External Visual Representations and the Scientific Expert

Introduction

This paper focuses on externalvisual representations and how they are used by expert and novicescientists.  First, I define the term“expert” as used in this paper.  Then Ilook at representations in sciences and math.  Finally I compare the novice and expertdifferences as they relate to interpreting and constructing visualrepresentations.  Along the way, Iexamine a very interesting and applicable extension of the informationprocessing theory, the cognitive load theory, and how it relates to visualrepresentations and expertise. 

 

The Expert Scientist

Who is an expert?  Is it someone that is competent in a specificfield, or is it the person that is among the top 1% of professionals in thatdomain?  There seems to be a discrepancyamong expertise researchers, as to what it means to be an expert.  Conceptually, most researchers would probablyagree with Ericsson’s (2006) definition of expertise as “outstandingperformance”, but the operationalization usually translates to years ofexperience (Sonnentag, Niessen &Volmer, 2006).

The ten year or10,000 hour rule of deliberate practice comes up in many definitions based onnumerous studies (Ericsson, 2006).  Someresearchers see this as the standard, and stipulate ten years of experience ina field the demarcation line between expert and non-expert.  However, many researchers point out thatexperience is not necessarily related to high performance (Sonnentag et al,2006; Durso & Dattel, 2006), and there needs to be another way ofdetermining who are the experts.  In thatregard, an expert is not a person that is only competent or even sociallyrecognized as one, instead is an individual who exhibits reproducibly superiorperformance on authentic tasks in their field (Ericsson, 2006).  Thus, the assessment of exceptional expertsneeds to be accurate, as the goal is to understand their superiorperformance.  

On the other endof the spectrum, it is possible to define an expert as a “relative expert” in away that the depth of knowledge and skill necessary to provide an explanationdepends on what is required in a particular context (Mieg, 2006).  In this sense, the expert only needs to berelatively more competent than the novice in the expert-noviceinteraction.  In this relative approach,the goal is to understand how we can enable a less skilled or inexperiencedperson to become more skilled (Chi, 2006).      

In this paper, Itake Chi’s (2006) definition of the expert as the basis for the analysis.  One advantage of this relative approach isthat researchers can be less precise about how to define expertise, sinceexperts are defined as relative to novices on the novice-expert continuum.  Most of the studies on scientific expertiseassume this definition, and operationalize the “expert” with proficiency tests(Jucks, Bromme, & Runde, 2007; Kohl & Finkelstein, 2008), academicqualifications (Kozma & Russell, 1997; Stylianou, 2002; Kohl &Finkelstein, 2008; Stylianou & Silver, 2004), or experience and seniority(Kozma, Chin, Russel, & Marx, 2000; Wood, 1999). 

I would like toalso point out, that even though I am not assuming Ericsson’s (2006) absolutedefinition of an expert, there is a hint of deliberate practice in thedefinition of “expert scientist”. Scientists become experts after many years of “practice”.  This practice is not automated and definitelygoal oriented.  Each new courseintroduces new ways of looking at the scientific principles.  Each course introduces new representationsand allows for that to get integrated into the growing schema of the buddingexpert.  Each new course has a feedbackintegrated mechanism with an expert professor evaluating the progress of eachstudent.  When the scientist startspublishing, the deliberate practice continues, with the goals and motivationscoming from within, while the feedback coming from supporting professors andpeer reviewers.   Thus, a physicist witha PhD having at least 10 years of experience has had the 10,000 hours ofdeliberate practice in the domain of physics (4 years undergraduate studiesfollowed by at least 6 years of graduate work). Ericsson (2006) specifies that the “key challenge for aspiring expertperformers is to avoid arrested development associated with automaticity and toacquire cognitive skills to support their continued learning and improvement”(p. 694).  While actively attending auniversity degree program, this arrested development is close toimpossible. 

What is more,there are so many different scientific domains and sub-domains, each scientistfinding their own niche.  In such acircumstance, each scientist is a super-expert in their own specific area ofinterest.  It would not be viable to finda task to measure the performance of the given expert in their sub-domain,without the guidance of another such expert. However, this second expert might not even exist.  Therefore Ericsson’s (2006) requirement of anobjective measure on a reproducible task demonstrating superior performance isnot at all practical in terms of expert scientists.  Consequently, the relative approach todefining the expert is the only appropriate way of investigating the scientificexpert.       

Finally, as ascience teacher, personally I find the relative approach to studying expertisemore relevant.  My goal is to helpstudents learn science, and in that respect understanding the differencesbetween novices (my students) and experts (people I want them to become) isextremely useful.  

