 5027.s).

be defined as the working memory resources available to addressthe element interactivity associated with intrinsic cognitive load(Sweller, 2010).

The current formulation of CLT draws on evolutionary theo-rizing by Geary (2008), in particular the distinction between bio-logically primary knowledge and biologically secondaryknowledge. The former is held to develop as a natural consequenceof human genetic heritage; examples include learning to listen toand speak in a “mother tongue”, or recognise faces. Such skills areheld to be acquired without conscious effort. In contrast, biologi-cally secondary knowledge represents the knowledge corpusrequired to function in contemporary society. Cultural institutionssuch as schools and universities have emerged to support the slow,conscious and deliberate processes of learning to use historicallyrecent artifacts such as writing systems and mathematics. Paas andSweller (2012) argue that such evolutionary perspectives oneducational psychology may provide the basis for novel cognitiveload theory effects, with the potential for biologically primaryknowledge to support teaching and learning of biologically sec-ondary knowledge without imposing a substantial additionalworking memory load on learners. Embodied cognition, includingthe role of gestures in cognition, is discussed by Paas and Sweller asa promising source of evolutionarily informed scholarship forcognitive load theory.

1.2. Embodied cognition perspectives and the potential of gesturing

Reviewing the increasing emphasis on embodied cognition incognitive science, Glenberg, Witt, and Metcalfe (2013) identified

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e9386

two general themes in embodiment scholarship. First, thinking isbest understood as a function of the brain and the body interactingwith the environment; thus, “thinking is grounded in the sensori-motor system” (Glenberg et al., 2013, p.576), rather than consistingof abstract symbol manipulation. Second, the need for the cognitivesystem to control action, i.e. interact with the environment, acts asa source of evolutionary pressure.

One of the main ways in which we interact with the environ-ment is with our hands. A rapidly expanding body of research hasdemonstrated that hand movement and position can substantiallyaffect cognitive processing. In particular, pointing gestures,accompanied or not by touch, are of particular interest in the cur-rent study for their potential to affect information processing andsubsequent learning. For the purpose of drawing attention, apointing gesture apparently could serve as a primitive but effectiveattention-guiding cue, as people start using pointing to managejoint attention and interest as young as 12 months of age(Liszkowski, Brown, Callaghan, Takada, & de Vos, 2012). Studies ofthe interaction between visual attention and hand position alsoprovide strong support for using pointing as an attentional cue.Positioning the hands near an object alters people's visual attentionand perception towards that object, so the object will stand outfrom its surroundings (Cosman & Vecera, 2010), and will be scru-tinised longer and deeper (Reed, Grubb,& Steele, 2006). In additionto pointing, hands support direct interaction with the environmentthrough touch, oftenwhile simultaneously looking at or listening tostimuli. Similar to research reviewed above, this body of researchhas found synergistic effects on attentional processes when visual,auditory, and/or tactile inputs are synchronised (for a review, seeTalsma, Senkowski, Soto-Faraco, & Woldorff, 2010). For example,Van der Burg, Olivers, Bronkhorst, and Theeuwes (2009) foundwhen participants searched for line segments in a complex displayincluding distractor line segments of various orientations anddynamically changing colour, search time and search slopes weresubstantially reduced when a tactile signal accompanied the targetcolour change. Based on studies of spatial cognition, pointing-basedcueing may be particularly suitable for instruction with a highspatial content such as geometry, as pointing at an object leadsattention to perceive that object in a more spatially oriented way(Fischer& Hoellen, 2004). Dodd and Shumborski (2009) found thatencoding spatial arrays with pointing movements towards the vi-sual display led to better memory performance, but not whenparticipants pointed to all objects in an array. While their resultsindicated enhanced perceptual and motor traces for items selectedfor action (i.e., through pointing), they also found relativelyimpaired memory for items that had not been pointed at. Under-pinning the various types of conscious cognitive activity discussedabove is a working memory architecture consisting of channels foreach of the sensory modes. Empirical research on the hapticworking memory processor lags substantially behind research onthe visual and auditory channels (for a review, see Kaas, Stoekel, &Goebel, 2008). Nonetheless, there is increasing recognition of theintersensory facilitation of visual processing by movement, suchthat Baddeley's (2012) most recent model of working memoryspeculates haptic sensory information, including kinaesthetic andtactile input, affects processing in the visuo-spatial sketchpad.

Considering gesture more generally, Alibali (2005) identified arange of ways in which self-generated gestures might affect spatialcognition, including activating both lexical and spatial represen-tations from long-term memory, increasing focus on spatial infor-mation, and helping to “package” spatial information with speech(cf. Alibali, Kita, & Young, 2000). This last possibility is particularlygermane to the present study, with its focus on cognitive load. Pingand Goldin-Meadow (2010) argued gestures “can provide anoverarching framework that serves to organise ideas conveyed in

speech, in effect chunking mental representations to reduce theload on working memory” (p.616). In cognitive load theory terms,mechanisms that act to chunk multiple elements of informationinto a single element are held to reduce intrinsic cognitive load andincrease the opportunity for schema construction and/or automa-tion. The present study extends such theorizing, testing if pointingand tracing gestures act to enhance learning of ideas conveyed inprinted (textual and diagrammatic) instructional materials.

1.3. Pointing and tracing gestures in education

There is a long history in educational practice of the use ofpointing gestures to learn, as well as a gesture incorporatingpointing, tracing a surface with the index finger. Learning torecognise letters of the alphabet by “Sandpaper Letters” is amethodused extensively in Montessori schools for over a century. Studentsare encouraged to trace letters cut out of sandpaper with theirfingers in the same sequence as writing the letter; while tracing,students simultaneously listen to the sound of the letter pro-nounced by their teacher (Montessori, 1912). This teaching tech-nique works through a multisensory approach, involvingsimultaneous input from several modalities; students listen to thesound, look at its representation in the form of a letter, and feel theway it is written as they touch and trace the sandpaper letter.

