Networks as integrated in research methodologies in PER

Jesper BruunDepartment of Science Education, University of Copenhagen, Oester Voldgade 3, Copenhagen, Denmark

In recent years a number of researchers within the PER community have started using network analysis as anew methodology to extend our understanding of teaching and learning physics by viewing these as complexsystems. In this paper, I give examples of social, cognitive, and action mapping networks and how they can beanalyzed. In so doing I show how a network can be methodologically described as a set of relations betweena set of entities, and how a network can be characterized and analyzed as a mathematical object. Then, as anillustrative example, I discuss a relatively new example of using networks to create insightful maps of learningdiscussions. To conclude, I argue that conceptual blending is a powerful framework for constructing “mixedmethods” methodologies that may integrate diverse theories and other methodologies with network methodolo-gies.

I. INTRODUCTION

This text is based on a presentation given at PERC2016 [1].It is an introduction to network theory as a methodologicaltool in physics education research. I wish to stress here thatthe scope of the paper is to give examples of how to use net-works in PER. I do not wish to give a comprehensive reviewof network analysis as it has been used in physics educationresearch. Nor is the scope of this paper a detailed analysis ofhow networks affect research methodologies. Network anal-ysis in PER is still a very new endeavor and we have yet tosee the impact of this methodological tool. I write this paperin the hope that researchers in PER will consider the poten-tially very broad range of application that I believe networkanalysis to have.

II. BOUNDARY CONDITIONS FOR NETWORKS AS ARESEARCH METHODOLOGY

A network is a collection of entities and a set of corre-sponding connections. In network terminology [2], the en-tities are called nodes or vertices depending on the field.The connections are either called links or edges and di-rected links and arcs if the direction of connections is rele-vant/determinable. See Fig. 1.

From a methodological perspective, working with net-works imposes a set of boundary conditions. First, the partic-ular phenomenon, system, or object under investigation willbe projected onto a network. Any such projection is a reduc-tion, which emphasizes the relational structure inherent to thephenomenon, system, or object; the projection will split thephenomenon, system, or object into parts, and it re-emergesas a network. Second, networks have a history; they werecreated in some way, and they may change when influencedby some kind of event. The networks we investigate are aproduct of that history, which means that we can expect net-works to be very different, even if they are meant to describethe same phenomenon. Third, and lastly, networks are het-erogeneous, meaning that each node is a unique entity. It isunique because of how it is connected to other nodes in the

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network. A network methodology can take this uniquenessinto account, which in turn may provide a very detailed anal-ysis of the phenomenon, system, or object. The followingsection describes examples of how network methodologiescan shape the theoretical insights that can be gained from dif-ferent types of implementation. These insights depend on the

edited by Jones, Ding, and Traxler; Plenary, doi:10.1119/perc.2016.plenary.002 Published by the American Association of Physics Teachers under a Creative Commons Attribution 3.0 license. Further distribution must maintain attribution to the article’s authors, title, proceedings citation, and DOI.

2016 PERC Proceedings,

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particular choices that researchers make for what represents anode, what represents a link, and how structures might be in-terpreted in terms of an underlying theoretical basis. The ex-amples will demonstrate how network methodologies bringout and emphasize the relational aspects of what has beenstudied.

III. EXAMPLES OF NETWORKS IN RESEARCHMETHODOLOGIES

In this section, I provide three contemporary examples ofhow Network Analysis may be employed as a methodologicaltool. The emphasis is on the kinds of choices a researcherwill make with regards to analysis and interpretation whenworking with networks.

A. Social networks

This example draws attention to the visual and the mathe-matical aspects of networks. The setting for this example is aDanish upper secondary physics class. For seven weeks dur-ing the fall period, students were prompted to indicate withwhom they communicated about physics. Each week wouldgive a different network with a directed link from student Ato student B, if A had chosen B on the roster. Network dia-grams of two of these networks can be seen in Fig. 2(A,B).The prompt had been developed using student reports on theircollaboration and a Communities of Practice (CoP) [4] in-formed framework (see [3] for details).