 

Visual Representations in Science

History of Representations in Science andMath

Representations in the history ofscience are very prevalent.  Kozma andcolleagues (2000) looked at the history of representations in chemistry, andestablished how influential were the representations on the type of “science”carried out during those periods.  Thebeginnings of modern chemistry can be dated back to the late 18^thcentury when Lavoisier devised a new representational system for the elements: nomenclature.  Consequently, instead of calling substancesby their physical appearances, as was done by the alchemists, the glass makers,and the smiths, the modern chemist started seeing objects made up ofelements.  There was a complete shiftfrom property to composition of substances based on this new representationalsystem. 

For most of the 19^thcentury, chemists were interested in the composition of substances, and wereconsumed by decomposing each compound into elementary pieces.  With a saturation of this type of analysis ofcompounds, chemists shifted their focus, and were thereafter concerned withsynthesizing new complex compounds.  Thenomenclature no longer provided sufficient representational usefulness and thusa new type of representation was created: the structural diagrams.  With this representational system, theelements making up the compound is not the central concern.  Instead, what is important is the spatialorientation of the different elements with respect to the other elements andthe bonds that link them together: this determines the type of compound andconsequently the properties of the given compound.  However, without the introduction of thestructural diagrams, chemists would have had a hard time progressing in thefield of synthesizing complex compounds (Kozma et al., 2000).                    

A similarhistory of visual representations in mathematics can be traced back to theorigins of mathematics in Mesopotamia and Greece (Stylianou, 2002).  For centuries, visual tools such as diagrams,graphs, and sketches were considered to be indispensable in the work ofmathematicians.  Geometry has alwaysrelied heavily on pictures, and, for a time, other branches of mathematics didtoo.  Arguments and proofs represented byEuclid, forinstance,  depend heavily on the use offigures.  The use of diagrams remained apopular and acceptable practice in mathematics well into the 18^thcentury.  However, the status of visualreasoning and argument lost its respect in the 19^th century when itproved misleading in several cases.  Thisled mathematicians to use only the formal model of reasoning, and abandonreasoning which involves diagrams. However, despite the rejection of visual tools in formal presentationsand publications, reports on mathematicians’ work indicate that mathematicianscontinued to use visual reasoning in their own work.  (Stylianou, 2002)

Until veryrecently, diagrams were not seen as proofs, but more heuristics. However, inrecent years, there is a new trend in mathematics, with mathematics journalsaccepting articles which rely heavily on pictorial representations.  An extreme example of this is: “ProofsWithout Words” forum of the MathematicsMagazine.  (Stylianou, 2002; Arcavi,2003)

 

 

 

Relationship between Internal and ExternalModels of Cognition

Some people believe they think inimages.  In fact, Einstein wrote: “Wordsand language, written or oral, seem not to play any role in my thinking.  The psychological constructs which are theelements of thought are certain signs or pictures, more or less clear, whichcan be reproduced and combined at liberty.” (as quoted in Stylianou,2002).  However, it is important not to fallvictim to the “resemblance fallacy”.  Externaland internal representations might be different (Scaife & Rogers, 1996;Kozma & Russell, 1997).  An expertchemist, when thinking of methane gas, might see the image of a structuraldiagram of methane; but a novice will most likely not picture a carbon moleculewith four hydrogen molecules attached. Instead, they might be focusing on the surface properties of any gasthey might have seen before.  Thereforewhen an expert inspects a structural diagram of methane, their internal modelmight match the extarnal model, however the novice will not find theconnection, and the visual representation will be a mismatch between internaland external cognition.  Thus, as peopleengage in visual pattern matching, the expert has an advantage over the novice,with the greater experience and exposure to the domain.

            Asa result, there is a need for prior knowledge to be able to “read” diagrams ormake inferences from visual representations in general (Kozma & Russell,1997; Goldman, 2003). Diagrams, just like words and symbols, need to be taught,learned, and transformed into internalized cognitive representations (Kozma& Russell, 1997).  There cannot be anassumption that visual representations are automatically easier to understandjust because they are pictures.  Becauseperceptions are conceptually driven we “see” only what we already know (Arcavi,2003).  Therefore in a pictorialrepresentation, the novice will see something completely different from theexpert: their prior knowledge is so dramatically different. 

            Anexample of this was amplified in an interesting study on how the utility of illustrationsby the expert pharmacist debilitates his ability to explain a scientificconcept to a complete neophyte. Jucks, Bromme, and Runde (2007) had fourth yearpharmacy students (relative experts) answer a patient query about laxatives andhow they work.   The experts working witha technical diagram (as compared to a bulleted list of technical terms in thecontrol group) were significantly less likely to present a comprehensiveexplanation to the neophyte patient.  Theauthors suggested that working with the illustration encourages experts tobecome immersed in their own knowledge, and thus the experts cannot comprehendthat the concept is hard for the novice to understand (Jucks, Bromme, &Runde, 2007).

