Epistemic stances toward group work in learning physics: Interactions between epistemology and social dynamics in a collaborative problem solving context
EEpistemic stances toward group work in learning physics: Interactions betweenepistemology and social dynamics in a collaborative problem solving context
Jessica R. Hoehn, ∗ Julian D. Gifford, and Noah D. Finkelstein
Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
As educators we often ask our physics students to work in groups—on tutorials, during in-classdiscussions, and on homework, projects, or exams. Researchers have documented the benefits ofgroup work for students conceptual mastery and problem solving skills, and have worked to optimizethe productivity of group work by assigning roles and composing groups based on performance levelsor gender. However, it is less common for us as a physics education research community to attendto the social dynamics and interactions among students within a collaborative setting, or to addressstudents views about group work. In this paper, we define epistemic stances toward group work :stances towards what it means to generate and apply knowledge in a group. Through a case studyanalysis of a collaborative problem solving session among four physics students, we investigate howepistemic stances toward group work interact with social dynamics. We find that misalignment ofstances between students can inform, and be informed by, the social positioning of group members.Understanding these fine-grained interactions is one way to begin to understand how to supportstudents in engaging in productive and equitable group work.
I. INTRODUCTION
With the increasing use of interactive engagementtechniques in physics education, we are more frequentlyasking our students to work in groups (on tutorials , dur-ing class discussions , on laboratory or classroom-basedprojects , and sometimes even on exams ). Interac-tive engagement, which often includes group work andcollaboration, is cited time and again for being bene-ficial for student learning as measured by performanceon conceptual assessments, problem solving assessments,or course grades . There are also many elements ofstudent learning that we care about beyond conceptualunderstanding and content mastery. Interactive engage-ment, including group work, can help students developpositive attitudes towards science, and a sense of com-munity, identity, and belonging . As physics edu-cators, we care about group work not only because itbenefits student learning, but because collaboration is akey element of science, and because collaborative envi-ronments can help facilitate positive experiences for stu-dents. However, the existence of group work in our class-rooms is not sufficient. We must also pay attention tohow it is implemented and consider in what ways and forwhom the group work is beneficial.The productivity of group work, both in terms of stu-dents learning and the creation of supportive and inclu-sive environments, hinges on the social dynamics amongthe participants. In a group work setting, students so-cial identities become increasingly relevant ; despite themany benefits that group work provides, interactions inthese collaborative settings may also lead to exclusiveor inequitable environments . Some researchers havefound that groups are more effective when they are in-tentionally formed to include mixed ability (as measuredby individual exam scores) , or to avoid mixed gen-der groups that are male-dominated , while otherssuggest that it is best to have students self assemble into groups so that they can work with people they aremost comfortable with . Regardless of how groups areformed, students views about the collaborative nature ofscience or their framing of the type of activity they areengaged in will also impact the social interactionsamong students and thus the productivity or effective-ness of the group work. Here, we attend to an epistemo-logical aspect of group work as a mechanism for fostering(or undermining) equitable group participation.In this paper, we present an analysis of a collabora-tive problem solving session in which we identify a newconstruct called epistemic stances toward group work —views about how knowledge will be generated and ap-plied in a group—and argue that the (mis)alignment ofthese stances among group members is connected to thesocial positioning of individuals within the group. Weapply this idea to examine how one student guides mostof the groups sense making, yet is simultaneously po-sitioned as less knowledgeable. We identify two differ-ent stances among four individual group members andfind that as one stance dominates the other in the groupsense making process, one student, whose behaviors arealigned with the non-dominant stance, is positioned asless knowledgeable. In this case, we argue that the mis-alignment of epistemic stances toward group work con-tributes to, and is reinforced by, this social positioning.The construct of epistemic stances toward group workbrings together the ideas of epistemology , framing ,group work , and social dynamics , and is one waythat we can begin to understand the participation and in-teraction among students in collaborative settings. Thepurpose of this paper is to introduce this construct anddemonstrate its utility through a case study analysis.Identifying epistemic stances toward group work allowsus to investigate the interactions between epistemologyand social dynamics and better understand the social po-sitioning of individual group members. In the next twosections we introduce the construct of epistemic stancestoward group work and then discuss how it fits in with a r X i v : . [ phy s i c s . e d - ph ] M a y relative theoretical constructs in the physics education re-search community: implementation of group work, analy-sis or assessment of group work, epistemological framing,and productivity of group work. II. EPISTEMIC STANCES TOWARD GROUPWORK
For many physicists and physics students, what itmeans to know, learn, and do physics (their epistemol-ogy of physics) includes group work and collaboration.Likewise, what it looks like to engage in group work ina given context can be determined, in part, by individu-als’ beliefs about what counts as knowledge. Ideas aboutthe form that group work should take and how it shouldfunction to generate knowledge may be different for dif-ferent people. For example, in a given context, one per-son may think that group work should involve delegat-ing individual tasks to individual people such that eachgroup member contributes unique expertise or knowledgeto the larger problem at hand, while another person maysee group work as an opportunity for multiple people towork together simultaneously on one collective task. Or,one may view the goal of a group work scenario to be toreach an answer to a particular problem, while someoneelse may view group work as a time to collectively thinkthrough relevant ideas or principles such that individualsmay later come to their own conclusions. These ideasabout the form that group work can (or should) take aresubsumed within the broader ideas of epistemology andgroup work.As shown in Fig. 1, we consider the domains of epis-temology and group work to be overlapping. Epistemol-ogy refers to beliefs about the nature of knowledge, whilegroup work includes collaboration among individuals andis facilitated by social dynamics. We define epistemicstances toward group work as views about how groupwork functions to generate and apply knowledge, exist-ing at the intersection of these two domains (see Fig. 1).Views about the role of group work in learning physicsare subsumed by, but distinct from, views about learningphysics more generally. Similarly, views or expectationsabout how group work should function exist as one ele-ment of the broader activity of group work, distinct fromother contributing factors such as social norms or ac-countability. Epistemology and group work have eachbeen the subject of extensive investigation within thephysics education research community , but we nowlook at the intersection. Zooming in on epistemologicalviews about group work allows us to gain a more nuancedand rich understanding of students views about what itmeans to learn and do physics. Specifically, attending tostudents epistemic stances toward group work allows usto investigate the social dynamics and interactions amongstudents that can support or inhibit productive and eq-uitable group work.Much like epistemologies in general, epistemic stances
FIG. 1. The construct of epistemic stances toward group worksits at the intersection of epistemology and group work. toward group work may be fluid and context depen-dent . The stances people enact may vary momentto moment, and they are likely informed by a multitudeof factors—interpersonal interactions, content domain,expectations set by the instructor, content and formatof collaborative tasks, relationships among people in thegroup, etc. In identifying students epistemic “stances,we refer to views that are enacted in the specific localcontext. These views may or may not be preferences orbeliefs held by the students, and they may or may notbe robust or permanent. We identify stances or viewsaligned with the students in the moment actions and be-haviors in a collaborative problem solving context, butdo not make claims about the students’ preferences orstability of stances beyond the local context.There are two different stances that we identify in ouranalysis. The first is the “Collective Consensus Build-ing stance, in which group work entails generating andmaking sense of ideas collectively. Aligned with this viewof group work, individuals contribute tentative ideas forthe group to collectively negotiate and the sense makingprocess is characterized by individuals thinking out loudand building off of each other’s ideas. This type of col-laboration has been described in prior research as “co-construction” . The second stance is “Explainer-Explainee. Here, group work means that individuals willcome to understand the ideas at-hand and then explainthem to others, a mutual process where if you understandsomething or know the answer, you then explain it to thegroup . Although we identify only these two stances inour data, we do not claim that these are the only possibleepistemic stances toward group work. We could imagineadditional stances, and also note that these stances donot have to be fixed—there could be many stances orblends of stances that individuals or a group as a wholemight take up. The goals of this paper are to introducethe construct of epistemic stances toward group work,identify the two above-mentioned stances as examples ofthe construct in the data, and explore how these stances(and the misalignment between them) can interact withthe social dynamics and sense making of a group in acollaborative problem solving setting. III. BACKGROUNDA. Implementation of group work matters
