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: Running head: Positioning and Social Location in VMT
Boundaries and Roles: Positioning and Social Location in the Virtual Math Teams (VMT) Online Community
Johann W. Sarmiento, Wesley Shumar
Drexel University
Acknowledgments
This research is part of a collaborative effort of the members of the Virtual Math Teams (VMT) project supported by the NSDL, IERI and SLC programs of the U.S. National Science Foundation. The principal investigators are Gerry Stahl, Wesley Shumar, and Steve Weimar.
Correspondence should be addressed to: Johann W. Sarmiento, College of Information Science and Technology at Drexel University, Philadelphia PA 19130, USA. E-mail: jsarmi@drexel.eduAbstract
As research in Computer-Supported Collaborative Learning (CSCL) expands its understanding of joint knowledge building and the participation frameworks enacted by it, new perspectives on how social reality is constructed become necessary. Our research concentrates on the diachronic trajectories of online groups as part of the Virtual Math Teams (VMT) project of The Math Forum, an online community supporting mathematical inquiry. We investigate how small virtual teams engaged in sustained knowledge work over time overcame the discontinuity of their fragmented episodes of collaboration and the naturalistic changes in their teams composition, to constitute knowledge building as a continuous activity. Here, we concentrate on describing, through the lens of positioning theory and the notion of social location, the type of interactional activities that allow co-participants to situate themselves, others, and their collective knowledge resources in dynamic participation frameworks. Our analysis suggests that positioning work is central to the constructing and management of a joint problem space, and that the configurations of positions and resources that co-participants put forward through interaction often change locally and across a teams trajectory over time. These changes constitute and are sensitive to the participants evolving sense of agency and represent the evolving co-construction of reasoning routines and other forms of joint participation uniquely related to the local and longitudinal knowledge-building enterprise. In addition, we show that the activity system that VMT represents, affords participants a level of disciplinary engagement which is, in part, illustrated by active engagement in positioning work. Finally, we suggest that the dynamic perspective on roles and participation afforded by an interactional approach provides a fruitful framework for researchers, designers, and practitioners interested in understanding, supporting and implementing engaging computer-supported collaborative learning interactions.
Boundaries and Roles: Positioning and Social Location in the Virtual Math Teams (VMT) Online Community
Research in the field of Computer-supported Collaborative Learning (CSCL) attempts to understand diverse learning contexts ranging from single episodes of collective problem-solving activity to the longitudinal development of online knowledge building communities. CSCL arrangements which involve joint activity spread over time and across multiple collectivities present to co-participants the challenge of overcoming a wide range of gaps including, for example, those related to attending to the activities of multiple participants, coordinating multiple sessions of work, and monitoring various ideas and topics. The complexity of such interactions, in turn, challenges researchers to strengthen and expand their perspectives on how social reality is constructed. For instance, when the diachronic evolution of knowledge-building groups is at the center of the analysis the dynamic aspect of how interactions shape the way participants engage over time become a key research concern.
Building collaborative knowledge (Stahl, 2006), the complex collective process of creating, testing, and improving conceptual artifacts" ADDIN EN.CITE Bereiter20032607 p. 1326075Bereiter, C.Scardamalia, M.E. De CorteL. VerschaffelN. EntwistleJ. van MerrienboerLearning to work creatively with knowledgePowerful Learning Environments: Unraveling basic components and dimensions of powerful learning environments2003PergamonBereiter200230306Carl BereiterEducation and Mind in the Knowledge Age2002Hillsdale, NJLawrence Erlbaum Associates(Bereiter, 2002; Bereiter & Scardamalia, 2003 p. 13) relies precisely on the successful engagement of multiple actors over time and on the effective management of their diverse activities and resources. Among the conceptual artifacts that form the joint space of knowledge building, one can include ideas, solution strategies, reasoning tactics, categories, theories, diagrams, and other reasoning devices created and used to make sense of particular situations. Such artifacts emerge from interactional activity (e.g. talk-in-interaction) through which participants develop and advance their evolving understanding -of a math question, a sociological theory, a controversial decision, etc.
Several studies have shown that successful collaborative knowledge building is closely related to the interactional manner in which the participants engage together ADDIN EN.CITE Scardamalia199141641617Scardamalia, MarleneBereiter, CarlHigher levels of agency in knowledge building: A challenge for the design of new knowledge mediaJournal of the Learning SciencesJournal of the Learning Sciences37-6811991Barron200360160117Barron, B.When smart groups failJournal Of The Learning SciencesJournal of the Learning Sciences307-359123Peer interactionclassroomperformanceachievementstudentsmathematicssciencesuccessworkinginfant2003Dillenbourg19951001005Dillenbourg, PierreBaker, MichaelBlaye, A.O'Malley, ClaireReimann, PeterSpada, HansThe evolution of research on collaborative learningLearning in Humans and Machines: Towards an Interdisciplinary Learning Science189-2111995Oxford, UKElsevierHausmann20042417241710R. HausmannM. ChiM. RoyK. D. ForbusD. GentnerT. RegierLearning from collaborative problem solving: An analysis of three hypothesized mechanisms26nd annual conference of the Cognitive Science society 547-5522004Lawrence ErlbaumKoschmann2005243324335Koschmann, T.Zemel, A. Conlee-Stevens, M.Young, N.Robbs, J.Barnhart, A. F. H. R. BrommeH. SpadaHow DO people learn?Barriers and biases in computer-mediated knowledge communication2005AmsterdamKluwer Academic PressWegerif20062432243217Rupert WegerifA dialogic understanding of the relationship between CSCL and teaching thinking skillsInternational Journal of Computer-Supported Collaborative Learning (ijCSCL)International Journal of Computer-Supported Collaborative Learning (ijCSCL)143-157112006(Barron, 2003; Dillenbourg et al., 1995; Hausmann, Chi, & Roy, 2004; Koschmann et al., 2005; Scardamalia & Bereiter, 1991; Wegerif, 2006). A central element of how these interactions get shaped involves the activities and roles that participants enact while engaged in collaboration. In addition, the degree of difficulty for succeeding in such collaborative settings rises when joint activity is conducted primarily online, dispersed over time (e.g. multiple episodes of joint activity, long-term projects, etc.) and, as in many naturalistic settings, distributed across multiple collectivities (e.g. multiple teams, task forces, communities, etc.). As a result of these challenges, sustained collaborative knowledge building in small virtual groups and in online communities requires that co-participants deploy unique interactional methods highly consequential to the creation and maintenance of a joint space that is both local and diachronic. The practices or methods that participants use to achieve such joint space represent the central concern of our inquiry here.