            Hence,when interpreting diagrams, the prior knowledge of the person influences what he/shecan infer from that diagram.  On theother hand, when the person actively constructs the diagrams, it seems thatthis process aids in their creation of an internal model (Reiner, 2009; Gobert& Clement, 1999; Stylianou & Silver, 2004). 

In an intriguingexperimental study, Gobert and Clement (1999) showed that diagram constructioncan be a very useful tool to create mental models. The researchers had onegroup of young students construct diagrams after reading a passage on plate tectonicswhile the other had to write a textual based summary of the same passage.  After this exercise, the students using thediagramming technique significantly outperformed the other control group oninference type questions.  The authorstheorize that the students that drew diagrams made a rich mental model,demonstrated by the higher-level inferences tested with the post test (Gobert& Clement, 1999).

 

Roles of Visual Representations

In the natural sciences andmathematics alike visual representations are regarded with highfunctionality.  Understanding chemistryrelies on making sense of the invisible and untouchable (Kozma et al,2000).  Understanding physics relies onunderstanding motion of objects and underlying but invisible physicalproperties of objects (Kohl & Finkelstein, 2008). Understanding mathematicsrelies on making the abstract concrete, finding patterns in data, or makingsense of theorems. Mathematics is a human and cultural creation that reliesheavily on visualization in its different forms at different levels (Arcavi,2003).  To this end, visualrepresentations are essential to the understanding of natural sciences andmathematics.

            Morespecifically, visual representations have several functions, depending how andwhen they are used.  For instance, Scaifeand Rogers (1996) point to two possible functions of diagrams: constraining orlimiting possibilities, and cognitive offloading.  For instance, when a novice mathematicianthinks of the relationship between the angles in an isosceles triangle, hemight have to draw an example of such a triangle and observe and measure itsangles.  The diagram of the triangle setslimits, with the specific angles, and sides. Out of all the possible isosceles triangles, the novice constructs thatspecific one.  Although this diagram nowis a constraint in a sense, instead of being abstract, it becomes concrete: thestudent can see it, manipulate it, measure it, work with it.  In the same sense, the diagram serves forcognitive offloading.  The novice mightbe able to visualize some version of an isosceles triangle within his limitedworking memory.  However, it is unlikelythat he would be able to measure the angles and compare them to each otherwithout the external representation.  Thediagram therefore helps with this limited cognition.     

Diagram constructioncan also be seen as a tool to help create mental models.  By self-generating a diagram after reading atext, the learners were more likely to construct a cognitive representation (schema)of the workings of plate tectonics and consequently, were able to infer fromtheir mental model (Gobert & Clement, 1999).

Text is linear,diagrams are not. Thanks to this property, more information can be stored indiagrams.  For example, the relative positioningof elements is implied in a diagram; or the relationship between the sizes anddirections of physical properties can be apparent simply from a scan of thediagram.(Gobert & Clement, 1999). However, because visual representations can carry so much information,they can be difficult to interpret, construct or use, especially with a lack ofprior knowledge in the field (Stylianou & Silver, 2004). 

            Arcavi(2003) points to many more roles of visual representations in mathematics.  With respect to data representations, graphscan be seen as a chunking mechanism, bringing novices closer to experts.   Also, it is hard to see patterns from alarge data set – hence, visual representations are essential to see theemerging patterns. In that sense, graphs can “reveal” data (Arcavi, 2003). 

Visuals also mayadd meaning to purely symbolic or algebraic properties.  It seems that if a mathematical property ispresented visually, it is more intuitive, and the novice (or expert) will bemore inclined to accept the premise (Arcavi, 2003).  Thus in mathematics, a visual representationmay: a) support essentially symbolic results; b) demonstrate a possible way ofresolving conflict between symbolic solutions and intuitions; c) re-engage withand recover conceptual underpinnings which may be bypassed by formal solutions(Arcavi, 2003).