The learning benefits of tracing have been established across anumber of recent experimental studies on letter learning andphoneme identification (e.g., Hulme, Monk, & Ives, 1987) as well asrecognition of geometrical shapes in kindergarten children(Kalenine, Pinet, & Gentaz, 2011). Using a within-subjects design,Alibali and DiRusso (1999) tested preschoolers' accuracy in count-ing chips across a range of conditions (no gesture, puppet pointing,child pointing, puppet touching, and child touching), and found aclear positive gradient in counting accuracy across the above con-ditions (see Fig. 1, p.46). Alibali and DiRusso speculated the resultscould be explained by at least two processes: greater proximity ofthe finger to the chip when touching rather than pointing, andreduced working memory load by providing an external place-holder in the set of counted objects. Drawing on research dis-cussed above, these results suggest themore sensorymodalities areactivated during the act of counting, the more accurate is perfor-mance; however, these results were generated during mathemat-ical problem-solving, rather than instruction.

Taken together, while the existing studies have demonstratedthat finger pointing, touching and tracing can enhance task per-formance, it remains to be established whether such benefitsextend to more complex instructions requiring higher levels ofabstract thinking and problem-solving skills, and whether a similargradient in performance is established when additional sensorymodalities are recruited during instruction. Moreover, to the best ofour knowledge, evidence for cognitive load explanations of point-ing and/or tracing effects on learning outcomes e such as throughsubjective ratings of cognitive load e has not yet been provided. (Incontrast, there is substantial evidence from dual-task studies forgesture's effects on cognitive load while processing informationmore generally; e.g., Ping & Goldin-Meadow, 2010).

In an initial attempt to investigate pointing and tracing effectson cognitive load and learning, Macken and Ginns (2014)hypothesised that explicit instructions to point to related textand diagrammatic elements on heart anatomy and physiology, andtrace out arrows indicating key blood flows across the heart'schambers, would enhance learning as measured on terminologyand comprehension tests. Large statistically reliable effects ofpointing and tracing were found on the above tests; however,there were no significant differences in post-instruction cognitiveload ratings between conditions. Thus, a cognitive load

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e93 87

explanation for the benefits of pointing and tracing therefore re-mains to be established. Alternative, potentially more sensitivemethods of assessing subjective cognitive load are considered inthe present study. For example, if tracing or pointing gestures actto chunk disparate elements of instructional text and diagramsinto a single schema more effectively than visual study, then thatschema should generate lower intrinsic cognitive load whenactivated into working memory for problem-solving during asubsequent test.

2. Hypotheses

The literature reviewed indicates pointing and tracing gesturesmay be highly effective means of managing attention, acting asforms of biologically primary knowledge that could supportlearning of biologically secondary knowledge. Based on the theo-retical frameworks of cognitive load theory and embodied cogni-tion reviewed above, the series of experiments presented next teststhe following hypotheses:

Hypothesis 1: students who are instructed to trace out elementsof geometry worked examples will outperform students whosimply study the materials, as measured by error rates, timetaken to solve problems, and test performance (Experiment 1).Hypothesis 2: students who are instructed to trace out elementsof geometry worked examples will rate the difficulty of testitems lower than students who simply study the materials,reflecting lower levels of intrinsic cognitive load as a result ofenhanced schema construction (Experiment 1).Hypothesis 3: on the performance variates above, the effec-tiveness of index finger movements for learning will follow agradient depending on how many working memory channelsare activated. Thus, students who trace on the surface ofinstructional materials (i.e., generating activity in the visual,kinaesthetic and tactile sensory modes) should outperformthose who trace in the air above the materials (i.e., generatingactivity in the visual and kinaesthetic sensory modes), who inturn should outperform those who simply study worked ex-amples (i.e., visual sensory mode only) (Experiment 2).Hypothesis 4: students' reports of test difficulty, reflectingintrinsic cognitive load, will also follow a clear gradient,depending on how many working memory channels are acti-vated. Thus, students who trace on the surface of instructionalmaterials (i.e., generating activity in the visual, kinaesthetic andtactile sensory modes) should report lower levels of test diffi-culty than those who trace in the air above the materials (i.e.,generating activity in the visual and kinaesthetic sensorymodes), who in turn should report lower levels of test difficultythan those who simply study worked examples (i.e., visualsensory mode only) (Experiment 2).

3. Experiment 1

Experiment 1 was designed to explore whether a significantdifference between instruction with tracing and without tracingcould be obtained, using mathematics worked examplesinstructing angle relationship involving parallel lines. Research onthe worked example effect (Cooper & Sweller, 1987; Sweller &Cooper, 1985) has demonstrated worked examples are an effec-tive and efficient way to teach novice students mathematicalmethods and principles; worked-example-based instructionalmaterials were used in Experiment 1 to determine whether in-structions to trace might further enhance learning from workedexamples.

3.1. Method

3.1.1. ParticipantsParticipants were 42 Year 5 students aged between 10 and 11

years (M ¼ 10.50, SD ¼ .51) from an independent boys' school inSydney, Australia. Students were novices with respect to the anglerelationships in the instructional materials. They were randomlyassigned to the tracing or the non-tracing condition.