In order to explore the longitudinal dynamics of online groups engaged in sustained knowledge building, we conducted a series of online sessions with virtual teams of secondary students participating in an online community dedicated to mathematics education. Our analysis of the dynamics of these collaborative interactions allowed us to explore the ways that participant roles were shaped through joint action and the ways that they evolved over time. In order to expand already established approaches to roles in CSCL (e.g. see other contributions to this special issue) we also set out to investigate the theoretical framework of Positioning Theory ADDIN EN.CITE Harr1999261426146Rom HarrLuk van LagenhovePositioning Theory: Moral Contexts of Intentional Action1999MaldenBlackwell PublishingDavies19902459245917Davies, B. Harre, R.Positioning: The discursive production of selvesJournal for the Theory of Social Behaviour Journal for the Theory of Social Behaviour43-63201990(Davies & Harre, 1990; Harr & Lagenhove, 1999) in social interaction. In the remaining sections we first outline the basic concepts of positioning theory and illustrate the ways in which it allowed us to focus on the dynamic aspects of collaborative knowledge building. We then present an analysis of longitudinal collaborative interactions from this perspective and evaluate its usefulness.
Positioning Theory and Social Location
Positioning, as activity, is defined then as the interactional phenomena through which, implicitly or explicitly, a participant is constituted as having or not having (or being seen to have) a certain set of possible actions. These positions can fluidly change over time, be imposed or self-adopted and even be subject to resistance. Positioning Theory attempts to redefine the traditional notion of role in the study of human interactions ADDIN EN.CITE Langenhove1999249124915Luk van LangenhoveRom HarrRom HarrLuk van LangenhoveIntroducing Positioning TheoryPositioning Theory: Moral Contexts of Intentional Actions1999MaldenBlackwell Publishing(Langenhove & Harr, 1999). Davies and Harr in particular ADDIN EN.CITE Davies19902459, p. 44245917Davies, B. Harre, R.Positioning: The discursive production of selvesJournal for the Theory of Social Behaviour Journal for the Theory of Social Behaviour43-63201990(Davies & Harre, 1990, p. 44) suggest that Position Theory attempts an immanentist replacement for a clutch of transcendental concepts like role and suggest that the focus be shifted from roles as static, formal, and ritualistic concepts to the study of the ways that participants in interaction orient towards the development and change of their relevant rights and duties. In CSCL in particular, significant attention has been paid to some discursive and emergent aspects of roles ADDIN EN.CITE Strijbos20052612e.g., 261247Jan-Willem Strijbos Maarten De LaatRob MartensWim JochemsFunctional versus spontaneous roles during CSCLComputer Support for Collaborative Learning2005Taipei, Taiwan International Society of the Learning Sciences (e.g., Strijbos et al., 2005) and, as such, Positioning Theory might constitute a promising expansion to such endeavors more than a significant redirection.
Positioning Theory integrates the concept of position as part of a triad of constructs that includes as well story lines and speech acts ADDIN EN.CITE Harr20032602, p. 926025Rom HarrFathali MoghaddamRom HarreFathaliMoghaddam Introduction: The Self and Others in Traditional Psychology and in Positioning TheoryThe Self and Others1- 112003Westport, CTPraeger(Harr & Moghaddam, 2003, p. 9). A storyline defines the principles or conventions that are being followed in the unfolding of an episode (e.g. a doctor and patient storyline) and incorporates, as its central elements, positions that relate the participants to specific possibilities for story-related actions (e.g. a person positioned as a doctor has a right to prescribe treatment and one positioned as a patient has a duty to furnish faithful details about his illness). The actions or, in most cases, the speech acts of participants in interaction are ascribed meanings, contingently and in an on-going basis, in relation to the story line and the related positions to which the participants orient to in the interaction (e.g. a conversational turn can be heard as a complaint within a storyline that positions participants in relation to power differential as something different within a different set of positions).