  As well, Arcavi (2003) explains that visualsare at the service of problem-solving.  Hediscusses the phenomenon called VMS (visually-moderated sequences), which isessentially analogous to the visualizer / analyzer (V/A) model of problem solving(described briefly below).  His exampleexplains this VMS process:

A student asked to factor x² – 20x + 96, might ponder for amoment, then write

x² – 20x + 96

( )( ),

then ponder, then write,

x² – 20x + 96

(x ) (x ),

then ponder some more, then continue writing

x² – 20x + 96

(x – ) (x – ),

and finally complete the task as

x² – 20x + 96

(x – 12) (x – 8)

The mechanism is more or less: look, ponder, write, look, ponder, write,and so on. In other words, a visual clue V1 elicits a procedure P1 whose executionproduces a new visual cue V2, which elicits a procedure P2,. . .and soon. (Arcavi, 2003, p. 224) 

Finally, a majorfunction of visual representations is their use as exploratory tools (Stylianou& Silver, 2004).  This is true more forexperts than novices, again due to their prior knowledge advantage, and thustheir higher ability to interpret and infer from the diagram.  As can be seen in the many problem solving studies,constructing a visual representation was only the starting point from which tolaunch a very specific higher level analysis (Stylianou & Silver, 2004;Stylianou, 2002; Kohl & Finkelstein, 2008).

 

V/A Model of Problem Solving (Zazkis et al,1996 as quoted in Stylianou, 2002)

Problem solving is at the core ofboth mathematics and physics.  Expertsare not only required to have an extensive knowledge of principles andunderstandings of physical phenomena (physics) or theorems (math), but are alsoexpected to be able to solve novel problems using their prior knowledge repertoire.  The ability to use external visualrepresentations is a huge asset for the expert in many problem solving cases(Stylianou & Silver, 2004; Kohl & Finkelstein, 2008). 

The V/A (visualizer/ analyzer) model of problem solving, based on Piaget’s analysis of the interdependenceof perception and intelligence, is a description of how the expertmathematician attacks a problem using complementary visualizations and analysistechniques (Stylianou, 2002).  Thethinking begins with an act of visualization V₁, which can be theactual drawing of a picture or the expression of a mental image.  This is followed by an act of analysis A₁,in which the person reasons about what was visualized in V₁.  Then follows a second visualization step V₂,enriched as a result of A₁. This process continues, with each iteration increasing insophistication, until the problem solver comes to a better understanding of theproblem he was solving (Stylianou, 2002).

Each visualizationis just really a translation, either from external to internal models (e.g. imagingin the mind), or internal to external representations (e.g. drawing).  By watching expert mathematicians solveproblems, along with verbal protocol methods and their diagramming, Stylianou(2002) was able to further the V/A model with a more detailed examination ofthe analysis steps.  In the end, asdescribed in Fig. 1, she found that the possible analyses steps were:  inferring additional consequences; elaborationof the “new” mathematical information that was gained by drawing the diagram; statinga new goal for the next representation; and finally, monitoring of own problemsolving (Stylianou, 2002). 

 

Fig.1.  The enhanced V/A model (Stylianou,2002)

It isinteresting to notice that this enhanced V/A model, with the finer distinctionsof the analysis step (evaluating, elaborating, goal setting, and monitoring) isalmost identical to a small scale version of the self regulation model(Zimmerman, 2006).  The performance phaseis analogous to the visualization, while the self-reflections and forethoughtphases can be mapped perfectly onto the analysis step in the V/A model.  And possibly, this is why and howmathematicians gain their superb abilities to problem solve: by using selfregulation during every problem solving activity.

 

Multi-Media: Multiple Representations in theSciences

In many scientific domains, theneed for multiple representations is evident (Scaife & Rogers, 1996).  The expert physicists solving problems use apictorial representation, then follow up with a physical representation of theelectrostatic interacting forces, then use the algebraic representation tofinally solve the problem (Kohl & Finkelstein, 2008).  In chemistry, the scientists need to be ableto change the intended structural diagram into a guess as to how it could becreated in practice, with actual chemicals. When the product is generated in the lab, to test whether it is theintended chemical, the expert interprets an instrument generatedrepresentation, translates it into bonds between elements, and maps the bondsonto a structural diagram (Kozma et al., 2000). The rationale of these multiple representations is to complement oneanother with regard to information or processes, and to constrain theinterpretation of one another (Cook, 2006). 

Transformation betweenrepresentations is an important issue as well. Some representations may be well suited to certain learning but to usethe information for other tasks, the learner may need to transform therepresentation to match the task demand (Goldman, 2003).  Additionally, it appears that changing textto graphic representation encourages learners to attend to key elements of thevisual representations in the learning material (Goldman, 2003).  As in the construction of a diagram followingthe plate tectonics text, the learners were able to create a mental model bytranslating one representation (text) to another (diagram) (Gobert &Clement, 1999). 

