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Roles_in_CSCL

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

Johann Sarmiento, Wesley Shumar: Drexel University

Plan

Define goals/questions

Define Positioning theory, triangle, first order, etc. -> Example?

Data/Methods

Case 1 T2/S2 then ask, is it stable?

tell story of T2, with contrasting cases from 1 and 3 or 4

tell story of T5 up to S4, contrast with case from S1

Wonder about the community level

Conclusions

What do we gain: dynamics, mathematics, change

It might be that we are observing early stages of role differentiation

Understanding the dynamics of roles/activities move us closer to the design of activity systems (i.e. tasks, roles, resources) that are productive, but interaction is contingent on ist situatedness

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 Interaction

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 of such situation might recognize instead that there are some preferred actions that are understood by members of a culture to follow from particular actions, and that such actions are the social reality of the rights, duties or obligations of a person in interaction. Any competent member of a culture might recognize such rights or obligations as being the conversational or interactional moves which are open to the person being positioned in that particular context. Co-participants might position each other in different ways throughout an interaction (interactive positioning) or they might attempt position themselves directly (reflexive positioning). 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 such 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, 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 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?

Positioning Case I: Letz check it

The excerpt below corresponds to the second time that this team meets together to participate in our Virtual Math Teams pilot project. In this session, they were presented by the facilitator with a list of nine questions collected by the project staff from all the teams that participated in the first session, and some additional ones created by the staff based on the teams' work.

 144  mathfun:	letz start working on number 8	 
 145  bob123:	we already did that yesterday	 	 
 146  qwer:	we did?	 
 147  mathfun:	but we did it so that there was only right and down	 
 148  bob123:	i mean tuesday	 	 
 149  mathfun:	i guess we will do it with left and up?	 
 150  qwer:	It would be almost the same.	 
 151  bob123:	it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1)	 	 
 152  bob123:	try it if you like	 	 
 153  mathfun:	nah	 
 154  mathfun:	if you are so sure...	 
 155  bob123:	i'm not	 	 
 156  bob123:	actually	 	 
 157  bob123:	take out the -2 and the -1	 	 
 158  mathfun:	then letz check it  
 159  bob123:	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  bob123:	yeah	 	 
 162  bob123:	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?

 - Chat Excerpt from Team 2, Session 2 -

The positioning dynamics of these short chat conversation are significantly rich. For our purposes, we will concentrate on the ways that this kind of interactional work relates to the teams' joint problem solving. 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 that could be supported or resisted in many different ways, but to which every one in the group has equal rights or possibilities for action. Bob123 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 all the members of the team at least in two different planes. First, with respect to their current alignment towards the task they are about to embark on. Second, with respect to their history together and the work that they did and might be accountable for remembering or responding for. Qwer questions such positioning (146) and mathfun mitigates the objection (147) ratifying the team's position in relation to their past activity but offering for assessment an alternative positioning for their current activity, that is, that despite them having done the problem "so that there was only right and down" they could now do it "with left and up?" 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." It is important to notice, however, not just that this activity is being conducted in a shared fashion (i.e. it could be that this role tends to revolve about the same person) nor that the way it is conducted is highly situated on their present concerns and their past experience together (i.e. over time it could end up being performed through some similar series of interactional moves) but that as the activity unfolds the participants are literally moving in their relative position to each other, to the current activity, and even to their past and future activities and the resources they entail.

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. 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 shiften 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 bob 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 shiften from expert-audience to, perhaps expert-collaborators, in a qualitatively significant way. This new orientation towards collective activity has a different alignment of the group members towards participation when compared to what had been established in the previous moment, and as such represents a significant change in knowledge building positioning within a session.

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 session 1. We can also investigate whether these positions are maintained or transformed for the rest of the two remaining sessions. We can use the following snippets as data to explore these questions:

 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  bob123:	tan of angle b=3/2, so you do tan^-1(3/2)=56.30993247	 
 204  bob123:	...	 
 205  mathfun:	which is ....?
 206  bob123:	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  bob123:	tangent=opp/adj	 
 212  bob123:	sine=opp/hyp	 
 213  Sith91:	ohh... i c	 
 214  bob123:	cosine=adj/hyp	 
 215  bob123:	cotangent is reciprocal of tangent	 
 216  ModG:	I posted the description of the world in the whiteboard
 217  bob123:	cosecant is the reciprocal of sine	 
 218  bob123:	and secant is reciprocal of cosine	 
 219  Sith91:	ok... thx	 
 220  bob123:		 
 221  Sith91:	so,... that would be 6/4=3/2	 
 222  bob123:	and then you set tan(angle B)=3/2	 
 223  bob123:	so tan^-1(3/2)=angle B	 
 224  bob123:	so then angle B=what i said earlier	 
 225  Sith91:	oh... sry, didnt see that	 
 226  mafun:	How many ways are there to get from A to B?
 227  bob123:	infinite, if you count overlap	 
 228  bob123:	otherwise, a lot	 
 229  Sith91:	yep

Session 1, Team 2

From Session 4:

 34  mathisfun:	 so bob u there?   
 35 bob123:	 yeah  
 36  mathisfun:	 k letz get started   
 37 bob123:	 the way i see it, you do the same thing you did with the circle  
 38  mathisfun:	 alright   
 39  mathisfun:	 so letz draw the triangular prism   
 40  mathisfun:	 there   
 41  mathisfun:	 so should i make the bird's eye view?   
 42  bob123:	 yeah  
 43  mathisfun:	 k   
 44  mathisfun:	 there   
 45 bob123:	 draw a line segment  
 46 bob123:	 on it  
 47  mathisfun:	 aren't we able to find out the little segments 
                        with an arrow to them?   
 48  mathisfun:	 bob?   
 49  eModerator joins the room  
 50 bob123:	 huh   
 51 bob123:	 oh   
 52 bob123:	 yeah   
 53 bob123:	 coordinate   
 54 jtcc:	 joins the room  
 55  eModerator:	 leaves the room   
 56  mathisfun:	 so then isn't the little length found too?    
 57 bob123:	 using law of cosines   
 58  mathisfun:	 or degrees    
 59 bob123:	 or maybe there's another way i;m not seeing   
 60 bob123:	 ?

Positioning Case II

Team 5. Session I

 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 :)

Conclusion and discussion

We have identified a set of interactional methods through which participants deal with the discontinuities relevant to their joint activity. Our analysis of this “bridging work” shows that it is a highly interactive achievement of groups and, possibly, very consequential undertaking for their knowledge building over time. In particular, we show how positioning plays a special role in the dynamic way in which teams construct and maintain a joint problem space over time, manage their ongoing participation, and constitute their collective history. Our analysis illustrates the dynamics of positioning in the collective engagement with past and projected work. Furthermore, our analysis suggests that these attempts to establish continuity in collaborative problem solving involve the collective recognition and use of discontinuities or boundaries as resources for interaction (e.g. temporal or episodic discontinuity), changes in the participants’ relative positioning toward each other as a collectivity (e.g. co-narrators and interactive audience), and also the use of particular orientations towards knowledge resources and perspectives (e.g., the problem statement, prior findings, what someone professes to know or remember, etc.). In addition, we suggest that the lens of positioning affords us a more interactive perspective on participation and engagement than the traditional concept of role, at least, within the analysis of long-term, multi-team learning interactions.

As Harre and Mogaddam (2003) point out, "since positionings are always relational, that is by positioning someone in a certain way someone else is thereby positioned relative to that person, the situation may look far more 'designed' by those who benefit from the positioning than is justified by an empirical study of the beliefs of the people in question" (p. 7).

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