Active learning strategies, which often include groupwork, have been shown to be disproportionately benefi-cial for students from underrepresented groups, in termsof course grades . Yet there is also evidence to suggestthat active learning classroom interventions can have dif-ferent impacts on different subpopulations of tradition-ally underrepresented students (e.g., ). Thus, whileinteractive engagement is generally thought to be goodfor student learning, we must investigate in what ways,and for whom, it is beneficial.Research in biology education identifies some of theways in which group work, despite its potential bene-fits, can actually be isolating or harmful for some stu-dents. Cooper and Brownell found that active learningstrategies incorporating group work can increase the rel-evance of LGBTQIA social identities in the classroom,which can lead to stress about whether it is safe to comeout, more opportunities for being misgendered, and in-creased cognitive load for students who are members ofthe LGBTQIA community. They state that active learn-ing changes the dynamics of the classroom so that whothe instructors and students are has a larger impact onthe student experience, particularly for students who arein the minority (p. 3). In another study, Cooper,Downing, and Brownell explored the relationship be-tween active learning practices and student anxiety, andfound that group work had the potential to either in-crease or reduce student anxiety. The impact on stu-dents depended on how the group work was implemented(e.g., allowing students to choose their groups or givingstudents time to synthesize their thoughts before shar-ing with their peers tended to reduce students anxiety,whereas feeling uncomfortable with group members in-creased anxiety). Along the same vein, some researcherscall on instructors and researchers to not only focus onimplementing interactive engagement and group work,but to pay close attention to the dynamics among stu-dents in collaborative settings, highlighting the implica-tions for equity and inclusion in our educational envi-ronments . In this paper, we respond to that callby investigating the social dynamics of one group of stu-dents in a collaborative problem solving setting and ex-plore how the social dynamics are tied to epistemologicalstances toward group work to effect the differing socialpositioning of group members.Tanner calls for instructors to design learning environ-ments that attend to both individual students and inter-actions among students through teaching strategies thatcultivate equitable classroom environments (e.g., estab-lish classroom community norms, use varied active learn-ing strategies, assign reporters for small groups) . As-signing and rotating through specific roles is one wayto encourage equitable group discourse, and has beenidentified in physics as a way to promote effective group work . Eddy et al. call on instructors to structure theirclassroom activities in a way that promotes equity by un-derstanding the differential participation and barriers toparticipation in peer discussions for some students . Ina study of introductory biology students working in self-selected groups, they found that students’ preferred rolesin group work were correlated with their social identities(e.g., race, nationality, gender). The authors identifiedthree barriers to participation in peer discussions: exclu-sion from discussion by group members, anxiety aroundparticipating in discussion, and low student perceptionsof the value of group work . They argue that in orderto promote equitable classroom environments, instruc-tors must first understand the barriers that lead to dif-ferential participation in group work. In our case studyanalysis we identify misalignment of epistemic stancestoward group work as a potential barrier to equitableparticipation in group problem solving.In line with these studies, other researchers have sug-gested the need to investigate factors that contributeto the construction and productivity of group work en-vironments (e.g., ). For example, while Lorenzo,Crouch, and Mazur report that use of interactive engage-ment reduces the gender gap on the Force Concept In-ventory (FCI) , Pollock, Finkelstein, and Kost reportthat interactive engagement alone is not sufficient andthat we must investigate the roles both instructors andstudents play in constructing norms around collabora-tion . Thus, in order to investigate the factors that al-low social dynamics to support (or hinder) equitable dis-course, we must attend to multiple dimensions of groupwork and the interactions among them. B. Attending to multiple dimensions of group work
Just as our community has documented that physicseducation is about more than content mastery, so too isgroup work more than assembling several individuals toa common task, or assigning roles to individual groupmembers. In K-12 mathematics education, Barron illus-trates through case study analyses how both cognitiveand social factors play a role in defining a collabora-tive mathematics problem solving environment amongsixth-grade students . She identified more and lesssuccessful groups as defined by problem solving perfor-mance and uptake of correct ideas. “Less successful”groups had “relational issues”, which included “competi-tive interactions, differential efforts to collaborate, andself-focused problem solving trajectories” (pg. 348)that impeded the group’s ability to engage in produc-tive problem solving. Barron suggests that one way thecognitive and social factors work together to constructa joint problem solving environment is through the “de-velopment and maintenance of a between-person stateof engagement” (pg. 349), which she describes as theawareness group members have for one another, rangingfrom “complete lack of joint attention” to “continual co-ordinated participation.” Along a similar vein, we attendto the ways in which social factors are intertwined withepistemology in the construction and dynamic evolutionof a joint problem solving space. However, in consider-ing the success or productivity of a group, we go beyondcontent mastery and correct answers. In our case studyanalysis, we consider the ways in which group problemsolving interactions may be cohesive (or not) along socialand epistemological dimensions, independent of concep-tual productivity.Pawlak, Irving, and Caballero identified four modesof collaboration by attending to three dimensions of in-troductory physics students’ interactions—social, discur-sive, and disciplinary . Along the social dimension, theycharacterized the overall tenor of students’ collaborationas consonant or dissonant . The discursive dimensionidentifies the interaction patterns among students: con-sensual (one student makes substantial contributions),responsive (multiple students make substantive contri-butions), elaborative (the substantive contributions frommultiple students build off of one another) , and argu-mentation (involving evidence, a subsequent claim, andjustification of how the evidence supports the claim) .Regarding disciplinary content, they characterized stu-dents’ conversations as specific or abstract. Treatingthe social, discursive, and disciplinary dimensions inde-pendently, Pawlak, Irving, and Caballero identified fourdistinct modes of collaboration—debate, informing, co-construction of an answer, and building understandingtowards an answer—each arising from a unique combi-nation of codes along the three dimensions . Similarto Pawlak et al. ’s study, we attend to multiple dimen-sions of students’ collaboration, but our analysis differsbecause we consider the interactions between those di-mensions and attend to finer-grained details of the socialdynamics in a collaborative setting.Sohr, Gupta, and Elby also attend to students groupwork interactions by using multiple analytical lenses .By investigating the intertwining of conceptual, epis-temological, and socioemotional dynamics, they illus-trate the multifaceted ways in which conflict can arisein collaborative settings, and identify one way studentsmay resolve those conflicts. In particular, they describean “escape hatch” as a series of discourse moves thatserve to relieve tension in the group by ending or shift-ing the conversation before a conceptual resolution hasbeen reached. On the surface, escape hatches (clos-ing statements) can appear to be purely epistemologi-cal statements—not recognizing the complex intertwin-ing of various factors might lead one to misinterpret thesemoves as an indicator of a groups co-constructed episte-mological stance rather than a result of, and resolutionfor, building tension within the group. Escape hatchescan be productive in that they can help to establish moreequitable group norms, or open up space for the groupto engage collaboratively in conceptual discussion. Thiswork provides an example of how interactional dynamicsin a group can be the result of entanglement of many dif- ferent factors. We build on this work by investigating theinteractions between sense making , epistemology, andsocial dynamics in group work, although not necessarilyin the presence of conflict or tension. C. Epistemological framing
The physics education community has attended to im-plementation and impacts of group work, but we havethought less about how the students think about groupwork, and how that interacts with their learning. Stu-dent perceptions of group work likely impact the rolesor positions individual students have access to within agroup . One way researchers examine students’ percep-tions or expectations of learning physics in a collabora-tive environment is through the lens of epistemologicalframing (e.g., ). Generally, in the disciplines ofanthropology and linguistics, framing refers to an indi-vidual or group’s sense of what is going on in a givensituation, including expectations about what could andshould happen, what should be attended to, and howone should act . Epistemological framing specifi-cally refers to a sense of what is taking place with respectto knowledge (e.g., Is this a situation for sense making,or for rote manipulation of formulas?); these frames canbe considered for individuals or groups and can vary mo-ment to moment . There are other aspects of framingas well, such as social framing, which refers to expecta-tions regarding individual and community roles and in-teractions in a social setting. In the physics educationcommunity we primarily attend to epistemological fram-ing, as the nature of knowledge has particular importancein school settings, although it is noted that different as-pects of framing can interact with one another, especiallyin collaborative settings .Scherr and Hammer describe a resource-based accountof epistemological framing in which a frame is a “locallycoherent pattern of activations” (p. 151) of epistemo-logical resources. As epistemological resources mayexist within an individual’s mind or be distributed acrossa group of people, this resource-based account links twodisparate approaches to framing—one with respect to in-dividual reasoning and another with respect to socialdynamics across groups . In a study of collaborativetutorial-style activities in an introductory physics class,Scherr and Hammer illustrate that verbal and nonver-bal actions together provide evidence of students’ episte-mological framing and insight into the dynamics of thisframing . Irving, Martinuk, and Sayre also explore thedynamics of epistemological framing by looking at thetransitions or shifts between frames . They identifiedtwo axes along which discussions could be categorized—expansive versus narrow, and serious versus silly—andobserved that the majority of frame shifts were initiatedby the teaching assistant facilitating the collaborativelearning situation.The notion of epistemological framing informs ouranalysis of the collective problem solving in a group offour students. Looking at our data through the lens ofepistemological framing, we would infer a coherent episte-mological frame, where the group has shared understand-ing around what kind of activity they are engaged in, evi-denced by both their verbal and nonverbal actions . Yetdespite this alignment, we see one student in the grouppositioned as less knowledgeable. To understand this po-sitioning, we identify an epistemological aspect of groupwork, and we associate students’ behaviors with expecta-tions as to how knowledge will be generated in the group(epistemic stances toward group work). We need this newtool to help us identify and describe different stances thatindividual group members might be taking regarding therole of group work in the construction and applicationof knowledge, despite a cohesive epistemological frameamong the group regarding what kind of activity theyare engaged in. Our analysis and discussion are distinctfrom epistemological framing because while framing caninclude group work as one of many factors, we focus on afiner grained analysis of just the epistemic stances towardgroup work and how these interact with other aspects ofthe social learning environment. As depicted in Fig. 1,we consider these epistemic stances toward group workto be interactions between epistemological and social as-pects of framing, where epistemological framing refers towhat is taking place with respect to knowledge, while so-cial framing refers to students sense of what to expectof each other, of their instructor, and of themselves (p.149). Social framing does not inherently include ideasabout knowledge generation, and epistemological fram-ing does not inherently include ideas about social inter-actions. In attending to epistemic stances toward groupwork, we consider the overlap, or blending, of epistemo-logical and social framing. D. What counts as productive group work?