In addition tothe useful representations for cognitive model creation, Kozma and Russell(1997) point to the numerous graphs and visual read outs from the technologicaltools of the scientist (mass spectroscopy, nuclear magnetic resonancespectroscopy, x-rays, ultrasound, fMRI, etc.). These tools mediate the work of scientists generating characteristictraces, changing nature into a representation. But these “traces” need to be analyzed and understood by chemists (Kozmaet al,  2000).  In this case, the representation has nocognitive offloading advantage, nor is it in any way intuitive or helps with internalmodel creation.  But all the same, thechemist needs to be able to “read” these graphs or visual outputs.  It is essential that the chemist is able tointerpret these traces correctly and be able to flow easily from onerepresentation to the next (Kozma et al, 2000).

 

Visual Representations through CognitiveLoad Theory

It is apparent from the numerousstudies that prior knowledge influences perception and attention: Learners useprior knowledge to select relevant information from graphics, add informationfrom their prior knowledge and develop a mental model (Kozma & Russell,1997; Stylianou & Silver, 2004; Kohl & Finkelstein, 2008).  But how does this prior knowledge influenceinterpreting and constructing visual representations?  In order to understand the underpinnings ofusing visual representations by novices and experts, Cook (2006) reviewed andapplied Sweller’s cognitiveload theory.

Cognitive load theory employsaspects of information processing theory to emphasize the inherent limitations of concurrent working memory load on learning duringinstruction. It makes use of schemas as the unit of analysis for the design of instructionalmaterials.  The premise of the theory isthat a learner has a limited working memory that interacts withan unlimited long-term memory.  There isa low-level of perceptual stream of information constantly entering sensorybuffers in the perceptual systems of the brain, however there is a limitedcapacity to further processing of this information and linking it to priorknowledge – this is called working memory(Cook, 2006).

When learning,working memory resources can be used by intrinsic cognitive load, germanecognitive load, and extraneous load.  Theintrinsic cognitive load is used for processing the elements that cannot beisolated and must be learned together in working memory.  The germane cognitive load is used for schemaconstruction and automation.  Finally theextraneous load is any other load placed on working memory used unproductively,wasting of the limited resources of working memory. The burden placed onworking memory can be reduced by increasing the capacity or reducing cognitiveload (Cook, 2006).

A possible wayto reduce cognitive load is by constructing schemas and automation.  According to schema theory, knowledge isstored in long term memory in schemas. Schemas help organize and link relevant information together.  Although schemas can hold a large amount ofinformation, it is processed as a single unit in working memory.  As a result, cognitive schemas reduce theburden of working memory system to only a few elements of information at onetime.  High levels of prior knowledgeimply that schemas have previously been constructed and can be retrievedeasily.  With fewer schemas, workingmemory is more likely to be overloaded, as happens a lot in novices (Cook,2006).

When thematerial imposes a low-intrinsic load due to the expertise of the learner orthe low complexity level of the material, the quality of instructional designis less likely to have an impact because there is enough memory space remainingto compensate for poor design.  When thisoccurs, the appropriate goal would be to encourage germane cognitive load, andthe creation of schemas or automation (Cook, 2006). 

When intrinsicload is high, schema formation will require more effort, and thus it isessential to minimize extraneous cognitive load.  When extraneous load is reduced, more resourcesare free for germane load.  In turn, withautomation and schema production, intrinsic load is reduced (Cook, 2006).  External representations can be used as aform of cognitive offloading, especially when intrinsic load is high (Scaife& Rogers, 1996).

Anotherinteresting property of the cognitive load theory is the dual-mode effect.According to dual coding theory, visual and verbal information are processed inindependent subsystems of working memory. The visuo-spatial sketchpad takes the visual input and ultimately createsa visual mental model.  The phonologicalloop takes the verbal input and ultimately creates a verbal mental model.  The two different kinds of mental models arefinally mapped onto each other.  By usingthe capacity of both systems, more information can be processed than wouldotherwise be possible with only one of those systems (Cook, 2006).

However, it isimportant to present the visual and verbal information concurrently in spaceand time, to take advantage of the split-attention effect.  Also, it has been found that auditory input(narration) is better than textual input when combining it with a visualrepresentation.  This is most likely dueto the initial visual property of text, thus there is an extra step for thetext to be changed into “sound” and then processed in the phonologicalloop.  This extra step takes up workingmemory as extrinsic load.  Finally it ispreferable to omit redundant material in the two visual and phonological modesas it uses up cognitive resources of working memory, thus decreasing learning(Cook, 2006). 