3.1.2. Materials and procedureStudents were tested individually, with each student being

withdrawn from class for approximately 30 min. The experimentbegan with an initial instruction phase, identical for both groups.This phase was followed by an acquisition phase involving study,with or without tracing, of two worked examples; each workedexample was paired by a similar practice problem. The experimentconcluded with a test phase of six questions. Each test questionwasfollowed by a test difficulty rating.

Initial instruction phase. Students had 5 min to study the threeangle relationships involving parallel lines, including vertical an-gles are equal; corresponding angles are equal; and the sum of co-interior angles is 180�. For each angle relationship, instruction wasprovided including its definition, diagrams displaying the locationsof the specific angles, and an example demonstrating how to usethis angle relationship to solve a problem.

Acquisition phase. All participants in the two conditions werethen shown two worked examples applying the three angle re-lationships to find a missing angle. The first worked example fromExperiment 1 with tracing instructions is given in Fig. 1.

In the worked examples for the tracing group, every solutionstep was followed by instructions in brackets on tracing. Studentswere given 2 min to read and try to understand the solution steps,while using their index finger of their writing hand to trace outspecified elements of the diagram following the instructions. Stu-dents in the non-tracing condition were instructed to read and tryto understand the solution steps for 2 min, with their hands placedon their laps. Each worked example was paired with a similarpractice problem, with a maximum of 2 min to solve the problem.Students who provided an incorrect answer were asked to try againwithin the 2-min time limit. Students who could not work out thecorrect answer when the time was used up were stopped. Theywere required to study the worked example again and then wentback to solve the practice problem until the correct answer wasattained. Among the 42 participants, one student in the tracingcondition and two students in the non-tracing condition re-studiedWorked Example 2. A Fisher exact test on number of participantsrestudying per condition was not statistically significant.

Test phase. The test phase consisted of two basic questions, withsimilar diagrams and similar solution steps to theworked examplesbut with different numbers, and four advanced questions. Unlikethe basic questions, which students could solve with two solutionsteps, all the advanced questions required a three-step solution,with varying permutations in the combinations of angle relation-ships across questions required to reach the correct solution. Sur-face features such as orientation and number of lines (parallel andnon-parallel) presented were also varied compared to the workedexamples and their practice problems. Students had up to 1 min tofind a solution for each question.

Test item difficulty self-reports. After each test question, studentswere immediately asked to rate the difficulty of the question theyhad just attempted as an indication of intrinsic cognitive loadduring the test phase; that is, students' experience of workingmemory load in recalling one or more schemas from long-termmemory and keeping that knowledge active while solving testquestions. Across the experiments reported in this article, a 5-point

Fig. 1. Worked example with tracing condition instructions from Experiment 1.

Table 1Means and (standard deviations in parentheses) for acquisition phase errors, time to

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illustrated subjective rating scale of test item difficulty rangingfrom 1 being “very easy” to 5 being “very difficult” was used. Thedesign of the present measure of cognitive load diverges from VanGog and Paas' (2008) recommendation to measure cognitive loadduring the test phase using mental effort ratings. Considering thatit might be difficult for young students to comprehend the conceptof “mental effort” in the commonly used mental effort rating scale(Paas, Van Merri€enboer, & Adam, 1994) or the metaphor of“heaviness” used by Van Loon-Hillen, Van Gog, and Brand-Gruwel(2012) (illustrated using a cartoon figure holding increasingamounts of blocks), the notion of test question difficulty was usedin the current rating scale. In the current experiment, a range ofresponses from 1 to 5 were possible, with two faces positionedabove the 1 and 5 anchors to help students indicate how they feltwhile solving a test question. A smiling face was put on top of thenumber 1, indicating that a test question had been straightfor-wardly solvedwith little conscious effort, i.e. on the basis of suitableschema easily retrieved from long-term memory, generating littleintrinsic load when comprehended in combination with otherpresent elements of the test question. In contrast, a frowning facewas put on top of the number 5, intending to capture an expressionof considerable concentration during problem-solving based on theschema that might be incomplete and/or difficult to retrieve intoworking memory, as well as hold active in combination with otherpresent elements of the test question. These two faces were drawnfrom the Faces Pain ScaledRevised (Hicks, von Baeyer, Spafford,van Korlaar, & Goodenough, 2001).

solution (Seconds), and number of correct solutions, and test phase numbers ofcorrect answers and errors, total time for test (Seconds) and ratings of test difficulty.

Variate Non-tracing Tracing

Acquisition PhaseNumber of errors .33 (.58) .14 (.36)Time to solution 102.43 (49.50) 100.76 (53.74)Number of correct answers 1.90 (.30) 1.90 (.30)Test PhaseA. Basic QuestionsNumber of errors .80 (1.03) .38 (.59)Time to solution (/120) 100.81 (21.53) 86.43 (26.27)Number of correct answers (/2) 1.05 (.80) 1.38 (.86)Test difficulty (/5) 3.14 (.91) 2.64 (.82)B. Advanced QuestionsNumber of errors .52 (.68) .05 (.22)Time to solution (/240) 215.33 (29.20) 172.05 (41.36)Number of correct answers (/4) 1.71 (.75) 3.24 (1.45)Test difficulty (/5) 3.13 (.85) 2.33 (.75)

3.1.3. Data analysisInitial checks on the distributional properties of data under

analysis used the ShapiroeWilks test of normality to evaluatedistributional assumptions. Where non-normally distributed re-sults (e.g., for error rates) necessitated the use of a non-parametrictest (the ManneWhitney U using an exact p value; Mehta & Patel,2012), a z-score associated with the ManneWhitney test wasconverted into the effect size r then converted to d using the typicaltransformation (see Chapter 7 of Borenstein, Hedges, Higgins, &Rothstein, 2009); 95% confidence intervals for d are also reported(Cumming, 2012). Where normality assumptions were not violated,the independent groups t-test assumption of equality of varianceswas assessed using Levene's test. Analyses of experimental datareported across the present article combined tests of significance,controlling the Type 1 error rate at 0.05, with estimates of the

standardised mean difference effect size (d). Based on a major re-view of over 800 meta-analyses of educational research, Hattie(2009) suggested the following benchmarks for effect size magni-tude: small d ¼ 0.20, medium d ¼ 0.40, and large d ¼ 0.60 andabove.