In much of the prior literature, group work is consid-ered productive or effective if the group engages in so-phisticated problem solving strategies or if they reach acorrect answer . We expand this consideration andattend to multiple aspects of productivity. If a group ismaking progress toward a correct or sophisticated con-ceptual understanding of the physics, we call that groupwork conceptually productive. Yet, as we will see in ouranalysis below, a conceptually productive group does notensure equitable discourse. A second aspect of produc-tivity is whether all students in the group have access toparticipation in a variety of roles. Using the language ofEddy et al. , we would consider a group to be moreproductive if there are fewer barriers to participationfor the individual group members. In our analysis, weforeground this latter view of productivity—a productivegroup is one that engages in equitable discourse—whilenoting that there are multiple factors that contribute to,and dimensions along which to view, the productivity of collaboration. IV. METHODOLOGY
The case study presented in this paper comes from abroader study of students mathematical sense making inquantum mechanics (QM) . In order to investigatethe ways students engage in MSM, we conducted a seriesof focus group studies with Modern Physics and QM stu-dents in which we gave them QM problems to work onin a group for one hour . While watching a video of oneparticular group and looking for elements of mathemati-cal sense making, we noticed that one student was beingpositioned as less knowledgeable despite guiding much ofthe group’s sense making. This motivated us to focuson this group and to analyze the intersections betweenepistemology and social dynamics during the collectivesense making process. We take an analytic case studyapproach in order to examine a puzzling phenomenonthrough observation, description, and interpretation of asituation in context, with the goal of producing a richand in-depth understanding .The group consists of four students—Penny, Morgan,Cam, and Sarah (pseudonyms)—from a modern physicsclass. We did not have relationships with these studentsprior to the one-time focus group session that took placein the last week of the semester. We recruited the stu-dents by sending an email to the class which framed thefocus group study as an opportunity to work throughQM problems with their peers before the final exam,but was not directly connected to their grade in thecourse. The professor of the course, however, offered ex-tra credit to students who participated. We organizedthe groups based on scheduling constraints, and the stu-dents were monetarily compensated for their time. Penny(she) identifies as a white female, and is a sophomoremajoring in chemistry and physics. Morgan (they) iden-tifies racially as white and responded to the gender ques-tion on our demographic survey with a question mark.They are a junior computer science major. We use theypronouns for Morgan , and note that their gender per-formance includes many attributes typically consideredto be masculine ; we believe this is important infor-mation for interpreting the social dynamics we observeamong the group, particularly because Morgan comesto fill the role of an explainer and engages in mascu-line forms of discourse that are common and favored inthe broader physics culture , and in at least onemoment other students in the group refer to Morgan us-ing “he pronouns (line 217 in the transcript). Cam (he)identifies as a white male, and is a sophomore physicsmajor. Sarah (she) identifies as a white female and isa sophomore majoring in astrophysics and creative writ-ing. While we suspect that gender plays a role in theinteractions among these four group members, we havenot yet analyzed the specific ways in which the interac-tions are gendered. Here, we focus on the entanglementof epistemological and social aspects of the group prob-lem solving, and we leave deeper analyses of gender andpower dynamics for a future paper. Although this pa-per does not provide analysis or claims around gender,we include gender information here because we believe itis important context for understanding and interpretingthe groups interactions.The focus group took place in a small room with thestudents seated around a rectangular table—Morgan andSarah sat on one side of the table, Cam on the other side,and Penny at the head of the table (see Fig. 2). Weframed the focus group session as a chance for the stu-dents to work on a few QM problems together. We askedthem to talk to each other and say what they were think-ing out loud as much as they could, and we noted that wewere more interested in their sense making rather thanthem arriving at a correct answer. One researcher (thesecond author) was present in the corner of the room,and chimed in every once in a while with follow up ques-tions for the group. We prepared four different problems(each with several sub-parts) for the students to workon; the question prompts were in line with QM contentthey had covered in their course. The three episodes wepresent here include the students working on two differ-ent problems. The first problem (see Fig. 3) is aboutan infinite square well. Part A) asks the students to de-termine which values they might measure for position,energy, and speed for a particle in the n=7 state of theinfinite square well. Parts B) and C) ask for the prob-abilities of finding the particle in the first and secondquarters of the well. The second problem (see Fig. 4) isabout a double square well, and has the students considerthe shape of the wave function when the well separationis: zero (i.e., one wider well), comparable to the width ofthe wells, and very large compared to the width of thewells.We transcribed the hour-long video, and watched itseveral times from different lenses, attending to: themathematical sense making students were engaging in(our original intention in conducting the focus groups),the interplay between social dynamics and sense mak-ing, the ways in which certain students get positionedas more or less knowledgeable, the inferred epistemic as-pects of students’ sense making, and the inferred epis-temic stances toward group work. For individual episodeswithin the hour-long focus group, we conducted a dis-course analysis in order to infer epistemic stances to-ward group work and explore the ways in which thoseinteracted with the social dynamics and sense making toresult in the positioning of students as more or less knowl-edgeable. We achieve an in-depth understanding of thegroup work scenario by attending to multiple aspects ofthe data—verbal interactions among the students (rep-resented in the transcript), non-verbal interactions (cap-tured in the transcript and in our narrative description),patterns of action and non-action (captured in the nar-rative description), and artifacts of the students writtenwork (not included in this paper as a site of analysis, but we refer to them to determine who has control over theproduction of written work).We selected three focal episodes for this analysis—onefrom the very beginning of the hour-long session, one 17minutes in, and the third 46 minutes in. We intention-ally chose episodes from different times throughout thesession when the students were solving and talking aboutdifferent problems to get a sense for how the groups inter-actions changed or stayed the same over the course of thehour. The episodes we selected contain rich conversationand interactions for which we could identify the inter-twining of epistemological and social elements. However,these three episodes are not unique in this regard—manyof the other episodes throughout the session contain sim-ilar interactions to those that we present here. Withineach episode, our analysis looks at both the episode over-all (a coarse grained view of what is happening, whatthey are talking about, the roles people are taking on,etc.) and a finer-grained look at the interactions amongstudents (line by line interactions, turns of talk, gestures,etc.). There are two objects of focus of the present anal-ysis that we first identify separately and then explorethe connections between: epistemic stances toward groupwork, and social dynamics. In order to infer epistemicstances toward group work, we look for evidence of stu-dents expectations of how knowledge will be generatedin a group. For example, if a student is leaning in tothe group and looking at other group members we wouldinfer that they were expecting to work together (versusan expectation of an individual activity). If a studentis thinking out loud, and asking other group membersto weigh in on their ideas, we infer that the student isenacting a stance that generating knowledge in a groupinvolves collective co-construction of ideas (versusan expectation of individual construction and subsequentsharing of ideas). Next, we attend to the social dynamicsof the group by noting who is talking when and how thegroup members are attending to one another (or not);this includes identifying the words students are using,their body language, physical positioning, gestures, toneof voice, pitch and pace of speech, and who has controlover the sense making the group engages in. Further,we ask how individual students are being positioned (bythemselves and each other) within the group. The in-ferred epistemic stances toward group work and the so-cial dynamics and positioning can be tightly intertwinedwith one another; looking for evidence of each indepen-dently helps us to explore the ways in which they areconnected.The analysis focuses primarily on Penny, Cam, andMorgan; the fourth student, Sarah, is engaged and lis-tening to the conversation (as evidenced by her postureleaning in to the group, smiling, nodding, looking atother group members, following along on her paper, andoccasionally chiming in with yeah) but makes very fewof her own verbal contributions. These types of contri-butions, which serve meta-conversational functions, aresometimes referred to as “back channeling” . The so- FIG. 2. Four modern physics students—Cam, Penny, Sarah, Morgan (starting on the left, going clockwise)—working collabo-ratively on QM problems.FIG. 3. Problem 1 from the focus group study asks about an infinite square well. In Episode 1, the students are discussingpart A) and in Episode 2, they are determining how to check if their answers to parts B) and C) are correct.FIG. 4. Problem 2 from the focus group study asks about a double square well. In Episode 3, the students are discussing partA) ii) when b ∼ a . cial dynamics involving Sarah (including her silence) areworthy of a study in their own right, but they remainoutside of the scope of the present paper.In the transcriptions, ellipses (...) represent pauseslonger than those natural in speech; gestures or non-verbal actions are indicated in [square brackets]; squarebrackets sometimes also contain information added to thetranscript by the researchers for clarity; em dashes (—) indicate interruptions in conversation or people talkingover one another. In the data we present below, there aremany instances of the students interrupting each other.When there is single pair of em dashes, the reader shouldread this as two consecutive turns in a conversation butwith the first speaker getting cut off and yielding to thesecond speaker. For example, Penny: according to the probability density—Morgan: —But they’d conform to whatever densityit is should be read as two turns in a conversation, wherePenny’s turn gets cut short and she stops talking asMorgan takes the floor. When there are multiple turnsof talk, with each speaker’s words book-ended with emdashes, this should be read as the individuals speakingover one other. For example,
Cam: —So basically like this—Morgan: —you draw that there’s gonna be sevenpeaks—Cam: —And really—Morgan: —and nine nodes—Cam: —if you actually did the probability it’ll ac-tually like bounce up like— should be read as Cam and Morgan each contributingtheir ideas to the conversation, but not listening and re-sponding to one another. In this case, Morgan interruptsCam’s statement, but Cam continues to talk, and viceversa. This exchange should be read as quick, consecutiveturns in a conversation, noting the interruptions and of-ten simultaneity of multiple speakers’ contributions. In atranscript of this nature, it may be helpful for the readerto read all of the statements from one speaker to get asense for what they were trying to say while the otherspeaker was also talking (i.e., reading Cam’s three state-ments contiguously, skipping over Morgan’s statements).Over the course of two years, discussions among sevenphysics education researchers (the three authors alongwith collaborators from the University of MarylandPhysics Education Research Group) led to many of theinsights and preliminary versions of the arguments in thispaper. Those arguments were then refined by the threeauthors, a team that includes two men and one woman .As a woman in physics, JRH has privileged access to in-terpretation of the social cues and norms we see play outin the conversations among feminine and masculine per-forming physics students. This perspective thus shapeshow we perceive and interpret the interactions amongthis particular group of students. Further, after reach-ing consensus among the research team, we validated andrefined our analysis through additional discussions with physics education researchers external to the project. V. DATA AND ANALYSIS
In this section, we present three episodes with inter-leaving presentation of transcript and analysis.