 

Expert – Novice Comparison in Terms of Visual Representations

Just like with reading and writingtext, visual representations need to be “read” and “written”.  The following two sections will compare thedifferences of novices and experts on, first, the understanding andinterpretation of visual representations, and second, on the construction ofvisual representations while problem solving. Finally, an overall summary of the differences between novices andexperts will be mapped onto the cognitive load theory.

 

Understanding and Learning from VisualRepresentations

Interpreting and understandingmultiple representations is a key feature of the expert chemist, doctor, orpharmacist.  To this end, four studieswere considered for the comparison of expert and novice characteristics withrespect to interpreting and understanding visual representations.  The first two studies deal with expert andnovice chemists.  The third studycompares the differences of an expert and novice radiologist interpreting anx-ray.  The last study looks at theengagement of an expert pharmacist with their internal cognition based on theinteraction with a visual representation.

            Kozma& Russell (1997) looked at the differences of experts and novices sortingof different chemical phenomena presented in multiple types of representations(diagrams, balanced equations, structural models, videos of an actual chemicalreaction, animation of a chemical reaction on the molecular level, etc.).  In their second experiment, the researchershad the experts and novices transform one type of representation toanother.  The results show that expertsused multimedia (many different kinds of media) more than novices; expertseasily transformed from one representation to another, while novices had a hardtime with the transformations; when sorting, experts grouped the differentrepresentations into bigger chunks as compared to novices; and finally, expertsused more types of representations as compared to novices in their groupings (Kozma& Russel, 1997).

            Inanother study observing chemistry experts, Kozma and colleagues (2000) analyzedthe chemists relationship with representations. Going into their laboratories, meetings and places of work, the authorshad the opportunity to see how chemists use visual representations in theirnatural habitat.  They found thatchemists change from one representation to another with great fluency.  In fact it appears that one of the hallmarksof being a chemist is to read and understand the different representations createdby the chemists themselves or from readouts from the different instruments. Inaddition, it seems that chemists use chemical structural formulas as a means ofcommunication.  Using multiplerepresentations for chemists is part of their community of practice.  For instance, they observed that a studentbecame a full participant in the chemistry community by using tools andrepresentations in the context of activity and discourse (Kozma et al., 2000).

            Radiologistsare often referred to as visual experts in the medical community (Wood, 1999).  Thus the third study compared the ways ofexpert and novice radiologists using their visual expertise.  The expert initially quickly scans the x-rayand spots the abnormality. Next, he scans the remainder of radiograph, but returnsquickly to the abnormality.  Whilescanning, the radiologist focuses on areas that also may show a relatedabnormality.  Novices, on the other hand,look systematically at all parts of the x-ray, starting from the peripheral ofthe image to the centre, and then back to the peripheral.  They do not use the scanning technique, nordo they return to any parts of the visual representation once they have goneover it once.  They also do not recognizerelevance and irrelevance of much of what they see.  To this end, the author states that to becomea visual expert one must first learn the knowledge, and then develop a memoryrepresentation of images and patterns along with the meaning of each of thesepatterns (Wood, 1999).

Wood (1999) hada few other observations when comparing expert to novice radiologists. Expertsspend more time in the initial mental model creation.  Also, they are more able to align their ownschemata to the specific elements and novel aspects of the case.  Novices, on the other hand, were less able tomodify their schema in response to added or conflicting data.  In addition, differences between experts andnovices in decision making errors were related to the inability or inaccuracyof the novice representing a problem in a mental information bank. Finally, theauthor suggests that speed and confidence in the early diagnostic steps allowedthe expert greater time for reflection and innovation in problem solving (Wood,1999).

            Inthe final study of the interpretation of visual representations by experts,Jucks, Bromme & Runde (2007) looked at the influence of using an externalrepresentation on their ability of explaining a pharmaceutical concept to alayperson.  Working with the illustrationencouraged the experts to become immersed in their own knowledge: the answers suppliedto the patients were more in expert jargon. The external diagram gave the experts “representational guidance”,however in turn this made them understand something so well that they thoughtit was too easy to explain to the lay-person (Jucks, Bromme, & Runde, 2007).  In this respect, it appears that the diagramwas used as cognitive offloading, and as such, the expert did not perceive thedifficulty of the task.

 

Constructing and Using Self Generated VisualRepresentations

To compare the abilities of novicesand experts in constructing and using these self-generated visualrepresentations, three studies were looked at. The first two studies looked at problem solving and visual representationsin higher level mathematics, and the third looked at the novice and expertcomparison in higher level physics and the influence of multiplerepresentations on problem solving. 

In the firststudy, Stylianou (2002) had expert mathematicians solve novel mathematicsproblems.  Using think aloud protocolsand keeping track of their diagram construction, she was able to observe andclassify the experts’ problem solving analysis and the treatment of the visualrepresentations in their problem solving process. 