3.2. Results

The variables under analysis were number of errors, total time tosolution of practice problems, and number of correct solutions topractice problems in the acquisition phase, and number of errors,total time to solution of test questions, number of correct solutionsto test questions, and ratings of test item difficulty in the test phase.Means and standard deviations are provided in Table 1.

Acquisition phase. Due to non-normal distributions of the dataacross both conditions as indicated by the ShapiroeWilks test, aManneWhitney test was used to analyse number of errors. Themean rank of the tracing condition (Mean rank ¼ 19.93) was notstatistically different to that of the non-tracing condition (Meanrank ¼ 23.07), U ¼ 187.50, p ¼ .346, d ¼ �.36 [95% CI �.97, .25]. Thedifference between the tracing condition's time to solution(M ¼ 100.76, SD ¼ 53.74) and that of the non-tracing condition(M ¼ 102.43, SD ¼ 49.50) was also not statistically reliable,t(40) ¼ �.11, p ¼ .917, d ¼ �.03 [95% CI �.64, .58]. As for number of

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e93 89

correct solutions across practice questions, the identical perfor-mance of the two groups prevented analysis of this variable.

Test phase e basic questions. Due to non-normal distributions ofthe data across one or both conditions as indicated by the Shapir-oeWilks test, a ManneWhitney test was used to analyse number oferrors, time to solution, and number of correct answers. The dif-ference in number of errors made by the tracing condition (Meanrank ¼ 19.07) and the non-tracing condition (Mean rank ¼ 23.93)was not statistically reliable, U ¼ 169.50, p ¼ .170, d ¼ �.45 [95%CI�1.06, .17]. Amarginally significant effect for time to solutionwasfound: the mean rank of the tracing condition (Mean rank ¼ 18.24)was lower than that of the non-tracing condition (Meanrank ¼ 24.76), U¼ 152.00, p¼ .081, d¼�.55 [95% CI �1.16, .07]. Fornumber of test questions correctly answered, the mean rank of thetracing condition (Mean rank ¼ 23.98) was not reliably higher thanthat of the non-tracing condition (Mean rank ¼ 19.02), U ¼ 168.50,p ¼ .164, d ¼ .44 [95% CI �.18, 1.05]. Lastly, on the overall ratings oftest item difficulty, a marginally significant effect was also found:the tracing condition rated basic test questions as less difficult(M ¼ 2.64, SD ¼ 0.82) than the non-tracing condition (M ¼ 3.14,SD ¼ 0.91), t(40) ¼ �1.87, p ¼ .069, d ¼ �.58 [95% CI �1.19, .04].

Test phase e advanced questions. Due to non-normal distribu-tions of the data across one or both conditions as indicated by theShapiroeWilks test, a ManneWhitney test was used to analysenumber of errors, time to solution and number of correct answers.A significant effect for number of errors was found: the mean rankof the tracing condition (Mean rank¼ 17.45) was lower than that ofthe non-tracing condition (Mean rank ¼ 25.55), U ¼ 135.50,p ¼ .007, d ¼ �.98 [95% CI �1.61, �.33]. A significant effect for timeto solution was also found: the mean rank of the tracing condition(Mean rank ¼ 15.33) was lower than that of the non-tracing con-dition (Mean rank ¼ 27.67), U ¼ 91.00, p ¼ .001, d ¼ �1.15 [95%CI �1.80, �.49]. For number of test questions correctly answered,the mean rank of the tracing condition (Mean rank ¼ 27.67) wasreliably higher than that of the non-tracing condition (Meanrank ¼ 15.33), U ¼ 91.00, p ¼ .001, d ¼ 1.19 [95% CI .52, 1.84]. Lastly,on the overall ratings of test item difficulty, a marginally significanteffect was also found: the tracing condition rated advanced testquestions as less difficult (M¼ 2.33, SD¼ 0.75) than the non-tracingcondition (M ¼ 3.13, SD ¼ 0.85), t(40) ¼ �3.21, p ¼ .003, d ¼ �.99[95% CI �1.63, �.35].

3.3. Discussion

Experiment 1 was designed to test whether tracing out thegraphical elements of geometry worked examples would enhancelearning. Instead of studying worked examples in a conventionalway, using only the eyes to read over and comprehend the mate-rials, students in the experimental conditionwere instructed to usetheir index finger to trace out the corresponding elements of thediagrams after reading each solution step in the worked examples.It was hypothesised that students who traced elements of workedexamples while studying during the acquisition phase wouldperform better on the subsequent test as measured by the numberof correct answers, error rate, and time to solution across theacquisition and test phases. Moreover, it was predicted students inthe tracing condition would consider the test items less difficultthan students who simply studied the materials without any handmovement, as tracing was hypothesised to promote schema con-struction and/or automation. We predicted better constructedschemas would be more easily retrieved and applied at test; hence,students who traced should experience lower levels of intrinsiccognitive load, as indexed by difficulty ratings.