A. Episode 1
Episode 1 takes place at the very beginning of the hour-long session. The students begin with question 1a (de-scribed above and shown in Fig. 2). They are each look-ing down at their individual papers, reading the prompt.The conversation begins when Penny reads the questionout loud and begins to share her thoughts:
Penny: “If you were to make independent mea- surements of the position, energy, and speed, what might you measure?” Uhmmm. So since the, like at every, every time you measured you’d just like get a different position. Right? Morgan:—Yeah— Sarah:—Yeah— Cam:—Mhmm— Penny: Those would just, like according to the probability density— Morgan: —But they’d conform to whatever density it is, I’m not quite sure. Penny: Like, whatever the, like the psi squared thing— [writing on her paper] Morgan: —Yeah— Cam: —Yeah— Sarah: —Yeah— Cam: —That would represent the distribution. Penny: And it would have to be zero at the edges so it would be like that. [drawing on her paper] Morgan: And since it’s the seventh excited state would there be— Cam: —Yeah, because we’re infinite— Morgan: —seven peaks I think? Cam: Yeah Morgan: It would be like— [draws wavy sine peaks in the air with their pencil] Sarah: —Yeah From the beginning few seconds of the episode, we in-fer that all four students have the expectation that theyare there to work together. This is evidenced by theirposture, who responds to the questions, and the tentativenature of their questions. All four students are leaning inwith their elbows on the table, looking down at their ownpapers but as the conversation begins they also look up ateach other and each other’s papers (see Fig. 2). WhenPenny puts forth her idea in lines 3-5 that you wouldmeasure a different position every time, and follows upwith a question (“right?”), the three other group mem-bers respond simultaneously (“yeah,” “Mhmm,” lines 6-8). Penny looks at Cam when she says “right?,” but heis looking down at his paper, as are Morgan and Sarah.The fact that all three students respond, despite not be-ing addressed directly or not looking at the person whoasked the question, suggests an expectation that any ideaput forth is for the group to make sense of and respondto.Additionally, to begin the hour-long problem solvingsession, the students put forth ideas with tentativeness,phrasing their ideas as questions (Penny lines 5, 14) andexplicitly saying they’re “not quite sure” (Morgan line12) or qualifying an idea with “I think” (Morgan line24). In the first few seconds of the episode, Penny andMorgan display this tentativeness, which sets the tonefor a collaborative sense making environment. As thehour progresses, however, we see this dynamic changeas Penny continues to be tentative while Morgan andCam adopt more authoritative ways of engaging in theconversation. Cam continues the conversation by puttingforth his own tentative idea:
Cam: Well, your n would be seven times pi I be- lieve, right? Inside the k equals... Morgan: Right. Penny: How does n change the number of like— Cam: —Uhmm because... Morgan: So, I think— Penny: —waggle things— Morgan: —I think it’s... Cam: [writing on his paper] Morgan: Right. That’s the, that’s what’s inside the sine function. Penny: Oh, like the sin(kx) Cam: So it’s 7 pi over a. Morgan: That’s what I thought, but I think what that...I think it means that if— Cam: —So basically like this [pointing to his paper]— Morgan: —you draw that there’s gonna be seven peaks— Cam: —And really— Morgan: —and nine nodes— Cam: —if you actually did the probability it’ll ac- tually like bounce up like— Morgan: —Right— Sarah: —Yeah— Cam: —that many times— Penny: —Ohhh yeah— Morgan: —’Cause in the second state it goes up once and then down— Penny: —It has that many nodes. Or does it have seven minus one or something? Cam: I don’t think we have a minus one here— Morgan: —I think there’s a, I think it’s a...Well because there’s one peak, I think that what you’ve drawn [to Penny] is the, is the— Penny: —Yeah— Morgan: —the ground state— Cam: —n = 1— Morgan: —n = 1. So that has one peak. So I think it would make sense for it to equal the number of peaks. Penny: And like— Morgan: —Oh, it’s n +1 uhh, zero points. That’s what it is. As the students try to figure out how many peaks the n = 7 wave function has, Cam and Morgan begin to talkover Penny, and one another. Penny attempts to ask aquestion and join in the sense making, but gets inter-rupted at lines 32 and 55. At line 58, she continues herthought that began with “Ohhh yeah” (line 55), talk-ing at the same time as Morgan and looking directly atCam. She asks if the number of nodes is “seven minusone or something,” and Cam and Morgan both begin toanswer her question. They do so tentatively, qualifyingtheir explanations with “I think” (Morgan line 62) or “Idon’t think” (Cam line 60). This exchange represents aturning point in the overall dynamic of the group, wherePenny begins to assume the role of “question asker” andCam and Morgan begin to assume roles as “explainers.”These positioning and role-taking tendencies that we seedeveloping in the first episode continue to evolve overthe course of the hour. Here, Cam and Morgan explainto Penny as they try to figure out how the number ofnodes depends on the state. This culminates when Mor-gan has an “aha moment” and states in an excited andauthoritative manner that “it’s n+1...zero points. That’swhat it is” (line 71). We note that in this instance wesee Morgan’s excitement around figuring out the answer(the “aha moment”) coincide with their assumption ofthe role of explainer. Next, Penny steers the conversationin a different direction by bringing up a question aboutthe graphs they are drawing on their paper (sketchingthe wave function on top of the potential energy graphgiven with the prompt): Penny: Well, also it doesn’t really make sense to draw this [wave function] on this [potential energy] diagram right? Because, or wait, like what is the height of this? [gesture?] Morgan: Well that...the height represents— Penny: —Isn’t that just like the number of— Cam: —The probability— Penny: —Yeah— Morgan: —It represents the probability— Sarah: —Yeah— Morgan: —of finding it there. Cam: Right, so that’s where you’re most likely to— Penny: So it just doesn’t belong...Like, what is V of x? Isn’t that potential? Morgan: Right. So that’s why, that’s why it’s sorta— Penny: —So you wouldn’t really draw this on this graph— Morgan: —not so great to draw there— Penny: —You’d just draw it like this [drawing a new graph]— Morgan: —because the axes aren’t the same— Penny: —and this [y axis] would be like, probability— Morgan: —Exactly— Penny: —and then this [x axis] would still be posi- tion. Morgan: And so that, drawing the probability curve makes sense, but yeah you’re right on that it doesn’t represent potential so it’s, it’s not the most mean- ingful curve there.
Again, Penny is the one asking the questions (lines 75and 85) that Morgan and Cam take up by explaining toher. At line 77, Morgan immediately takes up the ques-tion about drawing multiple graphs on the same axes;whereas in lines 60-62 Cam and Morgan’s explanationswere tentative, here Morgan answers in a more didacticmanner. The tentative qualifiers (“I think”) are no longerpresent, and both Morgan and Cam contribute ideas withmore conviction: “Well...the height represents” (line 77),“It represents the probability” (line 81), “Right, so that’swhere...” (line 84), “Right. So that’s why...” (line 87).Amidst these explanations, Penny tries to chime in andjoin the sense making but gets talked over (lines 78, 90,93, 96). From lines 85-100, Penny continues to verbalizeher thought process despite Cam and Morgan focusingon their own work and talking over her.In this episode, Penny has control over the conversa-tion in that she is the one asking questions or providingcontributions that prompt the group to engage in sensemaking (considering what the wave function looks like,and then what it means to draw the wave function on thesame axes as the potential energy). One might interpretPenny’s questions as an indication that she is confusedabout the content, or at least more vocal about her con-fusion than the other students. While it is likely thatsome of her questions correspond to genuine confusion ortentativeness, we also observe that Penny often framesideas in the form of questions or bids , even when shemay not be confused about the content. This is evidentin that she often presents an idea followed by “right?”(lines 5 and 75). Determining whether Pennys questionsindicate confusion or tentative presentation of more cer-tain ideas is not crucial for this analysis; the fact that hercontributions are consistently taken up by the group asquestions, or requests for explanation, serves to positionher as less knowledgeable within the group. Penny doesnot have agency in the conversation in the sense that sheis continually interrupted and explained to in a didac-tic manner. However, she does have agency in the sensethat her contributions (often taken up by the group asquestions) drive the sense making and topics of conver-sation within the group. With the confluence of theseinterruptions and explanations we begin to see Penny asbeing positioned as less knowledgeable within the groupdespite the fact that her ideas or contributions are theones guiding the flow of the conversation.We focus on Penny and Morgan in this episode andidentify them as enacting two different epistemic stancestoward group work. Penny’s tentativeness and orienta-tion toward inclusion are aligned with an epistemic stance that the way knowledge will be generated in the groupis through collective consensus building or sense making.By adding “right?” to the end of her ideas, Penny invitesothers to contribute or weigh in on her ideas, consistentwith a notion of collaboration that involves throwing outideas for everyone to collectively grapple with and buildon. Additionally, Penny proposes tentative ideas andthinks through them as she is talking. For example, inline 55 Penny begins a thought with “Ohhhhh yeah” andfinishes it in line 58 (“It has that many nodes”) afterMorgan inserts a statement. In line 75, Penny brings upthe idea of graphing multiple things on the same axes andinterrupts herself to ask, “Because, or wait, like what isthe height of this?” She continues by beginning to an-swer her own question, “Isn’t that just like the numberof ” (line 78). This happens again in lines 85-100, wherePenny’s five contributions are all a continuous thoughtinterspersed with Morgan’s explanations. Penny’s think-ing through ideas as she says them is characterized byslower speech. Overall, this slower pace of speech andasking questions where her pitch goes up at the end con-vey a tone of tentativeness and inclusion; she presentsher ideas with uncertainty and invites others to weighin. We associate these actions and this tone with a viewof group work as a collective consensus building process,i.e., the Collective Consensus Building stance.Morgan’s actions on the other hand are aligned with astance toward group work that it should involve individ-uals working to understand the ideas in order to explainto other group members. This is evidenced by their im-mediate responses to, or taking up of, Penny’s questionswith didactic explanations. In lines 33-34, both Camand Morgan interrupt Penny before she finishes askingher question. Morgan explains, tentatively still at thispoint in the episode, how n is related to the number ofpeaks or nodes in the wave function. In line 77, Morganimmediately takes up Penny’s question about the graph,and through line 103 explains to her why it does notmake sense to draw the wave function and potential onthe same axes. In this exchange, Morgan’s explanationscome across as certain and authoritative, in particular inlines 77 (“Well...the height represents”) and 87 (“Right.So that’s why...”). Additionally, in line 103 they validatePenny’s original idea that superimposing the two graphsdoes not make sense. This validation recognizes Penny’scontribution, while also placing Morgan in a position ofauthority. Morgan speaks at a quick pace, and their pos-ture is directed toward Penny especially at the end of thisepisode when they point at Penny’s paper while explain-ing. Morgan’s fast speech, posture, immediate responsesto questions, and didactic explanations convey a tone ofauthority and assuredness (primarily in the second halfof Episode 1). We see these actions and this tone as anenactment of a stance that group work means one per-son with the desired knowledge will explain to others, i.e.,the Explainer-Explainee stance. Cam engages in some ofthe same behaviors as Morgan (e.g., interrupting or im-mediately answering Penny), but it is less clear in this1particular episode that his actions are aligned with theExplainer-Explainee stance. For clarity, we focus primar-ily on Penny and Morgan in identifying the two differentstances in Episode 1.In Episode 1, we see the interactions between epis-temology of group work and social dynamics begin toresult in the positioning of Penny as less knowledgeable.Penny’s slower speech means that Cam and Morgan havetime to interrupt her, and her questions and tone of in-clusion create space for Cam and Morgan to take upexplainer roles. In particular, we see the interactionsof these factors in the exchange between lines 85-100.Penny asks and answers her question all at once (“what isV(x)? Isn’t that potential?”), and continues her thoughtthrough line 100. However, her slower speech and tenta-tive framing of questions, in addition to Morgan’s fasterspeech and tone of authority, result in Penny being inter-rupted, explained to, and positioned as less knowledge-able.In summary, Episode 1 sets the stage for Penny, Sarah,Morgan, and Cam to engage in group work around QMproblems. The group is cohesive in that they seem tohave a shared understanding that making sense of theseproblems will require both conceptual and mathemati-cal reasoning, and that as the learners they will need toconstruct meaning using different representations (e.g.,equations and graphs). We infer that all four studentshave the expectation that they will work together, yet asthe episode unfolds we see individuals engaging in groupwork in different ways. Penny begins to take on the roleof the question asker, while Cam and Morgan start as-suming roles as explainers. Sarah is engaged and listen-ing, and every once in a while affirms others’ statements.We infer two different epistemic stances toward groupwork: Penny reflects Collective Consensus Building, andMorgan is aligned with Explainer-Explainee. In this firstepisode, we see these epistemic stances interact with thesocial dynamics of the group in a way that begins to po-sition Penny as less knowledgeable despite the fact thather contributions are the ones driving the sense makingthat the group engages in. These roles and positioningcontinue to evolve and begin to solidify as the group con-tinues to engage in collective problem solving. B. Episode 2
Following Episode 1, the students continue to discussQuestion 1A, but when they get stuck wondering if thespeed of the particle in the well is constant and if thisviolates the uncertainty principle, they decide to move onto part B which asks them to determine the probabilityof finding the particle in the first quarter of the well if itis in the ground state ( n = 1). The students immediatelybegin writing down an integral. They recall the groundstate wave function, and integrate the square of the wavefunction from 0 to a . They do the same thing for partC which asks for the probability of finding the particle in the second quarter of the well (this time, integratingfrom a to a ). Less than seventeen minutes in to theproblem solving session, the group has finished the twointegrals resulting in symbolic expressions for the answersto Question 1 parts B and C. Episode 2 begins whenthey are looking at their resulting answers and trying tofigure out how to check if they are right. Penny beginsthe conversation by making a bid to check their answersagainst their intuition: Penny: Yeah, I don’t really know, I dunno how to have a good intuition about—
Cam: —Well one thing that does make sense—
Penny: —Well wait the probability should be less than one—
Morgan: —Uhh, those, those sum to one...that plus that plus that again plus that again [pointing to the paper in the middle of the table].