From a methodological perspective, positioning theory favors an analysis of the actual discursive processes which locate social participants in conversations and interactions. However, emphasis is place not in the content of discourse or what someone might be talking about ADDIN EN.CITE Strijbos20062613261317Jan-Willem StrijbosRob L. MartensFrans J. PrinsWim M. G. JochemsContent analysis: what are they talking about?Computers & EducationComputers & Education29-484612006January 2006(Strijbos et al., 2006) but more in the activities that are constituted by and performed through social interaction. This view is highly compatible with an interactional perspective which might recognize that there are some preferred actions that are understood by members of a culture to follow from certain interactional moves ADDIN EN.CITE Schegloff2006261526155Emanuel A. SchegloffN. J. EnfieldS. C. LevinsonInteraction: The infrastructure for social institutions, the natural ecological niche for language, and the arena in which culture is enacted.Roots of Human Sociality: Culture, Cognition and Interaction70-962006LondonBergPomerantz1984249024905Anita PomerantzJ. Maxwell AtkinsonJohn Heritage Agreeing and disagreeing with assessments: some features of preferred/dispreferred turn shapesStructures of Social Action57-1011984CambridgeCambridge University Press(Pomerantz, 1984; Schegloff, 2006). Such preferred actions are then the "social reality" of the rights, duties or obligations of a person in interaction. In other words, we can say that a person is being positioned in a certain way within a particular context because, as competent members of a culture, we recognize that a specific set of conversational or interactional moves are open to such person at the moment by virtue of what other interactants have done previously. Co-participants might position each other in different ways throughout an interaction (interactive positioning) or they might attempt position themselves directly (reflexive positioning). Naturally, participants in an interaction can resist the positioning attempts of other participants by ignoring them, explicitly challenging them, or by putting forward a new position for themselves or others. From this perspective, when the notion of a "role" is used as a recurring social typification perhaps we are forcing a static analytical concept to gloss over the dynamic ways in which participants in interaction constitute different types of actors and, especially how they emerge out of the relational interaction of people engaged in joint activity.
Positioning theory is very much linked to the ethnomethodological tradition of the study of interaction and to Goffman's views on social encounters. Goffman's late notions of "footing" and "participation frameworks" attempted to capture the ways in which participants in interaction find their relative alignment, or their "stance" relevant for the interaction. More importantly, Goffman showed that participants actively managed their footing and enacted specific participation frameworks (e.g. narrator and interactive audience) in ways that were directly related to the way they managed the production and reception of an utterance ADDIN EN.CITE Goffman19812487, p.12824876Erwin GoffmanForms of talk1981PhiladelphiaUniversity of Pennsylvania Press(Goffman, 1981, p.128). These insights have been advanced further by a diverse group of researchers primarily concerned with the detailed analysis of conversation and interaction ADDIN EN.CITE Sacks19924084086Harvey SacksG. JeffersonLectures on Conversation21992Oxford, UKBlackwell(Sacks, 1992). Studies of talk-in-interaction attend closely to the temporally unfolding of interaction and the ways that participants constitute each other as speakers, hearers, or any other social position they may occupy in an encounter and the ways used to demonstrate to each other their ongoing understanding of the events they are engaged in ADDIN EN.CITE Goodwin1981248624866Charles GoodwinConversational Organization: Interaction Between Speakers and Hearers1981New YorkAcademic Press(Goodwin, 1981).
In addition to inviting researchers in CSCL to continue paying special attention to the dynamic aspects of human interaction, the notion of positioning can also be enhanced by exploring particular aspects of learning and knowledge-building interactions. For instance, positioning in CSCL requires that we include the location and relative stance of participants within a content or knowledge space." Furthermore, we may be able to inquire about how knowledge artifacts are also subject to positioning and about the ways that this might affect collaborative problem-solving or knowledge-building work. Scaling up to larger contexts, positioning affords us the possibility of tracing, through interactional analysis, the "social location" of individuals and collectivities as they evolve over time and make relevant in their joint activity other aspects of their lives such as their membership in certain culture, their gender, attitudinal stances, etc.
In summary, the notion of position and, more importantly, the analysis of positioning as a relevant part of human interaction offer an expanded lens for looking at collaborative learning interactions and focusing on the discursive construction of knowledge and its intimate relationship with the discursive construction of selves. Other approaches to roles in CSCL have established a solid foundation for this are of research ADDIN EN.CITE Strijbos20072461e.g., 246117Strijbos, J. W.Martens, R. L.,Jochems, W. M. G.Broers, N. J. The effect of functional roles on perceived group efficiency during computer-supported collaborative learning: A matter of triangulation.Computers in Human BehaviorComputers in Human Behavior353-380232007(e.g., Strijbos et al., 2007) upon which this approach can build on. Next we present the Virtual Math Teams (VMT) project as the context in which we set out to investigate the applicability of positioning theory and introduce the types of CSCL interactions that we serve as data for our exploration of longitudinal knowledge building.
The Virtual Math Teams (VMT) Project
The Virtual Math Teams (VMT) project at the Math Forum investigates the innovative use of online collaborative environments for mathematics learning (Stahl, 2005). The Math Forum is an online math community, active since 1992, which promotes technology-mediated interactions among teachers, students, mathematicians, staff members and others interested in learning, teaching, technological supports for small-group interactions.
In the VMT project, small groups of students come together to work on open-ended mathematical problems through a special online environment ADDIN EN.CITE Wessner20062441244110Wessner, M.Shumar, W.Stahl, G.Sarmiento, J.Muhlpfordt, M.Weimar, SDesigning an Online Service for a Math CommunityInternational Conference of the Learning Sciences (ICLS 2006)2006Bloomington, Indiana(Wessner et al., 2006) that provides them with an array of tools to conduct their collaborative problem solving activity, sustain it over time, and interact with other interested individuals and groups (see Figure 1). No particular roles are assigned to the students participating in VMT and a large part of their experience is expected to be shaped by their own collaborative decisions as peers.
