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Characterizing Bridging: Interactional mechanisms used by Virtual Math Teams to sustain knowledge building over time

Dissertation Report I

Johann W. Sarmiento - College of Information Science & Technology - Virtual Math Teams, Drexel University

To-Dos

  • State your goals... remember this is not your whole dissertation, this is question I!!!. So describe the study as meeting that goal
  • Describe bridging practices: where they happen, how they are deployed, how they proceed
  • Talk about each component in detail, link to other cases (perhaps examples of only one component in action):
  • Participation/Positioining -> Legitimated peripheral participation, situated on people
  • Sequential/Temporal -> Sense of History, sense of unfolding
  • Epistemic Resources -> What is unknown, what is known, knowledge resources and possibilities of knowing
  • Expand the single case to the collection of cases/entire dataset
  • Implications for Design, Implications for a theory of sustained knowledge builidng
  • Findings, That there are mostly 3 relevant gaps in terms of episodes, individual participants and collectivities. Then take each one at a time. Then characterize different methods or purposes, for example the establishment of a joint problem space is sustained, Then talk about implications for design and what still needs to be found out. Emphasize that there was not reuse of the room... USE THIS FACT, for example to analyze how often graphical resources reappeard.

CREATE MAPS of TRAJECTORIES, for instance:

> Team 5> session 1 discovery, session 2 reuse and expansion, session 3 GAP, session 4 failed expansion!
> Team 2> session 1 solved X, we solved X/did we?, ???, dyad/change of roles
> ????
> A trajectory of graphical artifacts for one team
> A trajectory of just participation for all teams
WHAT ARE THE MORE NUANCED WAYS in which CONTINUITY or TEMPORALITY is co-constructed, not just the explicit ones
KANTS critique of pure reason and TEMPORALITY

Abstract

In naturalistic settings, the sustained knowledge building of virtual groups and online communities requires that co-participants overcome a wide range of gaps in their interactions, especially in the context of long-term activity across multiple episodes and collectivities. Here we present an analysis of sequences of online collaborative problem-solving sessions held by K-12 students participating in the Virtual Math Teams (VMT) online community in an attempt to explore to what extent the teams found constituted their activity as a continuos enterprise. Our analysis is aimed at understanding how the teams bridged the apparent discontinuity of their collaborative interactions (e.g. multiple collaborative sessions, teams, and problem tasks) and exploring the role that such bridging activity plays in their knowledge building over time. In particular, we examine whether bridging allows participants to construct and maintain a joint problem space over time and manage their participation based on it. In addition, we reflect on how these insights might inform the design of appropriate computational supports for long-term collaborative knowledge building.

Introduction

Knowledge Building can be defined as "the creation, testing, and improvement of conceptual artifacts" (Bereiter and Scardamalia, 2003, p. 13). Among such conceptual artifacts used as knowledge-in-the-world one can include theories, designs, solution strategies, plans, categories and other reasoning devices we use to make sense of particular aspects of situations we participate in. These resources are theorized to play a key role in the activities that individuals and collectivities engaged in to develop and maintain their understandings over time. For instance, an individual might internalize some resources developed by a group and create a cognitive artifact that later can be used as an interactional resource to do further work by the same or a completely different group (Vygotsky, 1930/1978, 1934/1986, Stahl, 2002). In this sense, knowledge building is primarily interactional activity (collective and individual) comprised of a set of methods through which people-in-interaction develop and advance their understanding -of a math question, a sociological theory, a personal decision, etc. Through the analysis of knowledge building interactions we can recognize the methods use to evolve the current understanding of individuals within a group and also those methods used to advance the understanding of what is known about something by others. In problem solving activity, for example, co-participants create, revise, manipulate, and monitor a set of resources, personal and collective, that allow them to advance their understanding of the problem as such and also project relevant aspects of their activity (e.g. partial results, impasses, reasoning procedures, candidate answers, etc.) towards other individuals or groups in the past or future. This dynamic "joint problem space" is comprised of different conceptual artifacts and is both the target and result of the interactional work of groups engaged in problem-solving over time.