To utilize the power of social network analysis, it is oftena good idea to bring in information that is external to the net-work. The nodes that represent boys in Fig. 2 are purple andthe nodes that represent girls are green. Links between girlsare green, links between boys are purple, and inter-genderlinks are black.

The visual side of the network diagrams clearly shows thatboys and girls are separate with few inter-gender links andthe boys forming a community of their own. Furthermoregirls seem to interact much more during the test week (B) ascompared with the lab week (A).

The node sizes are proportional to the target entropy, whichis a measure of the un-predictability of information comingto a node in a network. Large target entropy means less pre-dictability. Target entropy has previously been related to aca-demic success [5]. This measure of centrality can be inter-preted both on a node level basis and—because entropy isadditive—on a whole-network level. This is done by com-paring the whole-network target entropy for the network inquestion with a large number of randomized versions of thenetwork (see [3] and references therein for details). By doingso for different weeks one can see patterns in the data. Forexample, it seems that every time this class engages with lab-oratory experiments, the target entropy drops (as compared

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with randomized versions), meaning that it is easier to pre-dict from where a student gets information.

These results can be used to create candidate rules of in-teraction [6]. Here, one candidate rule of interaction couldbe: “When doing experimental work, these students are un-likely to share their experiences outside a small group.” Froma Communities of Practice (CoP) perspective, the class as awhole may not fruitfully be treated as a CoP. Rather, smallergroups may be CoPs. This insight was driven by the mathe-matical nature of these networks.

B. Cognitive networks

This example shows how Network Analysis provides for anew way of looking at questionnaire data. From a method-ological view point, I wish to show two things. First, be-cause of the relational structure of networks, we can also askquestions that link to theories, which hypothesize a relational

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FIG. 3. (A) A network of FCI response items based on student answers. (B) A matrix describing how often two items are grouped togetherin a module. (C) The impetus module. Sub-figures have been adapted from Brewe et al. [7] under the creative commons license (https://creativecommons.org/licenses/by/3.0/legalcode).

structure. Second, networks may or may not be viewed assystems in which information can flow and this distinctionleads to different kinds of questions.

Based on student post responses (N ≈ 150) to the ForceConcept Inventory (FCI, [8]), we constructed a network ofincorrect response items [7]. Two items are connected if atleast one student has indicated both items. Figure 3 A showsa backbone of this network, meaning only the strongest con-nections as seen from the individual node perspective. Thereis a strong connection (thick line) between 13C and 30E, in-dicating that students who chose 13C also tended to choose30E.

To find patterns in the data, one can employ a communitydetection algorithm, Infomap [9], to partition the network intomodules that are more densely connected to each other thanto the rest of the network. Infomap can be described as a ran-dom walker traversing the network by following links. If thewalker is ‘trapped’ for a period of time in a particular partof the network, that part becomes a module. One of thesemodules is shown in Fig. 3 C. This has been labeled an ‘im-petus cluster’, because many of the items resemble what hasbeen called an impetus understanding of Newtonian mechan-ics [7]. However, we also discover that many of the responseitems are only weakly connected to this cluster. A first indica-tion of this stems from the fact that many of the connections(lines) are thin. This is important because Infomap works byoptimizing a quality function, and this may result in slightlydifferent partitions each time Infomap is run. Running In-fomap 1000 times, it is apparent the impetus cluster is notclearly defined (the bottom square in the diagonal of Fig. 3C is not clearly red, but has many purple bits); it has a well-defined core (red portions in the bottom square in Fig. 3 B),but many of the items are often grouped into other modules.This contrasts the second module (the next square on the di-agonal), which is well-defined.

From a theory perspective, one could link this finding to,for example, the conceptual change discussion of knowledgein pieces versus knowledge as theory [10]. A knowledge as

pieces perspective might be linked to a fuzzy cluster such asthe impetus-cluster in Fig. 3 B and C, whereas a coherenttheory might be linked to clusters that are well-defined andform a coherent whole. This would require a deep analysis ofboth the results and of student reasons for making the choicesthey made.