(Insert Figure 1 about here)
As an illustrative example of the kinds of interactions that take place in VMT, and as a first example of how to apply Positioning Theory to an understanding of these types of settings, consider the following interaction. It involves secondary school students and an adult facilitator text chatting and corresponds to the first time that templar, #1math, Sancho, fogs and david meet each other to participate inVMT. After about 20 minutes of chat activity in which different participants are greeted and introduced to particular features of the online environment, the following exchange takes place:
106 MFMod: So, to get started with the math, we will describe a situation to you and you will then explore it, make up questions about it, discuss them as a group and try to answer the ones that you find the most interesting. o.k.?
107 templar leaves the room
108 MFMod: Here's the basic situation:
109 #1math: K
110 MFMod: See the grid I just pasted onto the whiteboard?
111 Sancho: uh huh
112 #1math: YES
113 MFMod: Pretend you live in a world where you can only travel on the lines of the grid. You can't cut across a block on the diagonal, for instance.
114 fogs: yep
115 MFMod: Your group has gotten together to figure out the math of this place. For example, what is a math question you might ask that involves those two points?
116 #1math: OK
117 david: What's the minimum distance to get from A to B?
118 #1math: I THINK 10 [Points to line 117
119 Sancho: 10 what?
120 Sancho: lines or squares?
130 MFMod: Looks like that was a good question.
-Chat excerpt from Team 3, Session 1-
The work of constituting ones identity as a participant in this setting becomes a relevant goal of the interaction to be achieved, mostly, through textual postings since the VMT environment does not present any additional information about the participants other than their self-chosen screen names. In this excerpt MFMod, the facilitator of the session, attempts to position herself and the group in particular ways. She first initiates a sequence of textual postings in line 106 through which she attempts to constitute herself as the one in charge of tasking the group with what they should do in this session. Interestingly, she uses the collective pronoun "we" to separate herself from the student participants while at the same time affiliating with VMT as an institution or, at least, a collectivity of facilitators in charge of guiding the activity of the students. She also speaks of future activities that will be done by this VMT collectivity ("we will describe a situation to you") and others that the students are to do afterward ("you will then explore it, make up questions about it..."). She ends her posting attempt with a call for assessment ("o.k.?"). This call, however, is not a neutral one in the sense that by positioning herself as "the one in charge" she could have made it a dispreferred action to disagree ADDIN EN.CITE Pomerantz1984249024905Anita PomerantzJ. Maxwell AtkinsonJohn Heritage Agreeing and disagreeing with assessments: some features of preferred/dispreferred turn shapesStructures of Social Action57-1011984CambridgeCambridge University Press(Pomerantz, 1984). Notice that this effect of her positioning work is just an interactional preference (i.e. derived from the sequential unfolding of this instance of talk) since nothing structural prevents a student from typing anything at all into the chat.
Interestingly, the positioning work continues, this time through the presentation of the task itself in lines 113 through 115. The facilitator continues to task the group and the task offered, in a sense, becomes an object of reference ADDIN EN.CITE Hanks20052574257417William F. HanksExplorations in the Deictic FieldCurrent AnthropologyCurrent Anthropology191-2204622005(Hanks, 2005) in relation to which participants can be positioned. In other words, the students are positioned in relation to each other as a collaborating group, in relation to VMT and the collectivity of facilitators as responsible for certain activities, and responsible parties in relation to the task of figuring out the math of the grid world (what is a math question you might ask that involves). Notice as well how MFMod is achieving such positioning work by sequencing postings that combine a narrative of an immediate past (your group has gotten together) with references to possible present and future activity (e.g. what is a math question you might ask) whereby the group is also placed in a time field with a common task. At this point, the set of possible actions available to the students is certainly wide. Interactionally they can also put forward a new organization of action and upheld in contrast to the current task.
If the students orient towards the participation framework put forward by the facilitator, any observer, if a members of the same culture, would recognize this participation framework and understand that the right to assess actions and outcomes, and the duties of performing solution work have been, although contingently, allocated through MFMod's sequence of postings and the students responses. In fact, in line 117, we see that david asks a question that confirms his orientation to the current activity as one who is supposed to create questions, but also whose questions can be assessed or responded to by the facilitator (line 130) or by his peers.
This sequence of interactional turns and positioning moves may be seen as being part of the "teacher-student" storyline in which a teachers usually selects and provides tasks for students while they, in turn, respond with assessable actions that others can respond to. The concept of story line is also central to positioning theory, and represents a cultural pattern of how certain events unfold (e.g. a typical visit to a doctor, an interview, etc.) as part of which different subject positions are constituted. Story lines might also provide habitual frameworks that influence how interactional moves are made sense of. It is possible that multiple story lines might coexist in a single interaction, and that different participants might orient to different story lines within the same interaction.
Before moving into the analysis of VMT interactions, we would like to note that collaborative learning interactions in the specific area of mathematical problem solving might involve some additional elements complementing the constructs of positions, speech acts, and story lines, offered by Positioning Theory. More notably, collaborative problem solving in mathematics engages participants with the manipulation of task resources and the creation of reasoning artifacts that play a central role in how a group engages in joint activity. A given problem, for example constitutes a set of resources, graphical or textual, that a group of problem solvers need to make sense of, manipulate, transform, and complement with possible new resources that lead to a solution. Access to these resources is no symmetrical across all participants in an interaction. A diagram constructed by one participant, or a known theorem that might be relevant to the problem but only known by some of the participants in a group, occupy then different "positions" in the interactional space of collaborative problem solving. Furthermore, the participants engage in activities that position themselves and others in specific ways in relation to such resources as we have seen in the brief excerpt presented earlier. As will be evident through the cases presented later on, we find it essential to include such type of positioning activity, not usually addressed directly by the positioning theory found in the literature, to fully account for the types of CSCL interactions we are interested in studying.