It becameevident that the diagrams provided the experts with “new” information.  Mathematicians did not however accidentallysee the additional information, but they searched for it purposefully aftereach drawing they constructed.  Prior knowledgeof the experts appeared to be essential – the expert mathematicians had theability to exploit mathematically the new observations given by the diagrams,and proceeded from there.  Diagrams werenot a goal in themselves but a means to aid the mathematician in gaining moreinformation for the problem situation (Stylianou, 2002).

In the secondstudy, to compare visual representations use of experts and novices inmathematics problem solving situations, Stylianou & Silver (2004)interviewed ten undergraduate students (novices) and ten mathematics professors(experts) and had them do a sorting task of mathematics problems.  Both experts and the novices also had tosolve a set of mathematics problems while the authors used think aloud protocolto trace their thinking, along with other empirical means, such as frequency ofvisual representation use, time spent on analyzing the representations, andcluster analysis. 

            Fromthis comparison study, it was found that novices see visual representations usefulmostly where they were taught to use them (e.g. geometry).  Experts, on the other hand, indicatedpotential use of visual representation in a wider range of problems.  Counter to previous research, however, both expertand novice saw visual representations as viable strategy in advancedmathematical problem solving.  Whileproblem solving, experts constructed visual representations more frequentlythan novices, and used them as dynamic objects to explore the problem spacequalitatively, to develop a better understanding of the problem situation, andto guide their solution planning and enactments of the problem solving. Novicesalso frequently used diagrams in problem solving.  However, they made little use of theirrepresentations.  The experts recognizedmeaningful patterns in the diagrams they constructed.  They seemed to have a rich structure ofschemata associated with the possible operations they could make on the visualrepresentations, thus they could actually use the diagrams they constructed.Novices on the other hand knew little about how to make diagrams a helpfultool, due to their lack of prior knowledge (Stylianou & Silver, 2004). 

            Inthe third study on diagram construction utility by novices and experts, Kohland Finkelstein (2008) looked at differences between first year undergraduatestudents (novices) and first year physics graduate students (novices) as theysolved atypical physics problems.  Theauthors used a variety of methods for the comparison: from think-aloudprotocols, to Schoenfeld-type diagrams to map each participant’s activity as afunction of time, to a comparison of type of representation usage as a functionof time, and finally to a complexity parameter to determine the frequency oftransitions from one representation to another.

            Inshort, their findings point to some clear differences: the experts solveproblems more quickly; experts exhibit more careful analysis and self checking;novices have weakly directed unplanned work; experts have a more flexiblestarting point; experts can flow from one representation to another moresmoothly and rapidly; and finally, experts are more flexible with theirinternal schema, while novices have more rigid internal models (Kohl &Finkelstein, 2008).

  However, in opposition to the consensus fromprevious studies, they found that experts and novices use the same amount ofrepresentations in their problem solving. In addition, the novices did notfocus more on surface features, and experts did not use more physicalrepresentations than novices.  However,similarly to the Stylinaou’s and Silver’s (2004) study, novices used thesemultiple representations without really understanding how they helped, or howto use them.  The experts used picturesto make sense of the problem, while the novices did not quite know what to dowith the picture they constructed. Experts demonstrated more analysis – explicit and goal oriented searches– and thus used representations in more productive ways. Novices, on the otherhand, were more likely to behave mechanically or algorithmically, and usedmultiple representations without being able to make much use of them (Kohl& Finkelstein, 2008).

 

Linking the Novice – Expert Differences toCognitive Load Theory

As is apparent from the abovementioned studies, novices and experts can be placed on a continuum of priorknowledge.  Prior knowledge influencesperception and attention (Arcavi, 2003). Learners use prior knowledge to select relevant information fromgraphics, add information from their prior knowledge and develop a mentalmodel.

Novices have fragmented knowledge,where pieces of information are only weakly connected (Durso & Dattel,2006).  They lack coherent and integratedexisting knowledge, and their understanding is limited to perceptual inputs(surface features) (Wood, 1999).  Theirmental models do not go beyond the perceptual level of processing, thus novicesare not able to easily coordinate features within and across multiplerepresentations to develop an understanding of the underlying concepts (Kozma& Russell, 1997).

Experts havemore domain knowledge, in the form of well organized schemas.  Thus they are able to understand theimportant core principles represented by a graphic (Kozma et al, 2000;Stylianou, 2002; Stylianou & Silver, 2004). They can concentrate more on the information which is relevant forconstructing of an effective mental model (Wood, 1999).  Also, they possess large schemas specific tothe domain (Kozma & Russell, 1997). Even when they are exposed to novel information, experts are able to userelevant prior knowledge as a starting point for interpretation (Kohl &Finkelstein, 2008).