Cam: Well the originally... yeah—
Morgan: —’Cause if it’s symmetric around a over two
Cam: Yeah
Morgan: Then these two should add to get one half [pointing to paper]—
Morgan: —And they do.
Penny: Aah. Wait... a over—
Cam: Aaaah. Yeah, they do!
Penny: Wait, isn’t—
Cam: —That makes sense.
Although Penny’s statement about intuition in line 105is not phrased as a question, functionally it serves as aquestion to the group, and is taken up as such. Pennyherself answers it in line 107, when she says “Well waitthe probability should be less than one.” For the firstfew lines of this episode, Morgan was hunched over theirpaper doing math—they wrote down an expression thatwas the sum of their answers to parts B and C (twice),and found that they summed to one. They finish thismath right as Penny suggests the probability should beless than one (line 107) and look up and immediatelybegin explaining (line 109), pointing to the graphs thestudents had previously drawn on a big piece of paper inthe center of the table. Here, we see Morgan again takingup the role of the explainer, speaking quickly and withcertainty. They explain the symmetry of the wave func-tion, with Cam chiming in affirmatively. Penny attemptsto join in and make sense of what they are saying (outloud, in the moment), but gets cut off by Cam in lines120 and 122 as he “gets it” and expresses excitement overunderstanding Morgan’s explanation. Penny finally getsin a question and asks Morgan to explain again:
Penny: Can you explain that again?
Morgan: So like, if we have, essentially this is our function right here.
Penny: Mhmm.
Morgan: And this divides it, a over two—
Penny: —So we went—
Morgan:—is the halfway point—
Cam: —Yeeahhh— Morgan: —so we basically, if you add these two together—
Cam: —You should be at the halfway point—
Morgan: —Then we should have this area—
Cam: —Which is one half [gestures at Penny with a quick bouncing finger pointing motion]—
Morgan: —Which should be one half—
Cam: —Which happens—
Penny: —Ohh—
Cam: —’cause these cancel
Penny: Ohhhhh! [smiles and silently claps]—
Morgan: —the 4 pi’s over two cancel
Penny: Oh that’s so!—
Cam: —And another way—
Penny: —And this is n = 1 so like, that is sym- metric—
Cam: —And it makes more se—
Morgan: —Yeah—
Penny: —So we know that it’s symme—
Morgan: And so, yeah
Penny asks Morgan, “Can you explain that again?”(line 123), reinforcing her position as the question askerand Morgan’s position as the explainer. Morgan imme-diately takes up the explanation and the following con-versation is characterized by Cam and Morgan talkingover one another while Penny tries to join in, but getscut off (lines 128, 139, 143, 149). In this section (123-142), Morgan and Cam are explaining to Penny (in thiscase, she explicitly asked them to). Yet Penny still triesto join in and make sense of the argument along withthem (e.g., “So we went...” in line 128). From the verybeginning of the episode, Cam has been trying to con-tribute an idea about how they can know their answersmake sense (“Well one thing that does make sense...” line106), but he keeps getting talked over (lines 144, 147).He finally contributes his thought as they finish up theconversation:
Cam: You should be able to say too that it makes...
B) makes sense because, B) being the first part of it, should be less—
Morgan: —Should be less than the second part—
Cam: —than the second part
Penny: Mhmm...
Cam: So if we’re taking the difference—
Penny: —Ohhh that makes sense!—
Morgan: —And that makes sense because...ya know, otherwise it’d be weird for it to sum to one.
Cam: Okay...
Penny: Good job team—
Cam: —alright. Well, at least it makes sense, or seems to make sense...Except I still don’t under- stand what that first one is asking for. [laughs]
Cam puts forth the idea that their answer makes sensebecause the integral for part B (first quarter of the well)should be less than that of part C (second quarter of thewell) given the shape of the wave function, but Morganinterrupts to finish his sentence for him (line 154). WhenMorgan completes the explanation of the symmetry ar- gument, Penny signals that she gets it by saying “Ohhhthat makes sense!” (line 158), and concludes the episodeby saying “good job team” (line 162).The majority of this episode consists of Morgan andCam explaining to Penny. Penny has assumed the roleof question prompter (line 105) or question asker (line123), while Morgan and Cam have taken up the rolesof “knowers” or explainers. These two different roles in-form one another; for example, in line 123 Penny asks“Can you explain that again?” which positions Morganand then Cam (who take up the question) as explainers.We see Penny being positioned as less knowledgeable inthis episode. Right off the bat, she prompts the ques-tion about connecting to intuition (line 105), and as sheputs forth an answer, she gets interrupted by Cam (line106) and then Morgan (line 109). Then when Morganbegins to explain the symmetry argument, Cam under-stands it first and his affirmative interjections (“Aaaah.Yeah, they do!” line 120 and “That makes sense” line122) prevent Penny from being able to join the collectivesense making process. She continues to be interruptedthroughout the episode when she attempts to contributeto the sense making (lines 128, 143, 149). Building onthe tendency we noticed in Episode 1 for Cam and Mor-gan to explain to Penny, Episode 2 is dominated by thesedidactic explanations (lines 109-118 and 125-142). Addi-tionally, in line 136, as Cam joins Morgan in explaining toPenny that their answers from parts B and C should sumto one half, he gestures to Penny with a quick, bouncingfinger-pointing motion. One might interpret this gestureas a manifestation of Cam’s excitement for figuring outthat their answer makes sense, or as a reflection of his po-sition as knower and transmitter of knowledge to Penny.We think both of these interpretations (and likely others)can coincide. Regardless of the intent or emotion behindthe finger-pointing gesture, it functions in the group asa symbol of the social position of Cam as a knower andexplainer and Penny as a questioner or receiver of knowl-edge.We identify the students’ actions in this episode to beagain aligned with two different epistemic stances towardgroup work: Penny as aligned with a Collective Consen-sus Building stance and Morgan and Cam aligned with anExplainer-Explainee stance. Perhaps most indicative ofthese stances are the different ways that Penny and Mor-gan react to not being sure about something. As Episode2 begins, Morgan is hunched over their paper working outsome math, and once they add up their symbolic expres-sions and find that they sum to one, they look up andbegin explaining to the other group members. This is oneexample of how when Morgan is not sure about some-thing, they retreat into individual problem solving modeand when they figure it out they re-engage with groupto explain their solution or idea to the other members ofthe group. We see this happen multiple times through-out the hour-long session; this tendency is aligned withan individualistic stance toward group work with the goalof understanding for yourself so that you can explain to3others. When Penny is confused or unsure about some-thing, she vocalizes her confusion, contributing ideas ten-tatively and thinking through them out loud in the mo-ment. One example of this occurs at the beginning ofEpisode 2 when Penny makes a bid for considering intu-ition (line 105) and then continues to put forth an answerto her own question (line 107). We see this tendency asbeing aligned with a stance that considers group work tobe a process of collective sense making where individualsput forth ideas they are unsure about and others grapplewith and build on them so that the group collectivelymakes sense of the idea in the moment.Penny’s contributions are tentative, yet she contin-ually tries to join in on collective sense making (lines119, 128, 146, 149), and praises the group’s accomplish-ment (“Good job team”, line 162). Through these ac-tions, Penny conveys a tone of tentativeness, inclusion,and excitement to be a part of a team. Cam and Mor-gan on the other hand, through fast speech and immedi-ately jumping in and talking over people (lines 109-118,127-142, 147-157), didactic or authoritative explanations(lines 109, 125-142), and pointing at Penny’s paper orthe common paper in the middle of the table in order toexplain (lines 109, 140), convey a tone of authority andassuredness, positioning them as knowers or explainers.We identified these two different epistemic stances to-ward group work in the first episode and see them againin the second episode and throughout the hour-long ses-sion. We note, however, that each individual studentdoes not always act in alignment with these stances orroles that we have identified. In line 123, Penny explic-itly asks for an explanation from Morgan, which could beevidence of an Explainer-Explainee stance. However, afew lines later, Penny tries to join in on the explanation,which we take as a bid for collective consensus building.This moment-to-moment variation in inferred epistemicstances toward group work is in line with the idea thatepistemologies can be context dependent or vary momentto moment . Likewise, there are instances where wesee Cam and Morgan engaged in practices that suggestan orientation to collective sense making (e.g., tentative-ness in the first half of Episode 1). We do not see these ascontradictions to the overall interpretation, but instancesof context dependence and fluidity of epistemic stances.Taking a global view of the hour-long session as a whole,we associate Penny’s engagement with a stance of Collec-tive Consensus Building, and Cam and Morgan’s actionswith an Explainer-Explainee stance.We have largely left Sarah out of our analysis, becauseshe does not often contribute verbally to the group, whichmakes it more difficult for us to make inferences abouther involvement in the group. There are two possible in-terpretations we might take from Sarah’s silence. One isthat her silence is indicative of an epistemic stance simi-lar to that enacted by Cam and Morgan—that is, groupwork is a process in which one individual with knowl-edge explains to other individuals. If Sarah took thisstance in this particular setting, and felt that she did not have knowledge relevant to their problem solving, thenshe might be inclined to not make many verbal contri-butions, and would assume more of a role of a listeneror consumer of the explanations provided by other groupmembers. An alternative interpretation is that Sarahtakes a stance more aligned with Penny—one of collec-tive consensus building—but that she does not see her-self as part of the collective group and thus she does notcontribute her ideas or vocalize her confusions. Both ofthese interpretations (and likely many others) are plausi-ble. For now, we continue to focus our analysis primarilyon Penny, Morgan, and Cam for whom we have moreverbal cues to analyze.In Episode 2, the interactions between the epistemicstances toward group work, social dynamics, and sensemaking result in Penny being positioned as a questionasker with Cam and Morgan being positioned as knowersand explainers. Penny’s slower speech and throwing outtentative ideas to think through on the fly, along withMorgan and Cam’s faster and quick-to-explain speech,result in Penny being interrupted and explained to (e.g.,lines 107, 119). In this particular episode, these dynam-ics lead to Penny not contributing as much (in terms ofturns of talk) as in other episodes. When Penny asksfor an explanation (line 123), Morgan and Cam take itup with fast-paced and authoritative explanations thatmake it hard for Penny to contribute when she attemptsto join in on the collective sense making (lines 119, 128,146, 149). Despite this social positioning, it is Penny’scontributions that again guide the group in the sensemaking they engage in—she prompts them to considerintuition in line 105 and symmetry in line 146. We notethat before this episode began, Morgan had already be-gun to check that their answers summed to one half, in-dicating that they were already considering symmetryand possibly intuition (although we suspect “intuition”might mean something different to Morgan than it doesto Penny). However, if Penny had not directly askedabout these aspects, we do not know if the group wouldhave engaged in conversation around them in the waythat they did in this episode.