Positioning in VMT: A case study
During the spring of 2005, a case study was conducted to explore collaborative knowledge building over time. Five virtual teams were formed with about four non-collocated secondary students selected by volunteer teachers at different schools across the USA. The teams engaged in online math discussions for four hour-long sessions over a two-week period. In the first session, teams were given a brief description of a non-traditional geometry environment: a grid-world where one could only move along the lines of a grid. Students were encouraged to generate and pursue their own questions about the grid-world, such as questions about the shortest distance between two points in this world. In subsequent sessions, teams were given feedback on their prior work and the work of other teams and were encouraged to continue their work.
Our qualitative analysis attempted to understand the dynamics of positioning within each one of the team sessions as well as to identify significant shifts in the teams positioning dynamics across sessions. We employ ethnomethodologically-informed approaches (Garfinkel, 1967) to examine sequences of interactions by using recordings and artifacts from the teams' sessions. For our current purposes, we examined 18 team sessions, paying special attention to the sequential unfolding of the sets of four problem-solving episodes in which each team participated. Constant comparison through different instances of bridging in the entire dataset led to our refinement of the structural elements that define positioning activity. This analysis is part of a larger attempt to investigate how teams of participants in the VMT online community bridge the apparent discontinuity of their interactions (e.g. multiple collaborative sessions, teams and tasks) and exploring the role that "bridging activity" plays in their knowledge building over time.
Three main goals guided the analysis of VMT interactions conducted. First, we were interested in examining the dynamics of role formation and enactment in interaction. We did not bring to the analysis a predefined set of role categories and instead, through the lens of positioning theory, we focused our analysis on the dynamics of how participants constituted each other and the activities they oriented to in interaction. Second, we wanted to investigate the trajectories of positioning across each of the four sessions conducted by each team. Finally, we were interested in exploring the relationship between positioning work and the problem-solving activity conducted by all the teams. To illustrate the analysis conducted and the results obtained, we will use the trajectory of one team in particular.
Case I: Then letz check it
The excerpt below corresponds to the second time that team two meets together to participate in Virtual Math Teams. In this session, a facilitator presented them with a list of nine questions collected from all the teams that participated in the first session plus some additional ones created by the VMT staff based on the teams' work.
144 mathfun: letz start working on number 8
145 bob: we already did that yesterday
146 qwer: we did?
147 mathfun: but we did it so that there was only right and down
148 bob: i mean tuesday
149 mathfun: i guess we will do it with left and up?
150 qwer: It would be almost the same.
151 bob: it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1)
152 bob: try it if you like
153 mathfun: nah
154 mathfun: if you are so sure...
155 bob: i'm not
156 bob: actually
157 bob: take out the -2 and the -1
158 mathfun: then letz check it
159 bob: after taking out the -1 and -2, you get 5c2 or 5c3,
doesn't matter, which is 10
160 mathfun: k so there are two ways right?
161 bob: yeah
162 bob: 2c1=2
163 Marisol: yes, I agree there are only two ways
164 mathfun: then there is a one by two
165 qwer: only two ways?
166 mathfun: is the one by two going to be 4 ways?
167 qwer: Can't you go, from A, right, down, right down, right, or right, right, right, down, down,
or down, down, right, right, right...
- Chat Excerpt from Team 2, Session 2 -
The dynamics of positioning moves in this short chat conversation are significantly rich. For our purposes, we will concentrate specifically on the ways that this kind of interactional work relates to the teams' sustained joint problem solving over time. In line 144 mathfun makes a proposal for the team to initiate together the activity of working on problem number eight. At this point this is an open proposal that calls for assessment leading to the support or resistance of the new activity being proposed. Everybody in the team has equal rights or possibilities for action in terms of this assessment which will be addressed towards mathfun, the originator of the proposal. Bob objects to mathfun's proposal indirectly by offering a reason that makes working on the problem not necessary: they already worked on that problem in their last session. This reply positions the members of the team in two different planes. First, with respect to their current alignment towards the proposed task as a possible joint activity. Second, with respect to their history together and the work that they did and which they might be accountable for (e.g. Marisol did not participate in the first session and, as such, would not be able to assess bobs claim without potential interactional trouble). Next, qwer questions bobs task claim (line 146) while mathfun mitigates the objection (lines 147 and 149) ratifying the team's position in relation to their past activity but offering for assessment an alternative positioning for their current activity. In doing so, mathfun ratifies the team's history as presented by bob in terms of having done the problem "so that there was only right and down" but suggesting that they could do it now "with left and up?"
Throughout this interaction, brief as it is, we can see how the participants establish and manage their position in relation to their past activity and a potential current activity as well as to certain knowledge artifacts as reference objects. In this sense, both inter-personal and epistemic or content stances are at play in how this interaction is unfolding. Deciding what problem to work on at a particular point in time, is certainly an activity that every team has to engage in, usually enacting activities that might be labeled as "leadership," "coordination," or "planning." In this short passage we see the team conducting this coordination work in a joint fashion without a clear leader or coordinator role. It could be, however, that mathfun's is usually the team member who suggests possible tasks for the team or that bob tends to be the one who reminds the team of what they have worked on before. We can investigate these hypotheses by following the trajectory of the team backwards and forwards, through multiple collaborative episodes. Before doing that, lets summarize our interactional analysis of the excerpt presented by stating that participants are literally moving themselves and attempting to move others in their relative position to each other, to the current activity, and even to their past and future activities. In doing so, they allocate and manage possible next actions, entitlements (e.g. who should respond to assessments) and the resources that are relevant to their work (e.g. problem-solving "memories").