From a methodological perspective, this network as com-pared with the networks in Fig. 2 A+B, contrasts betweenviewing networks as structural entities or as entities con-nected via information flow. The assumption for the targetentropy measure is the latter, and it seems appropriate forstudent interaction networks, because one can imagine thatinformation flowing (although not unchanged) when studentscommunicate. In the response item network (Fig. 3 A), in-formation might be seen as flowing in the sense that one re-sponse led to another. A contrasting view could be that nodesthat are linked act together, so that the groups found representnetworked cognitive structures. I believe that these two dif-ferent ways of viewing this network would lead to differentkinds of questions asked. In the first view, one might ask whatmakes a person choose particular items when having chosenparticular other items. In the second view, one might ask whatcharacterizes the cognitive structure.

C. ‘Action’ mapping networks

The purpose of this example is to show how data that de-scribes some kind of behavior can be treated as a network.This example pertains to how students click on a web page,but the general idea can be extended to more complex be-haviors, such as students interacting each other in a learningsituation [12] or how they answer questions during an inter-view [13]. With this example, I wish to highlight that Net-work Analysis of behaviors offers a novel way of analyzingthe structure of the occurrence of behaviors.

In this example, students interacted with problems in an

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online textbook by navigating via mouse clicks. For example,they could show hints and solutions to problems by clickingbuttons. If they subsequently wanted to hide hints and solu-tions from view, they would click on hide hint/solution [11].Students would primarily solve these problems during classeither alone or in small groups. Other navigational clicks onthe web-page were also recorded, meaning that it could beseen how they navigated the entire online textbook.

Here, clicks on links on the page were used as the basisfor creating networks; clickable text or graphics were repre-sented as nodes and links on the order of clicks. Two nodesare connected in the network if one link was clicked after theother. We defined sessions by using server log data, and weconverted sessions to networks based on recorded clicks. Fig-ure 4 B and C show two different types of session networks.

In this study, we made the theoretically informed choicethat clicks on show/hide hint/solution were to be recorded asparticular nodes. By being able to track students’ way of us-ing hints and solutions we might infer aspects of how thesekinds of problems can act as an artifact that students can useto internalize problem solving skills in a Vygotskian sense[14].

From a methodological perspective, an important point isthat other types of behavior could be mapped, such as behav-iors discernible from video, audio or classroom observations.All of these actions can in principle be mapped by order ofoccurrence or by dividing the data into chunks and then map-ping co-occurrence [12, 13, 15].

IV. A RELATIVELY NEW EXAMPLE: MAPPINGDISCUSSIONS

The following example shows a novel way of integratingnetwork analysis with qualitative discourse analysis to de-velop a bottom-up systematic approach to generating themesin data. The case is a student discussion of sustainability,which illustrates how this integration can make the analysismore sensitive to different voices in the discussion.

A. The cycle

Imagine a transcript of a group discussion. All referencesto individual students have been removed, so the transcriptonly contains information about what was said in the space ofthe discussion. Lindahl et. al [16] proposes a cyclic methodfor integrating network analysis with qualitative discourseanalysis to produce a thematic map of the discussion. Thecycle starts with conducting a qualitative discourse analysisand by creating a linguistic network [17] of the discussionwhere a directed link is drawn from word α to word β if αprecedes β in the transcript (Fig. 5 A1). Then Infomap [9]is used to partition the linguistic network into a map of con-nected modules (Fig. 5 A2). This is a candidate thematic map,and the modules are candidate themes to be interpreted interms of the results from the discourse analysis. We call thisprocess a trial characterization. This may result in changesin the discourse analysis. However, it is likely that the net-work analysis and the discourse analysis cannot be aligned ina meaningful manner. In that case, the trial characterizationwill serve as the basis for constructing rules for changes inthe transcript. These rules can be removal of common words,merging of synonyms or grammatical categories, and con-catenating words to phrases with specific meaning. Once therules have been made they are applied throughout the tran-script, resulting in a new linguistic network (Fig. 5 A2) and anew candidate map with new candidate modules (Fig. 5 B2).At some point the thematic map and the qualitative discourseanalysis should converge, and the result is a final thematicmap with an associated interpretation (Fig. 5 C). See [16] and[18] for details.