The successful construction and maintenance of a joint problem space—the intersubjective space of interaction emerging from the active engagement of collectivities in problem solving represents one of the central challenges of effective collaborative knowledge building and learning (Roschelle & Teasley, 1995; Stahl, 2006b; Suthers, 2005). Several CSCL studies have shown that it is the interactional manner in which this intersubjective problem space is created and use what determines the success of the collaborative learning experience (Barron, 2003; Dillenbourg et al., 1995) (Chi, 2000; Hausmann et al., 2004; Koschmann et al., 2005; Wegerif, 2006) . The challenge of maintaining a joint problem space is magnified when, as in many naturalistic settings, joint activity is dispersed over time (e.g. multi-session problem-solving engagements, long-term projects, etc.) and distributed across multiple collectivities (e.g. multiple teams, task forces, communities, etc.). As a result of these gaps, sustained collaborative learning in small virtual groups and online communities of learners requires that co-participants “bridge” multiple elements of their interactions continuously as they interact over time— a non trivial and possibly very consequential undertaking. As a result, it seems that an understanding of the interactional mechanisms associated with the overcoming of such gaps can advance our knowledge of how knowledge is built as a distributed or shared resource across participants and how do conceptual artifacts are re-used across collectivities and interactions over time.

The discontinuities emerging from multiples episodes of interaction and multiple participants and their relationship to collective knowledge work have been studied from a number of different perspecitves. The theory of knowledge building (Scardamalia & Bereiter, 1996), for instance, explores the progressive and communal nature of collective-knowledge development and the necessary conditions that allow communities to build knowledge successfully. The gaps that arise among events, perspectives, and people have also been an area of investigation in the study of individual and group creativity (e.g. Amabile, 1983; Sawyer, 2003) as well as in fields such as small-group research (Arrow et al., 2000; Bluedorn & Standifer, 2004), computer-supported cooperative work (CSCW) and knowledge management (Greenberg & Roseman, 2003; Ishii et al., 1993). Despite their interest in this crucial topic, most studies have concentrated on characterizing the visible outcomes of groups and communities overcoming discontinuities and few descriptions have been offered of the mechanisms or methods that lead to such outcomes. Among these outcomes we can list the existence of “information bridgers” in group-to-group collaboration (Mark et al., 2003) , the use of boundary objects in interdisciplinary collaboration (Star, 1989) , and the emergence of “shifting epistemologies” (Bielaczyc & Blake, 2006) and an orientation to knowledge advancement in knowledge-building communities (Scardamalia, 2002). It remains as an open challenge to characterize how these outcomes are actually achieved interactionally or how participants overcome the discontinuities they find relevant to sustain their knowledge building. Here, we concentrate on this type of “bridging activity.” and attempt to describe some of the methods that participants of a particular online collaborative environment use.

More about additional research literature on the notion of bridging

Bridging in the Virtual Math Teams community: A case study

The Math Forum is an online math community, active since 1992. It promotes technology-mediated interactions among teachers of mathematics, students, mathematicians, staff members and other interested parties interested in learning, teaching, and doing mathematics. As the Math Forum community continues to evolve, the development of new forms of interaction becomes increasingly essential for sustaining and enriching the mechanisms of community participation available(Renninger & Shumar, 2002). As an example of these endeavors, the Virtual Math Teams (VMT) project at the Math Forum investigates the innovative use of online collaborative environments to support effective secondary mathematics learning in small groups (Stahl, 2005). The VMT project is an NSF-funded research program designed to investigate sustained collaborative problem solving in computer-supported environments and to characterize how members of the Math Forum’s community of learners constitute their interactions over time to foster their development as learners of mathematics. VMT implements a multidisciplinary approach to research and development that integrates the quantitative modeling of students’ online interactions, ethnographic and conversation analytical studies of collaborative problem solving, and an iterative process of software design.