Turning our attention to how these dynamics of position intersect with their collaborative problem solving activity, we noticed an interest shift of relative positioning of the team around the middle of this excerpt. By qwer accepting that if they do the problem in the way suggested by mathfun "it would be almost the same" she has shifted her alignment from considering problem eight as a valid possibility to supporting bob in his idea that the problem was solved already. Bob then reports a candidate formula for the answer (in a sense, as proof of prior activity) and asks mathfun to check it. (Notice how the lense of positioning guides us in understanding that mathfun has been selected as the recipient of that posting). Mathfun declines in a way that leaves his position depending on how sure Bob is of "his" formula (lines 153/154). It is as a result of bob stating that he is not so sure about the correctness of that formula that the mathfun can then make a new bid for some collective activity to which they can all orient to: "then letz check it" Naturally, they are not orienting to this activity in exactly symmetrical ways. After all, this is Bob's formula and he has made the first bid for where the problem might lie ("take out the -2 and the -1"). The relative positioning of the team members to each other and to the resources at hand has shifted but bob is still positioned as the member in charge of assessing the way his formula is being checked. From this point on, however it is mathfun who structures the procedure through which the formula is going to be checked. He builds a series of cases, using the whiteboard, and asks the team to evaluate each one of them (e.g. 160 mathfun: k so there are two ways right?).
The story line has then shifted from "expert-and-audience" to, perhaps "expert-and-collaborators", in a qualitatively significant way. This new orientation towards collective activity has a different alignment of the group members towards participation specially when compared to what had been established in the preceding moments. As such, this represents a significant change in knowledge building positioning within an individual session and one that has been accomplished interactively by bob, mathfun and qwer together. Next we explore whether any of these two types of positioning (bob reporting on his knowledge or bob, mathfun, and qwer collaborating under bob's expert supervision) appeared in their first team session. Later on we will investigate whether these positions were maintained or transformed for the rest of the two remaining sessions.
Case II: I am only in algebra 1
In the first session held by this virtual team, four participants actively engaged in generating questions about the grid world. Following common patterns for first encounters, at the beginning participation seemed very equal with all team members posting at very similar rates. Interestingly, bob, who will position himself later as an expert, did not contribute a question to the list created by the team. The second question explored by the team is posted by qwer in line 201 of the following excerpt:
201 qwer: What about, what's the angle of B? I think it involves a sin.
202 mathfun: we can use tan, sin, or cos
203 bob: tan of angle b=3/2, so you do tan^-1(3/2)=56.30993247
204 bob: ...
205 mathfun: which is ....?
206 bob: 56.30993247 degrees
207 mathfun: k
208 mathfun:
209 Sith91: im only in algebra 1.... i havent covered sine, cosine, and tangent yet
210 qwer: neither have I
211 bob: tangent=opp/adj
212 bob: sine=opp/hyp
213 Sith91: ohh... i c
214 bob: cosine=adj/hyp
215 bob: cotangent is reciprocal of tangent
216 ModG: I posted the description of the world in the whiteboard
217 bob: cosecant is the reciprocal of sine
218 bob: and secant is reciprocal of cosine
219 Sith91: ok... thx
220 bob:
221 Sith91: so,... that would be 6/4=3/2
222 bob: and then you set tan(angle B)=3/2
223 bob: so tan^-1(3/2)=angle B
224 bob: so then angle B=what i said earlier
225 Sith91: oh... sry, didnt see that
226 mathfun: How many ways are there to get from A to B?
227 bob: infinite, if you count overlap
228 bob: otherwise, a lot
229 Sith91: yep
- Chat Excerpt from Session 1, Team 2-
Once a question has been proposed (line 201) and a candidate answer has been offered (lines 203 and 206), assessment is a possible and very common next action. In many cases, it is the person who has proposed the question who usually takes on the task of producing this type of assessment but others can take on this action as well. In this case, mathfun posts an acceptance token in line 207, aligned with his participation in the production of the candidate answer. However, after line 207, there is a long silence of about 20 seconds followed by a type withdrawal from assessment by Sith91 (line 209). This withdrawal is justified on the basis of lack of necessary knowledge and, at the same time, positioning the author in a different group as the author of the answer in need of assessment (i.e. Sith91 is "only in algebra 1"). Qwer seconds the withdrawal in line 210. Bob (and to a lesser extent mathfun) are then positioned to either accept this withdrawal and transition to a completely new activity or to respond to it directly by trying to ameliorate Sith91 and qwer's lack of knowledge. Notice how this set of "next-possible" actions for a participant follows from the way the current activity unfolds and the way participants position themselves. Bob quickly posts what looks like formula definitions of trigonometrical functions (e.g. tangent=opp/adj, sine=opp/hyp, cotangent is reciprocal of tangent, etc.) indexing some elements such as "opp," "adj," "hyp," and "reciprocal" that are never fully specified. This leads us to think that this type of explanation is done in a minimalistic way to further justify one's answer and seek acceptance of it rather than to attempt to repair the team member's lack of knowledge. In fact, Sith91's attempt, in line 221, to engage with bob's explanation is never acknowledged. Instead, the set of conceptual definitions are followed in lines 222 through 224 with a procedural account of how to get to bob's answer (in fact, a repetition of line 203). A type of acknowledgment and apology are produced by Sith91 completing the explanation-assessment sequence. This opens up the opportunity for the team to transition to a new activity which they do through mathfun's new question in line 226. We can see this sequence as a shift in relative positioning of the team from equal participants to two sub-collectivities with different levels of knowledge and, consequently, different sets of possible or expected actions.