B. Example: Sensitivity to different voices

As part of a teaching sequence, a group of Swedish stu-dents were to discuss conflicting views presented in a newspa-per article about the inbreeding of wolves in Sweden. Initiallyfor this group, the qualitative discourse analysis revealed adiscussion that appeared mostly one-sided. It seemed domi-nated by a single point-of-view (protect the Swedish wolvesby using fences). The one-sideness in the discussion appar-ently left little room for additional exploration.

This picture changed when we iteratively integrated net-work analysis; the thematic constructs the discussion is

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FIG. 5. (A1) A network from one of the cycles aligning discourse with network analysis. (A2) The corresponding trial thematic map. (B1)The final network. (B2) The final thematic map. (C) The final thematic map with interpretation. From [16].

weaved around are: concern for wolf survival,#reindeers, ef-fective fences and difficulties. See Fig. 5C. The final mapshows two distinct subsystems (there are no strong connec-tions between the two sets of modules in Fig. 5C) indicatingthat the structure of the discussion was not one-sided. Theone centered on concern for wolf survival, and the other, ob-stacle: #reindeers, being centered on obstacles arising fromissues relating to effective fences and the numbers of rein-deers. So instead of a one-sided discussion, this analysis re-vealed more of a tug-of-war between obstacles, being moreconcrete, and intrinsic values, being more abstract. For fur-ther illustrations and details, see Bruun, Lindahl, and Linder(2016) [18].

V. INTEGRATING NETWORK ANALYSIS IN MIXEDRESEARCH METHODOLOGIES

Throughout this text, I have attempted to draw attention tosome of the choices researchers have to make when work-ing with networks. These are quite fundamental and willhave consequences for the interpretations and explanationsthat network methodologies will provide for. While any de-tailed reflections about these choices are beyond the scope ofthis paper, Table I summarizes these choices.

A. Blend spaces and mixed methodologies

Working with networks in physics education research hasvery much to do with finding out what can be represented andhow that affects the study. I have found the idea of conceptualblending [19, 20] helpful when construing methodologies in-volving networks. Since methodology is intimately linked totheory, one can start with linking concepts from educationaltheory to the concepts from network science. For example,students, knowledge pieces, parts of self-efficacy, or types ofteaching/learning activities might be linked to nodes, whilestudent relationships or similarity, triggering of concepts, andsequences of teaching/learning activities might be mapped tolinks. What is important here is that not everything from thedomain of network analysis and not everything from the do-mains of educational theory gets to be mapped in any singlestudy. And furthermore, we can expect that the new domain,whatever we want to call it, will have new entities of interestemerge [19]. For example, the idea of ‘rules of interaction’in the sense that it has been discussed in recent PER liter-ature [3, 6] is new. In this literature, ‘rules of interaction’are social norms from which observable network structureswill likely emerge. Furthermore, the new domain containsa merger between educational theory and the mathematicaland visual parts of networks (illustrated in Fig. 6). And thesame kind of reasoning holds true for other methodologies.

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TABLE I. Things to keep in mind when working with networks.

Thing to keep Explanationin mind

What nodes and This is an ongoing negotiation and shouldlinks represent be treated dynamically throughout the

research process.Networks as flows or These two different views will facilitatescaffolding structures different kinds of questions that researchers

ask the data.Networks as Network theory offers a myriad of ways

mathematical objects of doing calculations on micro-, meso- andmacroscopic levels.

Modeling dynamics This line of research would investigate e.g.on networks how information spreads in a network

- taking the network nodes and links as given.Modeling dynamics This line of research would investigate how

of networks networks form and evolve in terms of nodesand links between them.