C. Episode 3
Episode 3 takes place 46 minutes in to the hour-longsession, when the students are working on Question 2A(see Fig. 4 above), sketching the ground state and firstexcited state wave functions for a double square well.They spent a small amount of time on part i), consideringthe situation in which b = 0. In this episode, they areworking on part ii) where b ∼ a . The group has agreedthat the wave function must be an exponential decaytowards infinity on either end and a sine function withineach well, but they are unsure what the solution insidethe barrier (the middle region) should be. They havetalked about an exponential decay coming from eitherwell to meet in the middle, and this episode begins as4they seek mathematical (formulaic) justification. Theyare trying to remember where the sine and exponentialsolutions come from in the first place, and Morgan beginsto write down the Schrdinger equation on the large pieceof paper in the center of the table: Morgan: So if we have a Schrdinger equation which looks essentially like negative—
Penny: —hbar squared—
Morgan: —a positive constant...
Cam: Yeah, okay—
Morgan: —times the second derivative of this [wave function]...uh...equals...
Cam: The E minus U of x—
Morgan: —E minus U of x
Cam: Times...Yuuuup—
Morgan: —times that [wave function] then when you rearrange this you get double prime of x equals...so if E minus U of x is negative, is less than zero, right this [ E − U ( x ) term] is negative this [ − Kψ (cid:48)(cid:48) ] is negative, so we get...essentially the solutions to that differential equation. [circling ψ (cid:48)(cid:48) = + kψ on the paper] From the beginning of the episode, Morgan assumesthe role of “math doer” as they have control of the largepiece of paper and thus the conversation. The other threegroup members are leaning in and all watching as Morganwrites down equations and explains out loud what theyare doing. While Morgan explains, Cam chimes in withaffirmations (lines 170, 175) that suggest he understandswhat Morgan is doing and also starts to help out with theexplanation (line 173). Penny continues the conversationby asking a question:
Penny: How does, uhm, the I guess like location along x determine whether E is like E minus U is less than zero or greater than zero.
Morgan: E is constant, but U of x is a function of x. Cam: Mhmm
Penny: Ohhh, yeah yeah yeah—
Cam: —Yes. And so yeah, you could look at the potential—
Morgan: —So as x changes this is gonna change.
If E-U(x)—
Penny: Is gonna change from being zero to being V of—
Cam:—V naught—
Penny & Cam: —Yeah—
Morgan: If it’s greater than zero though we get this one with a negative sign there, that’s a little hard to read. Uhm, and so the solutions of this are roughly...This is e to the x or e to the negative x.
Penny: Yeah, that’s usually—
Morgan: —And this is
Penny: What does that say? Psi...?
Morgan: Sorry. This? Yeah, I wrote that badly.
The double derivative of—
Penny: —Equals negative psi? Okay.
Morgan: Yeah. This leads to e to the i x which is the same as cosine x plus sine x—
Penny: —Isn’t it also just sine?—
Morgan: —With some, ya know, there’s constants here.
Cam: Right.
Penny: Just sine x?
Morgan: Hmm?
Penny: Doesn’t sine x satisfy this?
Cam: Yeah. But he’s writing out the general form and then A or B would be zero—
Penny: —Ohhhh. Yeah.—
Sarah: —Yeah—
Cam: —depending on—
Morgan: —Yeah—
Cam:—basically you’d model it to fit the well. And you’d decide cosine or sine. Usually, in most cases, we’d use sine. But if it did need to start at one instead of zero then you would use cosine.
In line 183, Penny prompts the group to connect theequation Morgan has written down (particularly the E-U(x)) term to the graph, a move that we consider to bepart of mathematical sense making . Morgan takesup this prompt and explains to Penny that the total en-ergy is constant but the potential energy is a function ofx, and Cam chimes in to refer to the graph (line 190).Penny then starts to join in the collective sense mak-ing (line 194), and Cam jumps in to finish her thoughtand help her out, saying “V naught” and pointing at thegraph on her paper (line 196). Morgan returns to thedifferential equations and continues to work out the so-lutions, with Penny asking for clarification about whatMorgan has written (lines 198-207). When Morgan saysthat the solution in the region where E-U(x) is positiveis cos(x)+sin(x) (with some constants), Penny vocalizesa question—“Isn’t it also just sine?” (line 210). Oncethe group hears this question, Cam jumps in to explainto Penny what Morgan is doing (line 217). He continuesthe explanation after both Penny and Sarah have indi-cated that they understand (“Ohhh yeah”, line 219 and“Yeah”, line 220). Midway through Cam’s explanationin lines 223-226, Penny looks down as if she has stoppedlistening to the explanation. Morgan returns to the mathon the paper and continues:
Morgan: Right...Okay...So it does have to be the decaying one in the middle. It can’t be a sine wave.
Well that’s nice.
Penny: Wait, why?
Morgan: Because here we have the, we’re in this condition [circling ψ (cid:48)(cid:48) = + kψ on the paper], because E minus the potential, the potential is high up here [pointing to the graph on Penny’s paper] and we presumably don’t have the energy.
Penny: Yeaahhh. I mean...I don’t know what E is.
What determines...So I guess the thing that deter- mines E is n.
Morgan: Right.
Penny: Through like [laughing] a relationship that we talked about already that we don’t remember— Cam: —Right, yeah. What you could do is you could actually do your double derivative here with your you know your n value and your k stuff and you could actually solve for the energies and stuff if you needed.
Morgan: Right...But like. That, this observation.
So like when U of x is high [pointing to the graph on Penny’s paper], above what we think the energy of our electron is...
Penny: Then...it—
Morgan:—Then—
Penny: —then it must be—
Morgan:—we know that...uh psi of x has to take on a form that’s a negative exponential. Or a posi- tive exponential, but the positive exponential can’t happen because of regularity conditions.
Penny: And then that’s, that is intuitively right.
Morgan: Yeah. There’s a lot of constants here and stuff that I left out ’cause I don’t actually know how to do ODE’s—
Penny: —That if the energy is, if the potential en- ergy is higher than the energy of the thing than the thing is not like as likely to be there.
Morgan: Right, well, yeah it drops off exponentially as you get further away from the uh low regions.