Central to the VMT research program are the investigation of the nature and dynamics of group cognition (Stahl, 2006a) as well as the design of effective technological supports for quasi-synchronous small-group interactions. In addition, VMT investigates ways in which distributed, asynchronous interactions contribute to the development of an online community of people interested in mathematics. During the Spring of 2005, we conducted a pilot case study to explore issues of continuity and sustainability of collaborative knowledge building over time. In this design experiment, five virtual teams were formed with about four non-collocated upper middle-school and high-school students selected by volunteer teachers at different schools across the United States. The teams engaged in online math discussions for four hour-long sessions over a two-week period. They used the ConcertChat virtual room environment (Wessner et al., 2006) with new rooms provided for each one of the sessions so that participants did not have direct access to the persistent records of the interactions. In the first session, the 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 (Krause, 1986). The 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, the teams were given feedback on their prior work and the work of other teams and were encouraged to continue their work or decide on new problems related to the grid world that they were interested in pursuing. Because of the sequential framing of the tasks provided and the continuous relevance of the properties of the grid world, we consider this a propitious setting for the investigation of members' methods related to continuity of knowledge building. The chats were facilitated by a member of our research project team. In each session, the facilitator welcomed students to the chat, introduced the task, and provided technical assistance regarding the special features of the collaboration environment. The facilitator did not actively participate in the team’s mathematical collaboration. More about the goals, set up, and data sources of this case study.


Figure 1. Team five's composition over the four problem-solving sessions.
(Each colored letter represents one participant. Dotted lines depict movement from one team to another)


Participation in the case study was voluntary in order to better resemble naturalistic interactions. This factor may have motivated the changes in team membership and variations in attendance recorded in our dataset. The variations in group composition were also propitious for the investigation of interactional continuity of the teams. In terms of attendance, two of the participating teams were highly stable (with 2 or more participants attending at least 3 of the 4 sessions), one was highly unstable and the others had mixed patterns of attendance. Figure 1 depicts the trajectory of participation and team composition of one of the teams in our case study (team five). Team five is particularly interesting for our purposes given the fact that for each intermediate session (excluding the first and last), there is at least one participant from the previous session and one newcomer joining the team (in two cases the newcomer was a transfer from another team as signaled by the dotted lines in the figure). Although we will use this team to illustrate most of our findings, even stable teams exhibited similar interactional processes.

The analysis presented in the following sections is aimed at understanding how teams of participants in the VMT online community manage the apparent discontinuity of their interactions (e.g. multiple collaborative sessions, teams and tasks) and exploring the relationship between such activity and the overall knowledge building enterprise over time. We employ the approach of ethnomethodology (Garfinkel, 1967) to examine the sequences of events by using recordings and artifacts from the team sessions in order to describe the ways in which participants established their knowledge-building interactions over time. Ethnomethodology is a phenomenological approach to qualitative sociology which attempts to describe the methods that members of a culture use to accomplish what they do, such as carrying on conversations (Sacks, 1992), using information systems (Button, 1993; Button & Dourish, 1996) (Suchman, 1987) or doing mathematics (Livingston, 1986). As part of the phenomenological perspective, ethnomethodology is based on naturalistic inquiry to inductively and holistically understand human experience in context-specific settings (Patton, 1990). For our current purposes, we examined each of the 18 sessions recorded, paying special attention to the sequential unfolding of the four problem-solving episodes in which each team participated and also the ways that movement of participants across teams triggered bridging work. Constant comparison through different instances of bridging in the entire dataset led to our refinement of the structural elements that define bridging activity and their interactional relevance.

The kind of interactional activity we are interested in is that which allows collectivities to cross over the boundaries of time and link together different episodes of collective action. We expect this type of activity, which we have tentatively labeled "bridging activity, to be achieved through a set of methods used by participants to deal with the discontinuities relevant to their collective engagement. Bridging thereby might tie events at the local small-group 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. Studying bridging may reveal linkages among group meaning-making efforts across collectivities or interactional episodes over time. In addition to the need to understand the interactional nature of bridging, there is also a crucial need to learn more about which aspects of the computer tools provided to support collaborative knowledge building attend to these types of activities, and how such designs might be enacted in particular contexts. In the remaining sections of this paper, we describe the nature of bridging activity in small groups and offer a preliminary characterization of ways in which bridging mechanisms might contribute to sustaining the collaborative knowledge building of small groups in the VMT online learning community.

Linking current tasks and prior activity: " last time, me and estrick came up that..."