Network science is New developments occur almost every dayevolving rapidly in many areas of network science.

NetworkScience

EducationTheory

[ThematicAnalysis]

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Emergent Patterns

Mathematical and visual

interpretations

Dicernedrules

Concepts

Relationships

HypothesizedStructures

Codes

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Themes

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FIG. 6. A simplified version of conceptual blending network sciencewith educational theory and other research methodologies.

From the perspective of conceptual blending, researchers whoembrace network methodologies will likely use their existingknowledge in conjunction with knowledge of network scienceto interpret both visual and mathematical results, to constructnew ways of visualizing network calculations, and to con-struct mathematical models of learning situations informedby networks.

B. Final remarks

Network Analysis is new territory in physics education re-search. Many methodological questions involving NetworkAnalysis as methodology are unanswered and will need to be

investigated. For example, what are the relationships betweenNetwork Analysis and statistical methods such as factor anal-ysis, clustering, and item response theory? Does NetworkAnalysis qualify as a methodology (or as an integral part ofmethodology) as I have argued or is it merely a new formof representation? As a methodological lens, what does Net-work Analysis allow researchers to capture, and what is leftoverlooked by these kinds of analyses? And perhaps most im-portantly, how can Network Analysis contribute to the devel-opment of theories and design of education to improve peo-ple’s learning of physics? Hopefully, in the years to come,many researchers will help provide answers to these ques-tions.

ACKNOWLEDGMENTS

In this paper, I have mostly referenced work that I havebeen involved with. This is solely because I find it easier toexplain my own work than the work of others. Therefore,I want to acknowledge the work of Ismo T. Koponen andhis group at the University of Helsinki, the work of MadelinBodin at the University of Umeå, the work of Cedric Linderand Jonas Forsman at the University of Uppsala, and manyothers. I have included references at the end of this paper thatmight guide the reader to other relevant network studies.

Appendix: Additional references

The following references appeared in the talk and are nototherwise included in the reference section of this paper.

• Virginia Braun and Victoria Clarke, “Using thematicanalysis in psychology,” Qualitative Research in Psy-chology 3, 77–101 (2006).

• Eric Brewe, Laird Kramer, and Vashti Sawtelle, “In-vestigating student communities with network analysisof interactions in a physics learning center,” PhysicalReview Special Topics–Physics Education Research 8,010101 (2012).

• Jesper Bruun, Networks in physics education research:A theoretical, methodological and didactical explo-rative study, Ph.D. thesis, University of Copenhagen(2012).

• Jesper Bruun and Ian Bearden, “Time development inthe early history of social networks: Link stabiliza-tion, group dynamics, and segregation,” PLOS One 9,e112775 (2014).

• Alan J. Daly, ed., Social Network Theory and Educa-tional Change (Harvard Education Press, Cambridge,MA, 2010).

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• Ane von der Fehr, Sølberg, and Jesper Bruun, “Val-idation of networks derived from snowball samplingof municipal science education actors,” InternationalJournal of Research & Method in Education , 1–15(2016).

• Jonas Forsman, Rachel Moll, and Cedric Linder, “Ex-tending the theoretical framing for physics educationresearch: An illustrative application of complexity sci-ence,” Physical Review Special Topics–Physics Educa-tion Research 10, 020122 (2014).

• Renee Michelle Goertzen, Eric Brewe, and LairdKramer, “Expanded markers of success in introduc-tory university physics,” International Journal of Sci-ence Education 35, 262–288 (2013).

• Jesper Juul Jensen, Formativ evaluering i AlmenStudieforberedelse, Master’s thesis, Department of Sci-

ence Education, University of Copenhagen (2015).

• Ismo T. Koponen and Tommi Kokkonen, “A systemicview of the learning and differentiation of scientificconcepts: The case of electric current and voltage revis-ited,” Frontline Learning Research 2, 140–166 (2014).

• Ismo T. Koponen, Tommi Kokkonen, and Maija Nou-siainen, “Dynamic systems view of learning a three-tiered theory in physics: Robust learning outcomes asattractors,” Complexity (2016).