The pattern of interaction exhibited in this excerpt is repeated with the next question that the team works on later in this session. The team enacts the "expert-and-audience" participation framework by posting an answer, followed by a procedural explanation and by requests for further explanation that are responded with conceptual definitions that fail to engage some members of the team in understanding the mathematical reasoning behind the proposed answer. In this sense, the shift from equal participation to an "expert-and-audience" participation framework and the relative positioning of the participants related to this organization of participation in one episode of problem-solving interaction permeates to a new episode. Furthermore, if we return to the first case presented here (second team session), we could argue that this "expert-and-audience" participation framework, has remained in effect beyond the boundary of their local engagement in one single session of collaboration. That being said, a different set of interactional conditions in that session made it possible for the team to transition again to the new "expert-and-collaborators" participation framework that we documented in our analysis of case I. These shifts, in fact, are not uncommon in the VMT dataset. They represent, more that the change in defined roles of an individual participant, the collective realignment of a team's participants into different relative positions with respect to each other and certain relevant resources. In a final case, we analyze a third shift to further illustrate the dynamics of this type of positioning activity.
Case III: Maybe there's another way Im not seeing
The fourth session of team two finds bob and mathfun working as a dyad. None of the participants who had worked with them in the first three sessions joined this last session. A unique shift in participation is also worth noting in this final session. Toward the beginning, the facilitator presents bob and mathfun with a new challenge based on their prior work: finding the shortest distance between any two points along a grid that has been folded to form a triangular prism. In their previous session, bob, mathfun, and qwer had worked on rolling the grid to form a cylinder and, as mentioned earlier, bob and mathfun dominated the conversation. This time, mathfun positions the dyad in what we have called a "exploratory collaborators" framework. The following excerpt illustrates the characteristic dynamics.
34 mathfun: so bob u there?
35 bob: yeah
36 mathfun: k letz get started
37 bob: the way i see it, you do the same thing you did with the circle
38 mathfun: alright
39 mathfun: so letz draw the triangular prism
40 mathfun: there
41 mathfun: so should i make the bird's eye view?
42 bob: yeah
43 mathfun: k
44 mathfun: there
45 bob: draw a line segment
46 bob: on it
47 mathfun: aren't we able to find out the little segments with an arrow to them?
48 mathfun: bob?
49 eModerator joins the room
50 bob: huh
51 bob: oh
52 bob: yeah
53 bob: coordinate
54 jtcc joins the room
55 eModerator leaves the room
56 mathfun: so then isn't the little length found too?
57 bob: using law of cosines
58 mathfun: or degrees
59 bob: or maybe there's another way i;m not seeing
60 bob: ?
61 mathfun: is that x?
62 bob: is what x?
63 mathfun: that
64 bob: no
65 bob: it's a 4
66 Moderator: x?
67 mathfun: oh
68 mathfun: see angle alpha?
69 bob: yes
70 bob: what about it?
71 mathfun: is that 60 degrees?
72 bob: yes
73 mathfun: can u use the degree, 2 length to find the last length of a triangle?
74 bob: i don't get what you're saying
75 mathfun: the two arrow pointed lengths and the angle can find the length A
76 bob: by what?
...
-Chat Excerpt from Team 2, Session 4-
Despite the fact that this sequence starts in a similar way that all of the sequences we have presented of this team; with bob making a solution statement shortly after a problem has been presented, his contribution makes it possible for a very different organization of the dyad's participation. Bob proposal, in line 37, that "you do the same thing you did with the circle" explicitly references their prior session in which mathfun has conducted the problem-solving work under his "expert watch". Mathfun engages with the problem in precisely that way, by asking for bob's confirmation that he should make "the bird's eye view" of the prism. What follows, are a series of postings that do not conform to the positioning and participation frameworks we had seen this team engage in. The work they are conducting seems much more exploratory with Bob being more open to considering mathfun's ideas as opposed to mathfun simply trying to test or understand bob's answer. Perhaps it is precisely because at this point the team does not have an answer to the problem but is engaged in the actual work of organizing the problem space and exploring it to construct a solution. There is a prior procedure available which the team can reuse but no direct answer available. Line 59 is specially telling about how the dyads' relative positioning can be said to have shifted from their prior encounters. Bob is still positioned as the person to assess mathfun's postings but not necessarily on the basis of his knowledge of the problem's answer but more as a knowledgeable collaborator. This allows the dyad to engage in exploratory work that lasts for quite some time and results in a candidate answer.
Discussion
We have traced the trajectory of team two and its members to illustrate how positioning work is accomplished in interaction and how common shifts in relative positioning and participation frameworks are common in VMT, within one single session and across sessions. We have selected a few representative cases from a larger set that included other significant shifts. Despite the diversity of participation frameworks exhibited by the teams in our dataset, similar positioning dynamics where observed in all the teams' trajectories. Many of these participation frameworks are at least implied in the roles literature on collaborative learning and collaboration, in general. However, their collective dynamics are rarely appreciated.