The differencesin the use of visual representations by experts and novices can be linked tocognitive architecture.  The cognitiveload theory assumes that individuals have a limited working memory, and whenoverloaded, learning will not take place. Because of the high intrinsic load of multiple representations exceedsthe capacity of working memory, novice learners do not make use of multiplerepresentations, usually relying on a familiar or simple one.  If switching between representations occurs,the learner has difficulty understanding the representations utilized (Cook,2006).  Because experts havewell-developed schemas, they attend to different information than novices:experts link their initial visual and verbal representations to underlyingprinciples of the content, and develop a more comprehensive mental model (Cook,2006).

 

Prior Research Influencing Most Recent Data Collection:

Novices of Today Different Than of DecadesPast

In a couple of the recent articles,there were several conflicting results about novices compared to welldocumented and empirically confirmed properties of novice learners.  In Kohl & Finkelstein’s (2008) study,novices were not reluctant to use multiple representations.  When solving physics problems, theyconstructed diagrams as readily as the compared experts, translated thesediagrams to force or motion representations and used mathematicalrepresentations to solve problems. Additionally, novices did not only see surface features, as would beexpected, and just like their counterpart experts, used the underlyingprinciples and physical relationships to attempt their problem solving. 

            Stylianouand Silver (2004) noticed a similar trend when observing novices solvingmathematics problems.  Novices frequentlyused diagrams in their problem solving attempts.  In fact all experts’ and novices’ firstaction after reading the problem in their study was to draw a diagram.  This contradicts previous studies on noviceproblem solving, where it was found that novices tended not to use visualdiagrams, and were more likely to use algebraic methods to solve the math problems.

            Bothstudies’ authors gave several possible reasons for this anomaly, stating thedifference of level of novice in their study compared to the previous studies;or the types of questions used, lending themselves to drawing diagrams; or eventhe methodology of the study, with the current study using interviewing andverbal protocol techniques, while the previous studies employing questionnairesand large scale testing.  However, themost interesting reason given in both studies was that the research onexpertise and the apparent effectiveness of multiple representations has leakedinto the curricula of math and science, and thus has influenced the teachingstyles of many physics, chemistry and math teachers. 

In the physicsproblem solving study (Kohl & Finkelstein, 2008), the authors’ give creditto the physics professor of the novice students.  They characterize him as being extremely wellversed in the physics education research, and as such, he used arepresentationally rich approach to teaching.  

In themathematics problem solving study, Stylianou and Silver (2004) speculate thatthe mathematics curriculum has undergone major changes in the last few decades.Undergraduate students in the past few years have been exposed to visualrepresentation to a larger extent than their counterparts two decades ago.  Therefore novices (students) do not seem to beas reluctant to using visual representations as their counterparts of decadespast. (Stylianou & Silver, 2004)

This is anencouraging sign.  Research of expertiseis not laying to rest on deaf ears.  Itis gaining momentum and is being applied to curricula and teaching in recentyears.  Consequently, novices haveevolved, and the novices of the past are different from the novices of thefuture.  Therefore, finer distinctionsbetween novices and experts are necessary to continue this positive trend. 

            Unfortunately,the apparently widespread use of multiple representations by novices does nottranslate to novices using these representations in a productive manner as theyare by experts.  So why aren’t the studentsable to use them more productively? Meta-level skills tend to be slow to develop.  Classes almost never teach meta-level problemsolving skills explicitly – they are learned and picked up over numerouscourses.  It is not clear how to teachthese skills formally or whether they can be consistently taught to novices atall in the short time available in introductory level courses. (Kohl &Finkelstein, 2008)

 

Conclusion

It is obvious that visualrepresentations are essential to the repertoire of the expert scientist.  From the numerous studies described above, itis apparent that the expert is extremely competent in constructing, utilizing,and transforming these visual representations. 

In recent years,it seems that the novice has become aware that these multiple representationsof knowledge are an essential part of becoming a scientist.  However, the novice has to still overcome thelong process of developing the knowledge schema and meta-skills required to beable to use the visual representations to their full potential.  According to Ericsson (2006), this takesdeliberate practice.  According toZimmerman (2006), it is a case of self-regulation. And yet to themathematician, it seems it’s as simple as practicing problem solving(Stylianou, 2002).

 Ultimately, expertise does not lay in thedecision to construct a visual representation or in the construction of thevisual representation, but what they can do with the visual representation.

 

 

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