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Boundaries and roles: Social location and bridging work in the Virtual Math Teams (VMT) online community

Johann Sarmiento, Wesley Shumar: Drexel University

Abstract

As research in Computer-Supported Collaborative Learning (CSCL) expands its understanding of diverse types of joint learning activities and the participation frameworks they enact, new perspectives on how social reality is constructed become necessary for analysis and design purposes. Along these lines, our research concentrates on the temporal development of online learning groups into teams and communities in the Virtual Math Teams project. We investigate the ways that small virtual teams engaged in sustained work over time cross to constitute learning and knowledge building as a continuous activity. We concentrate on describing the type of interactional activity related to ways that co-participants position themselves and other as well as the knowledge-building tasks and resources over time. Our analysis suggests some benefits in considering the dynamic situatedness of the concept of role in CSCL research, especially in the analysis of longitudinal work and when considere the dynamic co-construction of a sustained a joint problem space by small groups of learners.

Intro

CSCL research attempts to understand learning contexts that range from individual problem-solving episodes of small group activity to the longitudinal development of online communities of learning and knowledge building. These different arrangements of human activity, spread over time and across multiple collectivities, challenge researchers to strengthen and expand their perspectives on how social reality is constructed. For instance, when the temporal development of online learning groups is at the center of the analysis, the dynamic aspect of how interactions shape the way participants engage over time becomes central. It is in these kinds of contexts where we might be able to more productively combine the traditional notion of a "role" with the interactional analysis of how such role becomes enacted and emerges out of interaction.

In order to explore the temporal dynamics of groups engaged in knowledge building we turn to positioning theory, a dynamic lens on the traditional notion of roles. First, we outline the basic concepts of the theory and illustrate the ways it focuses its attention on "dynamic aspects of encounters" and how it contrast with the ways in which the use of 'role' has served to "highlight static, formal and ritualistic" aspects of interaction (e.g., Davies & Harre, 1990, p.261). We then analyze data from small online groups participating in the Virtual Math Teams project of the Math Forum, an online community dedicated to mathematics education, in order to illustrate how positioning theory allows a richer account of how such interactions unfold. Finally, we offer a series of practical reflections on how the combination of traditional role analysis and positioning theory can contribute to CSCL analysis and design work.

Positioning Theory and Social Location

Positioning Theory attempts to redefine the traditional notion of role in the study of human interactions (Langenhove & Harré, 1999). Its main interest lies on the study of the ways that participants in interaction orient towards the development and change of their rights and duties. From a methodological perspective, positioning theory favors an analysis of the actual discursive processes which locate social participants in conversations and interactions. Based on this analytical commitment, positioning can then be defined as the interactional phenomena through which, implicitly or explicitly, a participant is constituted as having or not having a certain set of possible actions. Usually, such possible actions are characterized as a reified set of rights, duties or obligations -the very definition of a role or a position. A more interactional account might recognize instead that there are some preferred actions that are understood by members of a culture to follow from certain interactional moves. 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, challenging them explicitly, or by putting forward a new position for themselves or others. From this perspective, the notion of a "role" as a recurring social typification is challenged as being too static a concept to describe the way 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, at least in part, motivated by the study of interaction and, in particular, 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 they "stance" relevant for the interaction. More importantly, Goffman showed that participants actively managed their footing and enacted specific participation framework in ways that were directly related to the the way they managed the production and reception of an utterance (Goffman, 1981 128). These insights have been taken further by a diverse group of researchers primarily concerned with the detailed analysis of conversation and interaction. For instance, conversational analyst Charles Goodwin describes in the following way how the dynamics of interaction are essential to the constitution of speakers and hearers, not as structural and abstract categories but as relevant constructs for the participants themselves:

 I investigate Participation as a temporally unfolding process through which separate parties demonstrate to each other 
 their ongoing understanding of the events they are engaged in by building actions that contribute to the further progression 
 of these very same events. Thus a hearer is not just a structural category, an addressee, but someone who displays detailed 
 analysis of, and stance toward, the unfolding structure of the talk in progress through visible embodied displays. Speakers 
 take such displays into account as they organize their own actions. Moreover, parties in interaction build action from the social 
 positions they occupy. This approach to participation, with its focus on analysis displayed through temporally unfolding action, 
 differs from approaches that proceed by constructing typologies of different kinds of participants. (Goodwin, 2007)

In addition, the notion of positioning opens up a set of new possibilities to approach learning and knowledge-building interactions. For instance, positioning allows us to include the location and relative stance of participants involved in problem-solving contexts to the abstract "problem space" (i.e. the set of cognitive artifacts that theoretically define the strategic action of a human problem solver) proposed by the information-processing perspective (e.g. Newell & Simon, 1972). Furthermore, we may be able to inquire about how knowledge artifacts are also subject to positioning and in what ways does this 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, are supported by both positioning theory and interactional studies of conversation. They might differ in the subtle ways in which they see human activity and the "meaning of actions" being related (e.g. contrast Harre and Slocum, 2003 p. 124 and Schegloff, 1988), a distinction that goes beyond the limits of this paper. However, our goal is to contrast this dynamic look at roles and the enactment of roles in social interaction from traditional studies of role theory. As an example, consider the following interaction. We will describe later some of the details that characterize the dataset from which this excerpt originates. Suffice to say, this is an online encounter that involves secondary school students and an adult facilitator text chatting. It corresponds to the first time that templar, #1math, Sancho, fogs and david meet each other online to participate in "Virtual Math Teams." 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?