In lines 228-229, Morgan says, “It can’t be a sine wave.Well that’s nice” with certainty as if to say, “Great, wehave the answer!” Penny begins to ask a question aboutthe total energy but then interrupts herself and answersher own question, in a tentative way (“I guess”, line 237).Earlier in the focus group session, the group recalled thatthe total energy (E) was determined by the value of n,but they could not remember the formula. Here, Camjumps in to explain how they could get that formula (bysolving the differential equation), although they do notactually pursue this. To conclude the episode, Pennyprompts the group to check their answer against their in-tuition (line 258). Morgan takes up this “intuition” ideaby considering mathematical formalisms, talking aboutthe constants they left out because they “don’t actuallyknow how to do ODE’s” (lines 259-261). Penny’s re-sponse indicates that she meant something different by“intuition”—“if the potential energy is higher than theenergy of the thing than the thing is not as likely tobe there” (lines 262-264). Morgan acknowledges Penny’sidea, but modifies it (“well, yeah it drops off exponen-tially” line 265), ending the episode in the didactic man-ner in which they started.In this episode, Penny again assumes the role of thequestion asker. As is characteristic of her contributionsthroughout the hour, she is particularly interested in con-necting to intuition, and it seems as though she does notwant to let her questions go until this intuitive aspect issatisfied. Morgan, in this episode, takes on the role of the“math doer” and explainer, controlling the shared pieceof large paper and driving the mathematical argumentthat the group constructs in order to answer their ques-tion of what the wave function should look like in the barrier in between the two wells. Cam plays a slightlydifferent role in this episode in that his contributions pri-marily validate, repeat, or add on to explanations. Whilehe does not “own” or create the explanations, the act ofvalidating what other people (usually Morgan) have saidplaces him in a position of authority in the group. Sarahis quiet as usual, but is paying attention and leaning into watch Morgan’s orchestration of the algebra that leadsthem through the sense making process.We see Morgan has having most of the control over theconversation in this episode, yet Penny still opens up thegroup for sense making and guides the conversation withher questions. She prompts the group to connect theiralgebraic equation to the graph (line 183) and to checktheir results against their intuition (line 258). As thequestion asker and prompter of these moments of sensemaking, we simultaneously see Penny being positionedas less knowledgeable within the group. Much like in theprior two episodes, Penny is interrupted (lines 202, 251,253) and explained to (lines 187-259, 217-226, 231-235)throughout the episode.We again identify two different epistemic stances to-ward group work. Penny’s tentative questions, ideas, andthinking out loud (lines 183, 237) and attempts to join inon the sense making process as Cam and Morgan explainto her (lines 194, 202, 251-253) are aligned with a Col-lective Consensus Building stance. Morgan’s actions andcontributions are consistent with an Explainer-Explaineestance, evidenced by their didactic explanations takingcontrol of the large piece of paper and sometimes point-ing at Penny’s paper. Cam’s actions are also alignedwith this more individualistic stance toward group work,but they vary from Morgan’s actions because Cam as-sumes more of a role of validator and explainer, as hecontinually validates, affirms, or repeats ideas (lines 170,175, 190, 196, 213) and explains what Morgan is doingor adds to their explanations (lines 217-226). Notably, inlines 242-246 when explaining how the group could figureout how exactly E depends on n, he uses “you” instead of“we”. We interpret the “you” to not be directed at anyone individual group member, but rather a replacementfor “one”. Had Cam used “we” instead, that would havereflected a different stance toward group work, perhapssuggesting he saw himself as part of a collective team,or that the knowledge could (and would) be generatedin the group through a collective process involving ev-eryone. The fact that he used “you” signals to us thathe is not enacting an epistemic view of group work as acollective consensus building process.Episode 3 occurs almost at the end of the hour-longproblem solving session. By this point, the tendenciesand role-taking that we noted in Episode 1 have solidi-fied as the students have learned or become comfortablein these particular roles. Throughout the hour, Pennyhas been interrupted, explained to, and positioned as lessknowledgeable. Yet more than 45 minutes into the ses-sion, she continues to make space in the group for sensemaking, and is still attempting to contribute to a col-6lective sense making process rather than just listeningto Morgan and Cam’s explanations (e.g., lines 194, 251).The interactions between the different epistemic stancestoward group work, the social dynamics, and the sensemaking processes are linked to the social positioning thatwe see develop in the group—Penny as less knowledge-able and a question asker, Morgan and Cam as knowersor explainers with positions of authority, and Sarah asa quiet listener who is not directly acknowledged by theother group members.
VI. DISCUSSION
In our case study analysis, we characterize the groupas being cohesive along some dimensions and not cohe-sive along others. The three most vocal group membersappear to be on the same page about what counts asmaking sense of the QM problems at hand, and theyengage in conceptually productive sense making . Weview this epistemological alignment in contrast to othergroups of students in our data set (that are not includedin the present analysis) in which we observe an epistemo-logical conflict because one student wants to talk aboutthe problems conceptually, while other students want toplug and chug through the mathematics and get answersto the problems. We view the sense making that thegroup engages in as conceptually productive because theydemonstrate making progress toward content mastery ,engage in metacognition, find different ways to checktheir answers, and seek coherence among multiple rep-resentations. While the group members seem to be onthe same page when it comes to epistemology of physics(what counts as learning physics or solving physics prob-lems), we observe different orientations toward what itmeans to collaboratively generate knowledge (epistemol-ogy of group work). Distinguishing between epistemol-ogy of physics and epistemic stances toward group workallows us to explore the connections between epistemol-ogy, group work, and social positioning. We argue thatthe group members enact different stances toward groupwork, and that this misalignment is one factor which in-forms, and is informed by, the social positioning of mem-bers within the group.We were motivated to conduct this analysis because wenoticed a puzzling phenomenon in this particular group—the student who was steering most of the group’s sensemaking (Penny) was simultaneously positioned as lessknowledgeable within the group. Second to the promptswe gave them, the students’ work is primarily guided byPenny’s questions and bids for sense making. Through-out the hour, Penny largely assumes the role of thequestion asker or question prompter, doing most of themetacognitive work that moves the group’s sense makingalong. Her interactions in the group are characterizedby slower, tentative speech, and thinking through ideasout loud. Morgan and Cam assume roles as knowers andexplainers, in many instances conveying a tone of author- ity and assuredness through their pace of speech, diction,posture, and gestures. There are two dimensions of epis-temic agency at play here: Penny has agency in the sensethat she is primarily controlling the topics of conversa-tion, but Morgan, and at times Cam, have agency in thesense that they are the ones doing the talking and ex-plaining.We have identified and inferred epistemic stances to-ward group work for individual members of the group,and see the dominance of one stance over the other mani-fest in the social positioning of students within the group.Time and again throughout the hour-long problem solv-ing session, Penny tries to break in to the conversa-tion with collective co-construction of meaning, but thesemoves are not taken up by the group (e.g., lines 128, 146,210). Instead, Cam and Morgans Explainer-Explaineestance emerges as the dominant approach toward collab-oration in this setting (e.g., lines 109, 217, 223). Penny ispositioned as less knowledgeable within this group, as ev-idenced by interruptions, didactic explanations, and thegroup taking up most of her contributions as questionsin need of explanation. Associated with this position-ing, the dominant epistemic stance toward group workincorporates an Explainer-Explainee paradigm, a stancewhich is at odds with Pennys stance of Collective Con-sensus Building.In this analysis, we have attended to both social dy-namics among the group of students and social position-ing of individual members relative to the group. Whenwe refer to social dynamics, we are referring to thefine-grained interactional dynamics—interruptions, tone,body language, etc. Social positioning, on the otherhand, refers to a broader story of the roles or positionsthat individual members play within the social activ-ity and how those positions interact with or relate toone another. The existence of, and misalignment be-tween, two different epistemic stances toward group workin this particular collaborative activity are intertwinedwith the fine-grained social dynamics. For example, Pen-nys speech is slow, consistent with thinking out loudand contributing tentative ideas to a collective meaning-making process (Collective Consensus Building), whileMorgans speech is fast and they have a tendency to jumpin and explain their understanding to Penny (Explainer-Explainee). The confluence of these dynamics and en-acted stances toward group work allow Penny to be in-terrupted and explained to often, which then perpetuatesthe interactional dynamics associated with the misalign-ment of stances. In this way, the epistemic stances andsocial dynamics mutually inform and feed off of one an-other to reinforce a particular social positioning. A resultof this feedback loop is the positioning of Penny as lessknowledgeable and Morgan and Cam as authority figures.There are some instances of unidirectionality in theanalysis, where we see the misalignment of epistemicstances driving the social positioning. For example, inEpisode 1, we begin to see Penny positioned as lessknowledgeable because she offers tentative ideas and7questions (aligned with Collective Consensus Building),which open the door for her to be explained to. However,in other instances, the directionality may go the otherway around, with the social positioning helping to rein-force or crystallize the epistemic stances toward groupwork and associated social dynamics. That is, as thehour-long session progresses, Pennys Collective Consen-sus Building stance and Cam and Morgans Explainer-Explainee stance may be reinforced because Penny hasbeen positioned as less knowledgeable (i.e., the position-ing of Penny as a “question asker” and Morgan andCam as “explainers” may provide more opportunities forPenny to be tentative and Morgan and Cam to be author-itative). We view the social dynamics and misalignmentof epistemic stances to be reflexively intertwined with thesocial positioning; they mutually inform one another asthe interactions among students play out, resulting in acrystallizing of the dominant Explainer-Explainee stancewhile Penny is positioned as less knowledgeable as com-pared to Cam and Morgan.While this paper presents a case study analysis of onegroup, we have examples from other groups in our dataset where we have seen this positioning happening (al-though it unfolds in different ways in different groups).We focus on one case study here to propose the con-struct of epistemic stances toward group work, and doc-ument how it can contribute to, and interact with, socialpositioning of students in collaborative problem solvingenvironments. From the perspective of epistemologicalframing, we would conclude that this group has a sharedframing of the type of activity they are engaged in—theyare all leaning in to participate, they are engaged in sensemaking (as opposed to answer making) , and theyhave some shared understanding that this sense makingprocess will involve both conceptual understanding anddoing math. However, focusing on only epistemologicalframing, we would miss out on the fine-grained social in-teractional dynamics that contribute to the positioning ofindividual students. The construct of epistemic stancestoward group work helps us to identify and unpack thesecomplicated interactions, which have implications for cre-ating and fostering equitable group work environments.The sense making that this particular group engagesin is beneficial for Penny, Morgan, and Cam in termsof making progress toward content mastery. However,there are other