Results supported hypotheses 1 and 2: the tracing conditionsignificantly outperformed the non-tracing condition across a

range of variates. While there were no statistically reliable differ-ences between conditions on acquisition phase variates, in thesubsequent test, marginal effects for basic test questions werefound on time to solution and ratings of test question difficulty, andlarge, statistically reliable effects for advanced test questions werefound for number of errors, time to solution, test performance, andratings of test question difficulty. The better test performance incombination with the lower level of test difficulty indicate thatstudents in the tracing group constructed better problem-solvingschemas from the instructional materials to handle the test ques-tions with lower cognitive demand, compared to students in thenon-tracing group. The significant advantages of the tracing con-dition over the non-tracing condition strengthen the argument thattracing out elements of worked examples facilitated schema con-struction over and above the typical benefits of learning fromstudying worked examples (Cooper & Sweller, 1987; Sweller &Cooper, 1985).

4. Experiment 2

The tracing instructions used in Experiment 1 aimed to activatehaptic working memory resources during the learning process.However, since the haptic modality is a composite of the tactile andthe kinaesthetic modalities (Kaas, Stoeckel, & Goebel, 2008), andactive touch plays an essential role in haptic perception (Gibson,1962; Klatzky & Lederman, 2003), it is at present unclearwhether the differential activation of the tactile and kinaestheticmodes will affect learning outcomes. In a learning context, some-times students will spontaneously hold a pointing finger makingtracing movements in the air of new words or graphic shapes thatthey are trying to learn. In that case, students add haptic inputcoming from the kinaesthetic modality only into their learningprocesses. In contrast, when the participants in Experiment 1 wereinstructed to put their index finger on the piece of paper and traceout the worked examples on it, we hypothesised that sensory inputfrom both the tactile and kinaesthetic modalities was received andincorporated with visual input into a representation initially heldin working memory, then encoded into long-term memory. Thisraises the question of whether multiple non-visual sensory mo-dalities are best used to maximise learning fromworked examples(i.e., tracing with the finger on the paper), or whether similar re-sults would be obtained if only one non-visual sensory modalitywas coupled with visual input (e.g., tracing with the finger in theair just above a worked example). This latter manner of embodiedinteraction with a worked example could be expected to enhancelearning given the focussing of attention around perihand space(Cosman & Vecera, 2010; Reed et al., 2006). However, since hapticperception heavily relies on active touch, it is assumed thatlearning will be enhanced to a greater extent when both tactile andkinaesthetic representations of to-be-learned information areactivated and integrated in working memory along with visualinput.

To address these questions, Experiment 2 tested hypothesisedgradients across experimental conditions, predicting that studentswho traced on the surface of instructional materials (i.e., affectingvisual, kinaesthetic and tactile working memory channels) wouldoutperform those who traced in the air above the materials (i.e.,affecting visual and kinaesthetic working memory channels), whoin turnwould outperform those who simply read worked examples(i.e., visual working memory channel only). A gradient in averagetest item difficulty ratings was also hypothesised, predicting thatstudents who traced on the surface of instructional materials wouldreport lower levels of test difficulty than those who traced in the airabove the materials, who in turn would report lower levels of testdifficulty than those who simply read worked examples.

Table 2Means and (standard deviations in parentheses) for acquisition phase errors, time tosolution (Seconds), and number of correct solutions, and test phase numbers ofcorrect answers and errors, total time for test (Seconds) and ratings of test difficulty.

Variate Non-tracing Tracing abovethe paper

Tracing onthe paper

Acquisition PhaseNumber of errors 0.46 (0.93) 0.08 (0.28) 0.08 (0.28)Time to solution (/240) 110.58 (54.07) 126.00 (63.42) 90.38 (47.12)Number of correct

answers (/2)1.63 (.49) 1.63 (.65) 1.92 (.41)

Test PhaseA. Basic QuestionsNumber of errors .42 (.65) .50 (.93) .29 (.62)Time to solution (/120) 82.88 (25.07) 88.04 (30.31) 71.79 (26.69)Number of correct

answers (/2)1.25 (.74) 1.38 (.77) 1.67 (.70)

Test difficulty (/5) 2.92 (.97) 3.06 (.88) 2.69 (.69)B. Advanced QuestionsNumber of errors 2.21 (2.77) 1.63 (2.50) 1.04 (1.23)Time to solution (/360) 320.54 (38.52) 303.67 (47.48) 292.46 (42.93)Number of correct

answers (/6)2.25 (1.65) 3.00 (1.64) 3.92 (1.02)

Test difficulty (/5) 3.58 (.74) 3.19 (.60) 3.12 (.62)

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e9390

4.1. Method

4.1.1. ParticipantsParticipants consisted of 72 Year 5 students, including 56 boys

and 16 girls, from 2 independent schools in Sydney, Australia. Allparticipants participated voluntarily, and were aged between 9 and11 years (M ¼ 9.94, SD ¼ .33). Participants were novices withrespect to the three angle relationships in the instructional mate-rials. They were randomly assigned to the tracing on the paper(tracing with touch) condition, the tracing above the paper (tracingwithout touch) condition, or the non-tracing condition.

4.1.2. Materials and procedureThe same instructional materials and timings used in Experi-

ment 1 were used in Experiment 2. The primary difference was inthe acquisition phase instructions.