Excerpt from VMT0510G3

In this short sequence, we can observe that MFMod, the facilitator of the session, initiates a sequence of activities in line 106 which she position herself as a the one in charge of tasking the group on what they should do in this session. Since the online environment that the participants are using does not present any additional information about the participants beyond their self-chosen screen names, the work of constituting oneself as a facilitator becomes specially relevant here. There are a number of interesting things in the way MFMod achieves this. For instance, she uses the collective pronoun "we" and speaks of future activities that will be done by herself ("we will describe a situation to you") and that the students are supposed to do ("you will then explore it, make up questions about it..."). She ends her posting 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 with her. Notice that this is just an interactional preference (i.e. derived from the sequential unfolding of this instance of talk) since nothing structurally 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 line 113. The way the task is presented also frames a situation in which students are positioned as being in a world with certain navigation constraints. In line 115, MFMod explicitly positions all the students present in the online chat at that moment, as those who "has gotten together to figure out the math" of such imagined world. Notice how MFMod is achieving such positioning work by presenting a narrative of an immediate past and constituting them as a peer collectivity ("your group"). Furthermore, a way for the group to proceed is presented: asking a math question that involve two points in a grid. The set of possible options for the students is certainly very varied at this point, both, within the "participation framework" that is being put forward (e.g. "instructor - instructee", or "commander - team"), or within a new one that would need to be presented and upheld in contrast to the current task. Whether the students orient towards this participation framework or engage with it, we, as members of a certain shared culture, would recognize that the right to assess actions and outcomes, and the duties of performing solution work have been, although incipiently, allocated through MFMod's postings. 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 by the facilitator or by his peers.

The previous sequence of positioning moves may be seen as being part of the "teacher-student" storyline in which teachers impose tasks on students and they, in turn, respond with actions that are assessed by the teacher. The concept of story line is also central to positioning theory, as it represents a cultural pattern of how certain events unfold (e.g. ones autobiography, a typical visit to a doctor, etc.) through which different subject positions are elaborated. Story lines might also provide particular interpretations of cultural stereotypes that influence how the material exchanges of an interaction are interpreted. It is possible that multiple story lines coexist in a single interaction, and that different participants orient to different story lines as an interaction proceed.

Given our interest in collaborative learning interactions in the specific area of mathematical problem solving, a number of story lines, a number of additional elements become relevant besides positions and story lines, which might not be fully accounted for 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. More importantly, 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. We find it essential to include such type of positioning activity, not usually addressed directly by the positioning analysis found in the literature, to fully account for the types of interactions we are interested in studying. (Note: I am not sure if this paragraph follows here. Perhaps, since this is a modification of positioning theory, we can present it as a contribution to it, later on? From here we can easily go to an interactional account of the "joint problem space" and contrast that with the traditional notion of "problem space" from information processing theory)

Before presenting our analysis of how the analysis of positioning might contribute to our understanding of collaborative knowledge building over time, we first describe the Virtual Math Teams project, the source from where our dataset comes.

Virtual Math Teams at the Math Forum: A Case Study

The 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. It promotes technology-mediated interactions among teachers, students, mathematicians, staff members and others interested in learning, teaching, and doing mathematics. Central to the VMT research program are the investigation of the nature and dynamics of group cognition (Stahl, 2006) as well as the design of effective technological supports for small-group interactions. In this particular study we investigate the ways that small virtual teams engaged in sustained work over time, crossing over the boundaries of episodes, collectivities, and perspectives to constitute and advance learning and knowledge-building as a continuous activity. We refer to this interactional activity as "bridging" work. Bridging is achieved through a set of methods through which participants deal with the discontinuities relevant to their collective engagement. Bridging thereby might tie events at the local smallgroup unit of analysis to interactions at larger units of analysis (e.g. online communities, multi-team collectivities, etc.) as well as between the individual and small-group levels.

Data sources and goals

During the spring of 2005, an experiment 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 aimed at understanding 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 such bridging activity plays in their knowledge building over time. We employ ethnomethodological approaches (Garfinkel, 1967) to examine sequences of episodes 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 bridging activity.