dimensions along which we might con-sider the group’s interactions to be productive or unpro-ductive. Considering who has access to certain roles orpositions, we characterize this group as inequitable, andthus unproductive along the equity dimension . WhilePenny engages in scientific practices that we see as pro-ductive (metacognition, checking ideas against intuition,seeking coherence, etc.), she probably does not benefitfrom always being the questioner. That is, Penny, andthe group as a whole, would likely benefit from her some-times assuming the role of an explainer. Likewise, we seeMorgan and Cam engaged in sophisticated sense makingprocesses and clearly demonstrating some level of con- tent mastery, but we posit that these students could alsobenefit from engaging in practices like questioning, andchecking ideas against intuition. Additionally, through-out the problem solving session, the group continues tocome back to the Explainer-Explainee stance where Camand Morgan are often explaining to Penny. Yet we imag-ine that it would be beneficial for the group as a whole(as well as individual members) to be able to play dif-ferent kinds of games, sometimes incorporating an “ex-plainer” and sometimes not. Some studies have shownthat when one individual dominates the group work, in-dividual members of the group demonstrate lower con-tent mastery . Leupen, Kephart, and Hodges sug-gest that group work that is interactive and construc-tive is beneficial for students’ conceptual understandingbecause “Constructive actions such as explaining or de-bating ideas and posing or answering questions involvestudents in generating new understandings and mak-ing meaning. When students are interactive as well asconstructive, taking turns and building on one anothersthoughts, they draw on the power of socially mediatedlearning to prod each other along paths in their thinkingthat they would otherwise not take” (p. 2). Theobald et al , in a study of how group dynamics impact studentlearning of biology, also found that inequitable participa-tion in group work settings helped to perpetuate socialstatus of students in the group . Likewise, in our casestudy we see the social positioning of students within thegroup informing and being informed by the misalignmentof students epistemic stances toward group work. Yet ouranalysis is more complicated than just a dominant indi-vidual or “personality hindering productive group work;while the dominance of Cam and Morgans Explainer-Explainee stance may be a barrier to equitable participa-tion in the group , Penny is not just a “timid and “silentrecord keeper . Rather, Pennys ideas drive the groupssense making while Morgan does most of the math andCam and Morgan do most of the explaining. In this way,each of the three students (Penny, Morgan, and Cam)have some form of epistemic agency.The interactions we observed among this group of stu-dents are in line with the documented gendered speechpatterns and social discourse norms in science and engi-neering that favor masculine ways of engaging in conver-sation . Motivated to understand the positioning ofmembers within this group and the potential discountingof a female student who steers the groups sense making,we zoom in on epistemological aspects of these social in-teractions. Although we do not directly address the gen-dered interactions in the present analysis, focusing on theintertwining of epistemology and social dynamics mayprovide one plausible mechanism for the gendered inter-actions and resulting social positioning. That is, investi-gating the interactions between epistemology and socialdynamics gives us some insight into how this social po-sitioning can happen in a collaborative problem solvingsetting. We attend to this epistemological aspect as afirst step, and then in future work will dive more deeply8into understanding the roles that gender, power dynam-ics, and ideology play in creating and driving interactionsin this group problem solving setting. VII. CONCLUSIONS AND IMPLICATIONS
We frequently ask students to work together in ourphysics classes, and while there are some instances wherewe attend to the group work by assigning roles or con-structing groups based on gender or performance lev-els , it is not a leading discourse in the physics ed-ucation community to consider how to support studentsin engaging in group work productively and equitably.Through this exploratory analysis, we echo the calls ofother researchers to not only implementgroup work in our physics classes, but to attend tothe dynamics among students, investigate factors thatcontribute to collaborative environments, and constructgroup work settings that promote equity. Motivatedby the observation that one student (Penny) continuallysteered the group’s sense making and was simultaneouslypositioned as less knowledgeable, we investigated the in-teractions between social dynamics and epistemology.Through our analysis we see that it is not as simpleas Morgan having more epistemic agency at the expenseof Penny having less. Instead, we look at multiple di-mensions of epistemic agency: who is controlling thetopic, and who is doing most of the talking. We in-ferred students’ epistemic stances toward group work—their stances about what it means to generate and applyknowledge in a group—and explored the ways in whichthe misalignment of these stances between individual stu-dents and the dominance of one stance over the other inthe group as a whole contributed to, and was reinforcedby, the social positioning of Penny as less knowledgeable.The misalignment of the two different stances, alongwith the roles the students assume and the ways in whichthey engage in discourse, are intricately linked with thesocial positioning of Penny as less knowledgeable andCam and Morgan as occupying positions of authority.We recognize that there are many factors at play in thissocial problem solving setting, including gender, powerdynamics, and cultural norms and discourse patterns,and we identify the misalignment of epistemic stancestoward group work (and the dominance of one over theother) as one factor that contributes to, and is also in-formed by, the social positioning of students within thegroup.We might consider possible reasons that the Explainer-Explainee stance dominates the group in this particular setting: Is it because there are more students in the groupaligned with this particular stance (Cam and Morgan)than the other (Penny)? Or because the students alignedwith this stance present as masculine? Or maybe it isbecause of the stance itself, as a more aggressive form ofgenerating knowledge? Or perhaps because the more in-dividualistic stance is more aligned with broader culturalnorms in physics (or physics education)? Likely, most (orall) of these are at play. With the present analysis, wecannot answer these questions about why the Explainer-Explainee stance comes to dominate the group, but notethat this is undoubtedly a complex phenomenon, and at-tending to epistemic stances toward group work is justone piece of the puzzle. The Collective Consensus Build-ing and Explainer-Explainee stances embody different hi-erarchies; a forthcoming paper will include a complemen-tary analysis of this same group that takes an even finer-grained look at how the local interactional dynamics re-produce, and derive from, broader patterns of discourseand cultural practices, and how power dynamics play arole in the interactions and social positioning .Understanding how multiple factors interact to privi-lege or exclude contributions from students in a group isa first step in learning how to cultivate, and support stu-dents in cultivating, equitable group work. The specificanalysis we have presented is not meant to be general-izable to other groups of students or other contexts; ev-ery local situation will have different epistemological andsocial factors that contribute to how a group problemsolving session might play out. However, the constructof epistemic stances toward group work can be appliedin many situations within physics (or other discipline-based) education research. We have provided an exampleof how to attend to epistemic stances toward group workamong a group of students, and demonstrated its utilityas a tool for investigating interactions among students.Identifying students epistemic stances toward group workmay be a helpful tool for instructors and researchers inworking towards cultivating equitable group work.
ACKNOWLEDGMENTS
The authors would like to thank the anonymous stu-dents in this study and our University of Marylandcollaborators—Andy Elby, Ayush Gupta, Erin Sohr, andBrandon Johnson—without whom this analysis and pa-per would not exist. This work is supported by NSFgrant Nos 1548924, 1625824. Viewpoints expressed hereare those of the authors and do not reflect the views ofNSF. ∗ [email protected] Lillian C. McDermott and Peter S. Shaffer,
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Frame Analysis: An Essay on the Organiza-tion of Experience (Northeastern University Press, Boston,MA, 1986). David Hammer and Andrew Elby, “On the form of a per-sonal epistemology (in B. K. \ nHofer & P. R. Pintricheds.),” Personal epistemology: The psychology of beliefsabout knowledge and knowing , 169–190 (2002). David Hammer and Andrew Elby, “Tapping Epistemologi-cal Resources for Learning Physics,” Journal of the Learn-ing Sciences , 53–90 (2003). David E. Brown and David Hammer, “Conceptual Change in Physics,” International Handbook of Research on Con-ceptual Change , 127–154 (2008). Considering a global view of their overall behaviors, wecharacterize the students in the group as sharing episte-mological frames, while noting that individual and groupframes can and do vary moment to moment. Benjamin W. Dreyfus, Andrew Elby, Ayush Gupta, andErin Ronayne Sohr, “Mathematical sense-making in quan-tum mechanics: An initial peek,” Physical Review PhysicsEducation Research (2017), 10.1103/PhysRevPhysEdu-cRes.13.020141. Brandon James Johnson, Erin Ronayne Sohr, and AyushGupta, “How social-media and web-accessible learningresources influence students’ experiences in a quantumphysics course: A case study,” in
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Physics Education Research Conference 2019 (Ameri-can Association of Physics Teachers (AAPT), Provo, UT,2019). Sharan B Merriam, “The case study in educational re-search: A review of selected literature,” The Journal ofEducational Thought , 204–217 (1985). We regret that we did not ask the students which pronounsthey prefer, and thus use “they” for Morgan given the “?”response to the gender field. We have now made it a normto ask students for their pronouns when conducting focusgroup and interview studies. Judith Butler, “Performative Acts and Gender Constitu-tion: An Essay in Phenomenology and Feminist Theory,”Theatre Journal , 519 (1988). Joanna Wolfe and Elizabeth Powell, “Biases in Interper-sonal Communication: How Engineering Students PerceiveGender Typical Speech Acts in Teamwork,” Journal of En-gineering Education , 5–16 (2009). Katherine Hawkins and Christopher B. Power, “GenderDifferences in Questions Asked During Small Decision-Making Group Discussions,” Small Group Research ,235–256 (1999). Anna Sfard, “There is more to discourse than meets theears: Looking at thinking as communicating to learnmore about mathematical learning,” Educational Studiesin Mathematics , 13–57 (2001). In the analysis, we sought to remove our own views as muchas possible, but note that we personally view group work ina way that is mostly aligned with how we perceive Penny’sactions in the group (i.e., valuing externalization of confu-sion, and thinking through ideas in the moment with otherpeople). We do not pass value judgements on which stancetoward group work is “right” or “better”, but note thatour personal stances are generally aligned with CollectiveConsensus Building (although these stances are certainlycontext dependent) and that there are many other stanceswithin the physics and physics education communities. The tendency of women to frame ideas as questions is welldocumented in feminist discourse literature ? . This, amongother finer grained analyses of these interactions, will bethe subject of a forthcoming paper. MacKenzie Lenz, Kelby T. Hahn, Paul J. Emigh, and Eliz-abeth Gire, “Student perspective of and experience withsense-making: a case study,” in
Physics Education Re-search Conference Proceedings (American Association ofPhysics Teachers (AAPT), 2017) pp. 240–243. A common element of the group’s problem solving, as ini-tiated by Penny, includes valuing intuition as a tool forsense making, though we see possible variation within thegroup as to what counts as “intuition.” We do not explorethis variation in the present analysis, though it would bean interesting site for future investigation. Making progress toward content mastery includes gettingthe right answer, but also understanding the conceptsalong the way well enough to be metacognitive, ask follow-up questions, check their answers, etc. Ying Chen, Paul W. Irving, and Eleanor C. Sayre, “Epis-temic game for answer making in learning about hydrostat-ics,” Physical Review Special Topics - Physics EducationResearch , 010108 (2013). Frederick Erickson,