Within our longitudinal analysis of VMT interactions a unique type of activity and its associated positioning dynamics are worth mentioning. Because the participating teams were engaged in sustained activity over time, many teams engaged in what we have called "bridging activity," interactional work directed at overcoming the gaps created by the different team sessions and the changes in attendance. This type of activity positions the individual team members, the sub-collectivities they form, their history of interaction, and their problem-solving work in unique ways that bear further analysis, specially as they seem to intersect with the sustainability of knowledge building activity. This will constitute the focus of our future work.
In following the trajectory of participation of one team and use episodes in that trajectory to illustrate the dynamic ways in which the members of the team position each other and the problem-solving resources relevant to their activities. Such activity is pervasive throughout the entire dataset and as such constitutes a central feature of collaborative problem solving and knowledge building. Using the lense of positioning theory and the methods of interaction analysis we attempted to reconsider the notion of role in this type of CSCL research. As a result, we believe that both perspectives can co-exist and inform each other. Although the attention to dynamic unfolding of interactions provides especially rich descriptions of human activity, it is possible that our descriptions correspond to the process of "role formation" or "role differentiation," especially when taken as longitudinal trajectories of a collectivity with a certain history of engagement. If that is the case, both frameworks are highly compatible and serve different purposes at different scales of CSCL and learning research.
As Harre and Mogaddam (2003) point out, "by positioning someone in a certain way someone else is thereby positioned relative to that person" (p. 7). This "relational" aspect of positioning is clearly confirmed through the three cases analyzed where positions have always been characterized as pairings of positions (e.g. expert-and-audience). In itself, this way of thinking about roles seems to indicate an interesting departure from the notion of defined or static roles. In addition, the participation frameworks that are enacted collectively through interaction can also exhibit many variants. For instance, through the different cases examined we presented different arrangements of the "expert role" positioned in an "expert-and-audience" or "expert-and-collaborators" framework. Shifts in positioning appear especially interesting through our analysis since they indicated individual and collective changes in participation within a single session and throughout multiple sessions of the same team.
It should be noted that position theory exists within a range of assumptions. The assumptions of individuals like Davies and Harre are referred to as radical constructivism by Holland et al ( 1998:14, 290 n.11). This view on positioning is radical in that it sees all determinants of structure and agency occurring within fluid conversational situations. As such identity, personhood, social structure are always fluid and in the process of construction at each moment the interlocutors interact. But a more compromising view of positioning would suggest that there are larger structures and in fact positions exist within a field of social relationships and that field is comprised of more stable social symbols such as capital, status, regulation etc. So while there is a great deal of fluidity to positioning in conversation, conversations exist in larger fields of power and control that can indeed be changed but are much more resistant to change.
In a general theoretical discussion on positioning the concept would need to be brought into dialogue with Bourdieus notion of position within a social field (See Holland et al. 1998). The interactional forms of positioning always occur within more fixed systems relations of power where access to capital and status is to some extent rigged by the rules of that game and they ways that social actors are forced to take up different locations within that social field. As noted above the more interactional forms of positioning still exist within these structured field but their effectively is much less room for social actors to move and hence limits on their agency.
The VMT on the other hand is a very unique social field in that it is one where there has been a concerted effort on the part of the project staff to flatten the field and make interactions more egalitarian. In this more egalitarian environment where differential access to knowledge and capital (in this example about math) are limited and all students are given problems that are more open ended and encourage thought. It is certainly the case that students come into the VMT environment with different amounts of mathematical knowledge and a different sense of their own agency around math problem solving. Nevertheless the VMT environment encourages student to share knowledge and engage in open dialogue. In such an environment the concept of positioning is particularly useful in that there is less of a hierarchical institutional structure to limit the forms of interaction that students engage in.
Finally, we believe that attention to the unfolding of positioning moves and its relation to problem-solving or knowledge-building work have the potential to illuminate a wider range of phenomena than what traditional role analysis. To mention a few, we intent to pursue our analysis to explore phenomena such as resistance to positioning moves, collective shifts in positioning, and the use of diverse external resources in positioning activity (e.g. school context, past history of participation, gender, etc.) In addition, promising applications emerge when considering the practical applications of this type of analysis and its results. First, educators and instructional designers interested in scaffolding and scripting collaborative learning interactions might benefit from these detailed descriptions of participation frameworks and positioning activity and might be able to translate them into training or support materials that aid learners in understanding activities such as making and managing knowledge proposals, conducting joint exploratory work, and co-constructing explanations. In addition, there seems to be an opportunity to use these cases to illustrate the interdependency between the social and epistemic dimensions of collaborative interactions. Finally, designers of CSCL environments might be able to utilize this type of longitudinal analysis of collaborative interactions to better approach the creation of mechanisms to capture and present the social and epistemic "history" of a team and its members. Further work is needed to achieve these practical applications but we feel that the type of analysis presented shows great promise. References
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Positioning and Social Location in VMT PAGE 8
(3) When someone types a new chat message, they can select and point to an area in the whiteboard or to a previous message, displaying a connecting graphical line (as shown in the figure)
(2) The shared whiteboard allows chat participants to create drawings and share graphic information with each other. Every whiteboard action is recorded. Users can manipulate a slide bar to navigate through all changes made in the whiteboard since the creation of the chat room.
Figure 1. VMT online collaboration environment
(1) Chat conversations are persistent during and after each session. Latecomers can load all previous messages at will.
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