Goals of the Analysis

How is that positions and positioning work are dynamic? In one interaction? Across interactions? Do the participants orient to positions as dynamic or stable?
what position are relevant in the data we observed? Do they change over trajectories?
Is positioning (and positions) to be attribute to individuals? To the group? To the "situated" group? Are they produced by individuals in cooperation with others? Are they co-produced and maintained? For a long time?
Is there a visible relationship between the activity of positioning in learning interactions and learning or knowledge building activity? Does this tell us something about whether scaffolds are necessary? About the nature of such scaffolds? (e.g. role frames that are interdependent, rotations, etc.)
How does positioning theory and the analysis of positioning in interaction contribute to the design or analysis of collaborative learning beyond what role theory has already contributed or is able to contribute?

Case I: Letz check it

The excerpt below corresponds to the second time that this team meets together to participate in the Virtual Math Teams pilot project. In this session, they were presented by the facilitator with a list of nine questions collected from all the teams that participated in the first session plus some additional ones created by the 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 and, because disagreement is a disprefered position, he does not do it explicitly but by offering a reason that makes working on the problem not necessary: they already worked on that problem the day before. 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 might be accountable for. Qwer questions such positioning (line 146) and 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 we can see how the participants change their position in relation to their past activity and a potential current activity. Both social as well as epistemic stances play a role 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 but it could be that mathfun's is usually the one suggesting possible tasks for the team or that bob tends to be the one who reminds the team of what they have worked on in the past. We can investigate these hypothesis by following the trajectory of the team backwards and forwards, through multiple collaborative episodes. Whether we can validate them or not, it is clear that in the activity being conducted in the passage above the 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 notice an interest shift of relative positioning of the team around the middle of this excerpt. By qwer accepting that even if they do the problem in the way suggested by mathfun it "it would be almost the same" she has shifted her alignment from considering problem 8 as a possibility to supporting bob in his idea that the problem was solved already. Bob then provides a candidate formula for the answer and asks mathfun to check it. Notice how positioning guides us in understanding that mathfun has been selected as the receipient 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 a collaborative session and one that has been accomplished interactively by bob, mathfun and qwer.

In addition, we can ask, 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. We can also investigate whether these positions are 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 engage in generating questions about the grid world. Following common patterns for first encounters, early on participation seems very equal with all team members posting at very similar rates. Interestingly, bob, who later will position himself as an expert, does 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
 
-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 engages as part of this session. Bob enacts the "expert-audience" participation framework by posting an answer, followed by a procedural explanation, and responding to a member's request for further explanation with some conceptual definitions that fail to engage the team in understanding the reasoning involved in his answer and the relevant mathematics. In this sense, the shift from equal participation to an "experts-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 excerpt in case I, from the second session of this team, we could argue that this "experts-audience" participation framework, has remained in effect beyond the boundary of their local engagement in one session of collaborative activity. That being said, a different set of interactional conditions in that session make it possible for the team to transition again to the new "expert-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 I;m not seeing

The four session of team's two trajectory of participation finds bob and mathfun working as a dyad. None of the participants who have worked with them in the first three sessions join this last session. In fact, qwer, the only additional participant in session three, only makes about twenty postings in the entire one-hour chat. It is very difficult to interpret lack of participation or non- attendance without interviewing participants directly. Perhaps, the participation frameworks that the team has been enacting have resulted in a positioning of qwer that might be responsible for this shift in participation. Another shift is also wort noting in this final session.

In this session, 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 "exploratory-collaborators." The following excerpt illustrate the characteristic dynamic.

 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?
 ...
 
 -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.

In summary, 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, within one single session and across sessions. Similar dynamics where observed in other teams' trajectories although a number of other participation frameworks, different than the ones described here, were also observed.

Additional Cases:

we arent getting anything done

 212  	dragon:	 I'll work at the bottom	 
 213 	MFmod:	 i can alway put the questions back if you want them later	 
 214 	meet_the_fangs:	 lets get to it	 	 	 
 215 	dragon:	 ok @: Message 213: To whole message	 
 216 	dragon:	 I'll be green from now on	 
 217 	meet_the_fangs:	 aiite ill be red	 	 	 
 218 	estrickmcnizzle:	 we arent getting anything done
 219 	meet_the_fangs:	 any suggestion?	 	 	 
 220 	estrickmcnizzle:	 i dont know, maybe just a more simple problem
 221 	estrickmcnizzle:	 less time consuming
 222 	gdog, 20:52 (20.05): drop the questoin	 	 
 223 	dragon:	 I think I know the answer...	 
 224 	gdog, 20:52 (20.05): more simpel one that i can understnad plz :)
 
 -Team 5, Session 4-

Expert turned Deviant

In session 2 of team 2, towards the end bob turns very disruptive drawing red lines repeatedly on the whiteboard, moving the diagrams the team was using at the moment, etc. and states that he is bored:

 256  bob123:  draw radii to A and B
 257 mathisfun:  that ?
 258 bob123:  and a perpendicular bisector to AB
 259 bob123:  making two right triangles
 260 bob123:  then you can find AB
 261 mathisfun:  k
 262 bob123:  but then you have to compensate for the 3rd dimension
 263 qwer:  Do you need the bisector? @: Message 258: To whole message
 264 bob123:  up and down
 265 bob123:  you don't need to draw any of it
 266 bob123:  as long as you know what you're doing
 267 mathisfun:  who is doing that?
 268 bob123:  me
 269 bob123:  i'm bored
 270 qwer:  So you make the A B line the hypotinuse of a vertical triangle and use pythag.
 271 mathisfun:  dude stop
 272 bob123:  fine
 273 bob123:  be that way
 274 mathisfun:  i will
 275 qwer:  What's that? @: 
 276 mathisfun:  a master piece by bob
 277 bob123:  it's running away!!
 278 mathisfun:  arg
 279 mathisfun:  stop it 
 280 qwer:  arg, too
 281 bob123:  hilarious
 
 -Team 2, Session 2-

Discussion

We have followed the trajectory of participation of one team participating in VMT 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 of the analysis conducted, we believe that both perspectives can co-exist and inform each other. Although the attention to dynamic unfolding of interactions provides a specially rich description of human activity, it is possible that our descriptions correspond to the process of "role formation" or "role differenation," especially when taken as longitudinal trajectories of a collectivity with a certain history of collaborative 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-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-audience" or "expert-collaborators" framework. Shifts in positioning appear specially 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.

In summary, 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

Davies, B., & Harre, R. (1990). Positioning: The discursive production of selves. Journal for the Theory of Social Behaviour, 20, 43-63.

Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs, NJ: Prentice-Hall. Hare, P. (2003). Roles, relationships, and groups in organizations: Some conclusions and recommendations. Small Group Research, 34, 123-154.

Goffman, E. (1981). Forms of talk. Philadelphia: University of Pennsylvania Press.

Goodwin, C. Research Projects: Participation. Retrieved February 12th, 2007, from http://www.sscnet.ucla.edu/clic/cgoodwin/projects.htm#003

Goodwin, C. (1981). Conversational Organization: Interaction Between Speakers and Hearers. New York: Academic Press.

Harre, R., & Moghaddam, F.M. (Eds.). (2003). The self and others: Positioning individuals and groups in personal, political, and cultural contexts. Westport, CT: Praeger.

Langenhove, L. v., & Harré, R. (Eds.). (1999). Positioning Theory. Oxford: Blackwell.

Martens, R. L., Jochems, W. M. G., & Broers, N. J. (2007). The effect of functional roles on perceived group efficiency during computer-supported collaborative learning: A matter of triangulation. Computers in Human Behavior, 23, 353-380.

Newell, A. & Simon, H. (1972). Human Problem Solving. Englewood Cliffs, NJ: Prentice-Hall.

Pomerantz, A. (1984). Agreeing and disagreeing with assessments: some features of preferred/dispreferred turn shapes. In J. M. Atkinson & J. Heritage (Eds.), Structures of Social Action (pp. 57-101). Cambridge: Cambridge University Press.

Renninger, K. A., & Shumar, W. (2002). Community building with and for teachers at the Math Forum. In K. A. Renninger & W. Shumar (Eds.), Building virtual communities (pp. 60-95). Cambridge, UK: Cambridge University Press.

Schegloff, E. A. (1988) Goffman and the Analysis of Conversation. In P. Drew & T. Wootton (Eds.), Erving Goffman: Exploring the Interaction Order (9-135). Cambridge: Polity Press.

Stahl, G. (2005). Group cognition: The collaborative locus of agency in CSCL. In T. Koschmann, D. Suthers & T. W. Chan (Eds.), Computer supported collaborative learning 2005: The next 10 years! (pp. 632-640). Mahwah, NJ: Lawrence Erlbaum Associates.

Stahl, G. (2006). Group cognition: Computer support for building collaborative knowledge. Cambridge, MA: MIT Press. Strijbos, J. W.,

Van Langenhove, L., & Harre, R. (1999). Positioning. Oxford: Blackwell.

Boundaries and roles

From Jsarmi

Revision as of 20:55, 21 August 2007

Contents

Boundaries and roles: Social location and bridging work in the Virtual Math Teams (VMT) online community

Abstract

Intro

Positioning Theory and Social Location

Virtual Math Teams at the Math Forum: A Case Study

Data sources and goals

Goals of the Analysis

Case I: Letz check it

Case II: I am only in algebra 1

Case III: Maybe there's another way I;m not seeing

Additional Cases:

we arent getting anything done

Expert turned Deviant

Discussion

References

Views

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