Acquisition phase. In theworked examples for the “tracing on thepaper” group, every solution step was followed by instructions inbrackets on tracing. Students were given 2 min to read and try tounderstand the solution steps, while putting their index finger oftheir writing hand on the paper to trace out specified elements ofthe diagram following the instructions. Students in the “tracingabove the paper” condition were instructed to keep their indexfinger about 5 cm above the paper and trace out specified elementsof the diagram following the instructions without touching thepaper. Lastly, students in the non-tracing conditionwere instructedto read and try to understand the solution steps, with their handsplaced on their laps. Students who could not work out the correctanswer when the time was used up were required to study theworked example again and then went back to solve the practiceproblem until the correct answer was attained. Across the 72 par-ticipants, one student in the tracing on the paper condition and onein the tracing above the paper condition re-studied both of theworked examples. One student in the non-tracing condition re-studied Worked Example 1 only; four in the tracing above the pa-per condition and six in the non-tracing condition re-studiedWorked Example 2 only. Using a Fisher exact test, there was astatistically significant ordinal association (Somer's d¼�.16; Fisherexact test p ¼ .021) between condition and amount of additionallearning opportunities. Importantly, however, the directionality ofthis association was in the opposite direction to results for theacquisition phase and test phase variates (see Section 4.2). Thus,any potential benefit of extra study during the acquisition phase didnot translate to enhanced performance in the acquisition and testphases.

Test phase. The test phase consisted of two basic questions, withsimilar diagrams and similar solution steps to theworked examplesbut with different numbers. Four of the advanced questions wereidentical to those used in Experiment 1. The two additionaladvanced questions required the same solution steps used in thesimilar questions but with an additional step of subtraction, as thetarget angle was divided into two adjacent angles by an extra line.Students had up to 1 min for each question.

Test item difficulty self-reports. After each test question, studentswere immediately asked to rate the difficulty of the question theyhad just attempted as an indication of intrinsic cognitive loadduring problem-solving. This 5-point subjective rating scale wasidentical to the one used in Experiment 1.

Data analysis. When testing hypotheses with sequence order(i.e., condition 1 > condition 2 > condition 3, or vice versa), usingstatistics that incorporate information about the hypothetical rankorder will typically result in higher power compared to conven-tional analysis of variance procedures (McKean, Naranjo, &Huitema, 2001). Given the clear hypotheses described aboveregarding expected gradients on variates across conditions,

analyses consisted of bootstrapped estimates of Spearman's rank-order correlation coefficient between the independent variableand median scores for each condition on dependent variables un-der analysis. This method is robust for analysing variances ofexperimental designs with an expected order of dependent vari-ables (McKean et al., 2001), and has the benefit over alternativemethods (e.g., Terpstra, 1952) of generating an effect size (Spear-man's r) in addition to a p value. Values of Spearman's r presentedbelow were accompanied by values of d, along with the 95% con-fidence interval for both r and d. Bootstrapped p values were one-sided given the directional hypotheses used in the current experi-ment. Complementing the above analytic approach were multiplecomparisons between conditions. Because data screening indicatednon-normal distributions across most variates across all conditions,effect sizes and confidence intervals for each comparison werecalculated using trimming and bootstrapping methods that arerobust to variance heterogeneity and non-normality (Keselman,Algina, Lix, Wilcox, & Deering, 2008). Given that there were threelevels of the grouping variable, Fisher's two-stage procedure wasused to control the familywise error rate at 0.05; multiple com-parison tests were assessed at a¼ .05 only if an initial omnibus testwas statistically significant (see Keselman, Cribbie, & Holland,2004).

4.2. Results

The variables under analysis were number of errors, total time tosolution of practice problems, and number of correct solutions topractice problems in the acquisition phase, and number of errors,total time to solution of test questions, number of correct solutionsto test questions, and ratings of test item difficulty in the test phase.Means and standard deviations are provided in Table 2.

4.2.1. Acquisition phaseIn order to test the hypothetical sequence order of students'

performance (tracing on the paper > tracing above thepaper > non-tracing for number of correct answers; tracing on thepaper < tracing above the paper < non-tracing for number of errorsand time to solution), Spearman's rank-order correlation coefficientbetween experimental condition and the three variates from theacquisition phase was estimated. A statistically reliable gradientwas found for number of errors, r ¼ �.24 [95% CI �.45, �.01],

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e93 91

p ¼ .021, d ¼ �.49 [95% CI �1.00, �.01], but not time to solution,r ¼ �.15 [95% CI �.37, .08], p ¼ .108, d ¼ �.30 [95% CI �.79, .16]. Thegradient for number of correct answers was also statistically reli-able, r ¼ .30 [95% CI .10, .48], p ¼ .006, d ¼ .62 [95% CI .19, 1.08]. Theomnibus test of an overall group effect was not statistically signif-icant for time to solution, F(2, 28.19) ¼ 2.31, p ¼ .134. Omnibus testsusing trimming and bootstrapping could not be calculated fornumber of errors and number of correct answers, possibly due tofloor and ceiling effects respectively on these variates; however,omnibus tests based on ordinary least squares estimators were notstatistically significant number of errors: F(2, 42.04) ¼ 1.83,p ¼ .173; number of correct answers: F(2, 44.49) ¼ 0.38, p ¼ .687.

Test phase e basic questions. Spearman's rank-order correlationcoefficient was also used to test hypothesised gradients betweenexperimental condition and the four variates from the test phase(tracing on the paper > tracing above the paper > non-tracing fornumber of correct answers; tracing on the paper < tracing abovethe paper < non-tracing for number of errors, time to solution, andratings of test item difficulty). The gradient for number of correctanswers was statistically reliable, r ¼ .27 [95% CI .04, .48], p ¼ .012,d ¼ .55 [95% CI .08, 1.09]. The gradient for number of errors was notstatistically reliable, r ¼ �.10 [95% CI, �.32, .13], p ¼ .195, d ¼ �.20[95% CI�.67, .25], nor was the gradient for time to solution, r¼�.15[95% CI �.37, .07], p ¼ .105, d ¼ �.31 [95% CI �.80, .13], or ratings oftest item difficulty, r ¼ �.07 [95% CI �.31, .16], p ¼ .264, d ¼ �.14[95% CI �.63, .32].