• Maija Nousiainen and Ismo T. Koponen, “Conceptmaps representing knowledge of physics: Connectingstructure and content in the context of electricity andmagnetism,” Nordic Studies in Science Education 6,155–172 (2010).

[1] Jesper Bruun, “Network analysis as a research methodology inPER,” (2016), invited talk at 2016 Physics Education ResearchConference.

[2] Mark Newman, Networks: An Introduction (Oxford UniversityPress, Oxford; New York, 2010).

[3] Jesper Bruun, Networks in physics education research: A theo-retical, methodological and didactical explorative study, Ph.D.thesis, University of Copenhagen (2012).

[4] Etienne Wenger, Communities of Practice: Learning, Mean-ing, and Identity (Cambridge University Press, 1998).

[5] Jesper Bruun and Eric Brewe, “Talking and learning physics:Predicting future grades from network measures and ForceConcept Inventory pretest scores,” Physical Review SpecialTopics–Physics Education Research 9, 020109 (2013).

[6] Jonas Forsman, Cedric Linder, Rachel Moll, Duncan Fraser,and Staffan Andersson, “A new approach to modelling studentretention through an application of complexity thinking,” Stud-ies in Higher Education 39, 68–86 (2014).

[7] Eric Brewe, Jesper Bruun, and Ian G. Bearden, “Using moduleanalysis for multiple choice responses: A new method appliedto Force Concept Inventory data,” Physical Review Physics Ed-ucation Research 12, 020131 (2016).

[8] David Hestenes, Malcolm Wells, and Gregg Swackhamer,“Force Concept Inventory,” The Physics Teacher 30, 141–158(1992).

[9] Martin Rosvall and Carl T. Bergstrom, “Maps of random walkson complex networks reveal community structure,” Proceed-ings of the National Academy of Sciences 105, 1118–1123(2008).

[10] Gökhan Özdemir and Douglas B. Clark, “An overview of con-ceptual change theories,” Eurasia Journal of Mathematics, Sci-ence & Technology Education 3, 351–361 (2007).

[11] Jesper Bruun, P. Jensen, and Linda Udby, “Mapping student

online actions,” (2015), poster presented at Complenet 2015,New York, United States.

[12] Julie Hougaard, Using virtual experiments as a preparation forlarge scale facility experiments., Master’s thesis, Departmentof Science Education, University of Copenhagen (2015).

[13] Madelen Bodin, “Mapping university students’ epistemicframing of computational physics using network analysis,”Physical Review Special Topics–Physics Education Research8, 010115 (2012).

[14] Lev S. Vygotsky, Mind in Society: The Development of HigherMental Process (Harvard University Press, Cambridge, MA,1978).

[15] David Williamson Shaffer, David Hatfield, Gina NavoaSvarovsky, Padraig Nash, Aran Nulty, Elizabeth Bagley, KenFrank, André A Rupp, and Robert Mislevy, “Epistemic net-work analysis: A prototype for 21st-century assessment oflearning,” International Journal of Learning and Media 1, 33–53 (2009).

[16] Mats Lindahl, Jesper Bruun, and Cedric Linder, “Maps of stu-dent discussions about sustainability,” (2016), invited posterpresentation at 2016 Physics Education Research Conference.

[17] A. P. Masucci and G. J. Rodgers, “Network properties of writ-ten human language,” Physical Review E 74, 026102 (2006).

[18] Mats Lindahl, Jesper Bruun, and Cedric Linder, “Forthcom-ing,” (2016).

[19] Gilles Fauconnier and Mark Turner, “Conceptual blending,form and meaning,” Recherches en Communication 19, 57–86(2003).

[20] Noah S. Podolefsky and Noah D. Finkelstein, “Analogical scaf-folding and the learning of abstract ideas in physics: An ex-ample from electromagnetic waves,” Physical Review SpecialTopics–Physics Education Research 3, 010109 (2007).

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