As in the acquisition phase, omnibus tests using trimming andbootstrapping could not be calculated for number of errors andnumber of correct answers, possibly due to floor and ceiling effectsrespectively on these variates; however, omnibus tests based onordinary least squares estimators were not statistically significant(number of errors: F(2, 44.95) ¼ 0.47, p ¼ .628; number of correctanswers: F(2, 45.93) ¼ 2.10, p ¼ .131). The omnibus test usingtrimming and bootstrapping was not statistically significant fortime to solution, F(2, 29.26) ¼ 1.96, p ¼ .164, nor was the same testfor ratings of test item difficulty, F(2, 28.29) ¼ 1.25, p ¼ .314.

Test phase e advanced questions. Testing the same hypothesisedgradients as for basic test questions, the gradient for number ofcorrect answers was statistically reliable, r ¼ .41 [95% CI .22, .58],p < .001, d ¼ .89 [95% CI .45, 1.42], as was the gradient for time tosolution, r ¼ �.28 [95% CI �.48, �.06], p ¼ .010, d ¼ �.57 [95%CI �1.07, �.12], and ratings of test item difficulty, r ¼ �.25 [95%CI �.48, �.02], p ¼ .015, d ¼ �.53 [95% CI �1.07, �.04]. The gradientfor number of errors was not statistically reliable, r ¼ �.16 [95%CI, �.38, .07], p ¼ .093, d ¼ �.32 [95% CI �.82, .14].

The omnibus test using trimming and bootstrapping was sta-tistically significant for number of correct answers, F(2,27.23) ¼ 4.59, p ¼ .024. Multiple comparisons between conditionsrevealed a statistically reliable difference between the tracing onthe paper and control conditions favouring the former condition,d ¼ .87 [95% CI .42, 1.65], and a difference between the tracing onthe paper and tracing in the air conditions favouring the formercondition that approached significance, d ¼ .43 [95% CI �.04, 1.09].The difference between the tracing in the air and control conditionswas not statistically reliable, d¼ .37 [95% CI�.17, 1.10]. The omnibustest using trimming and bootstrapping was not statistically signif-icant for time to solution, F(2, 29.80) ¼ 1.94, p ¼ .165, number oferrors, F(2, 28.52) ¼ 0.89, p ¼ .426, or ratings of test item difficulty,F(2, 29.42) ¼ 2.41, p ¼ .124.

4.3. Discussion

Considering the haptic sensory modality consists of the tactileand the kinaesthetic modalities, Experiment 2 was designed tofurther explore the tracing effect by examining whether tracing

with or without the sense of touch would affect learning outcomes,compared to a control group relying on visual study only. It washypothesised that, when students put their index finger on thepaper and traced the worked examples on it, working memoryresources from both the tactile and kinaesthetic modalities wouldbecome active to be used along with vision-based learning pro-cesses. This expansion of available working memory for learningwas expected to be reflected in relatively better test performance,and relatively lower ratings of test difficulty, compared to the otherconditions. In contrast, students who kept their index finger abovethe paper and made tracing movements were hypothesised toincorporate kinaesthetic input only with visual input in workingmemory, thus expanding working memory capacity available forlearning but to a lesser extent. Students in the control conditionwho kept their hands on their laps without any movements werehypothesised to rely on visual working memory only to supportlearning. Based on previous research demonstrating that inputfrom multiple modalities results in better performance on amathematical task (Alibali & DiRusso, 1999), it was predicted thatstudents in the tracing on the paper condition, who learned withthree types of inputs from the tactile, the kinaesthetic and the vi-sual modalities, would have the best performance at the post-testand report the lowest level of perceived test difficulty. Studentsin the non-tracing condition, learning with only visual input, wouldhave the worst performance and report the highest level ofperceived test difficulty. Students who traced above the paper wereexpected to perform mid-way between these extremes, reflectingthe partial expansion of working memory capacity available forlearning through the kinaesthetic channel, alongwith the focussingof visual attention on the instructional materials in perihand space.

Results supported most of the hypotheses presented above,particularly with regard to problem-solving performance. First,during the acquisition phase, the hypothesised gradient was foundfor errors and number of questions correctly answered, but nottime to solution. Second, during the test phase, the hypothesisedgradient on basic test questions was found for test scores, but noterrors, time to solution, or ratings of test question difficulty; foradvanced questions, the hypothesised gradient was found for testscores, time to solution, and ratings of test question difficulty, butnot number of errors made. These results stand in contrast, how-ever, to those based on omnibus tests and follow-up multiplecomparisons. Using such analyses, the only statistically reliabledifference between conditions was found for advanced test ques-tion score, between the tracing on the paper condition and thecontrol condition; the difference between the tracing in the air andtracing on the paper conditions may also have represented a realeffect. In contrast, the difference between the tracing in the air andthe control conditions was not statistically reliable. Taken together,we interpret the results of Experiment 2 as demonstrating thatwhen instructional design of worked examples incorporates thekinaesthetic modality (i.e., instructions to move), the inclusion ofthe tactile modality (i.e., instructions to touch thematerials) furtherenhances students' learning outcomes.

5. General discussion

The present series of experiments explored whether explicitinstructions to trace out elements of worked examples with theindex finger would enhance novices' learning of geometry rules.CLT seeks to generate instructional designs based on well-established knowledge of human cognitive architecture. Histori-cally, this has involved a consideration of working memory sub-systems for processing visual and/or auditory information. Thepresent study draws on notions of evolutionary educational psy-chology (Geary, 2008), embodied cognition perspectives (Glenberg

F.-T. Hu et al. / Learning and Instruction 35 (2015) 85e9392

et al., 2013) and seminal theorising and instructional design byeducationalists such as Maria Montessori (1912), to expand thescope of considered working memory systems to those involvingthe hands. Specifically, we argue that pointing gestures are a formof biologically primary knowledge that may support the construc-tion of biologically secondary knowledge, such as mathematicalrules. We base this argument on developmental research showingthe natural emergence, without explicit instruction, of pointinggestures (Liszkowski et al., 2012); basic laboratory studiesdemonstrating clear effects of hand position and pointing gestureson attentional processes (e.g., Cosman & Vecera, 2010; Reed et al.,2006); and educational research demonstrating the benefits forlearning of tracing gestures (e.g., Bara, Gentaz, Col�e, & Sprenger-Charolles, 2004; Hulme et al., 1987; Kalenine et al., 2011; Macken& Ginns, 2014).

This theorising supported hypothesis generation across twoexperiments. Focussing on post-test results as the primary sourceof evidence for hypotheses, in Experiment 1, students instructed totrace elements of worked examples on parallel lines geometrysolved basic test questions more quickly and rated them as easier,and solved more advanced test questions more quickly while ratingthem as easier and making fewer errors, than students in the non-tracing condition. Students who traced also rated the test questionsas lower in difficulty than students in the control condition,consistent with the argument that tracing reduced intrinsic loadduring the test phase. Results of Experiment 2 extended the aboveresults, finding statistically reliable gradients in basic and advancedtest scores, and advanced test question time to solution and ratingsof test item difficulty. Taken together, these results are consistentwith the hypothesis that the greater the number of workingmemory modalities (visual, tactile and kinaesthetic) activatedduring learning, the better the problem-solving schemas con-structed, particularly given the strongest results were obtainedwith advanced test questions requiring transfer of learning fromthe worked examples studied (cf. Cooper & Sweller, 1987).

These findings have a range of implications for educationalpractice. They indicate that learning of geometry principles bynovices may be enhanced substantially by the simple addition ofexplicit instructions to trace elements of instructional materials.Such instructions were instantiated in paper-based instructionalmaterials, representing a low cost for schools; however, somecaution regarding cost effectiveness is warranted given the presentresults were generated under individualised instruction and testingconditions. We are cautiously confident such effects could begeneralised to more realistic classroom settings, and to other sub-ject areas, but further research is clearly required. Notwithstandingthe limits of the present study, we note that the use of individu-alised instruction mimics the attention that students will receivefrom teachers, teachers' aides and parents during remedial workwith students.

Another aspect of the study that argues for caution relates to thedifferential findings in Experiment 2 depending on whether a“gradient” or omnibus test followed by multiple comparison”approach to analysis was taken. As discussed above, the omnibusapproach has been argued to lack statistical power when there is aclear ordering in hypotheses (McKean et al., 2001). The only sig-nificant or near-significant multiple comparisons (following a sig-nificant omnibus test) were found on the number of advanced testquestions solved correctly. These results aligned with the expec-tation that tracing on the paper would enhance learning, and theadditional expectation that the greater the number of sensorymodalities activated the more learning would be enhanced (i.e.comparing tracing on the paper with tracing in the air above thepaper). Nonetheless, it is clear more research is needed to under-stand the mechanisms by which differing levels of sensory

modality activation may enhance learning. The research design andsample size used in Experiment 2 appeared sufficient for investi-gating gradient effects for some (but not all) variates, and largerstudies may be required for more fine-grained investigations oftracing effects, whether on a surface or in the air.

The present findings have some limitations that can informsubsequent investigations of tracing effects. First, hypothesesregarding intrinsic cognitive load during the test phase were testedusing self-report scales. Future investigations should continue togather process data to strengthen the case for a cognitive loadinterpretation of performance data. For example, future studiesshould collect students' ratings of cognitive load during both theacquisition and test phases, and supplement self-reports of cogni-tive loadwith eye-tracking data (Van Gog& Scheiter, 2010). Second,the present studies measured effects on learning immediately afterinstruction; future investigations with delayed post-tests willprovide more robust tests of learning. Third, while the effects oftracing were strong for the inherently visuo-spatial-based mathe-maticsmaterials used in the experiments described here, it remainsto be seen how tracing instructions might be incorporated intotopics that are less obviously visuo-spatial in nature. Fourth, thepresent series of experiments did not consider the role of any in-dividual differences. The extent to which the effectiveness oftracing changes with prior knowledge would be worthy of inves-tigation, since research on the expertise-reversal effect (Kalyuga,2007) suggests that instructional designs that are effective fornovicesdsuch as those recruited in the present experimentsdmaydecline in effectiveness as prior knowledge increases. Anotherpotential aptitude-treatment interaction might relate to spatialability (H€offler, 2010); if tracing effects operate substantiallythrough their effects on spatial processing (cf. Alibali, 2005), thenstudents higher in spatial ability might find instructions to tracerelatively redundant. Lastly, and related to the previous point,research on effective sequencing of instructions involving tracingwould be worthwhile. For example, in describing an instructionalsequence for sandpaper letters, Montessori (1912) noted “thechildren, as soon as have become at all expert in this tracing of theletters, take great pleasure in repeating it with closed eyes, lettingthe sandpaper lead them in following the form which they do notsee” (p. 276; italics in original). Such a sequence has considerableparallels with instructions used in generating the imagination ef-fect (Ginns, Chandler, & Sweller, 2003), where students firstconstruct a schema through studying materials, then partially orfully automate the schema by closing the eyes and imagining theinstructions.

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