In order to identify instances of bridging activity we traced the trajectory of each one of the five teams individually, following the explicit references made by the participants from one session to another. The first step in our analysis consisted then of a detailed examination of the second session of all of the five participating teams where one would expect the team to engage, if relevant, with revisiting prior work. This second session would be, for new participants the first time the encounter the mathematics of the “grid-world,” a world where one could only move along the lines of a rectangular grid. Figure 2 shows how the task was presented to the students in session 1.


Figure 2. Grid world task


Session two was then an opportunity for the work conducted during the first session to become relevant as they were asked to continue working on problems about this grid world. For example, in teams five's previous session, drago and estrick worked on exploring the grid-world and attempted to create a formula for the shortest distance between two points A and B. In session two, two days later, they are joined by two new team members; gdo —who had worked on this problem with another team once before— and mathwiz —who is new to the task and to the team—. At the beginning of the session, the moderator posted on the shared whiteboard a set of questions collected, in-between sessions, from the work of all the teams in session one and complemented with some additional questions added by the moderators. The team was instructed to continue their work by identifying and answer questions from the list which interested them, or to create new questions and work on them. The following was the list of questions presented:

Team Questions:
 1. What is the shortest path along the grid between the two points? 
 2. How many possible routes are there from point A to point B? 
 3. What is the maximum distance from point A to B if you can only travel on each POINT once? 
 4. How many ways are there to get from A to B in rectangle ABCD? 
 5. Make a right triangle with AB as the hypotenuse. What is the area of the circumscribed circle? 
 6. Can you go off the edge and come back somewhere else? 

Moderator Questions inspired in Teams work
 7. What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)? 
 8. How many shortest paths are there from A to B and how does this vary with changes 
   in the positioning of A relative to B? 
 9. Suppose the right and left edges of the grid are connected. 
   How does that change the distances between points? 

After the initial greetings, team five worked on question 6 but ends up abandoning it because they found it too complex. Then, they agreed to work on question 7. After exchanging some ideas about some features of the virtual meeting environment in which they are working, the following chat interaction takes place:

 302 	gdo:    now lets work on our prob (Points to Whiteboard) 
 303 	drago:  last time, me and estrick came up 
 304 	drago:  that 
 305 	gdo:    .... 
 306 	drago:  you always have to move a certain amount to the left/right 
                and a certain amount to the up/down 
 307 	gdo:    what? 
 308 	drago:  for the shortest path 
 309 	drago:  see 
 310 	drago:  since the problem last time 
 311 	drago:  stated that you couldn't move diagonally or through squares 
 312 	drago:  and that you had to stay on the grid 
 313 	gdo leaves the room
 314 	mathwiz: would you want to keep as close to the hypotenuse as possible? 
                  or does it actually work against you in this case? 
 315 	drago:  any way you go from point a to b (Points to line 314) 
 316 	gdo joins the room
 317 	drago:  is the same length as long as you take short routes 
 318 	gdo:    opps 
 319 	gdo:    internet problem 
 320 	gdo:    internet problem 
 321 	drago:  you always have to go the same ammount right, and 
                the same ammount down (Points to line 317) 
 322 	gdo:    ok   (Reference to line 314)   

This excerpt illustrates how the participants of this interaction chose to start an episode of joint activity and "task" themselves. They have started the work of recognizing and defining a problem out of the text of question seven. It is also easy to recognize that they are also engaged in using prior interactions as relevant resources in the definition of their current task or problem. This signals to us that a particular interactional method (a "members' method) might be in use to accomplish such specific work. A close examination of this passage—by attending to the ways that the participants demonstrably orient to the interaction moment-by-moment—can help us develop ideas about how this “bridging activity” is being accomplished.

Initially, we recognize gdo's posting in line 302 as an attempt to initiate some new activity (“now lets work on our prob”) which calls for the group to do some assessment or alignment work. Drago’s response in line 303 (“last time, me and estrick came up”) stands as an uptake of gdo's proposal in a unique way. The juxtaposition between these two postings indicates to us the beginnings of the group's particular orientation to the problem-solving task. The contrast of drago’s “last time” with gdo’s “now”, seems to constitute a particular kind of episodic continuity or “relevant history” for the team. By gdo responding to a call for present action with a report of prior action he has began to constitute prior doings (in which he and others participated) as relevant resources for working on their problem now. In addition, this sequence seems to position gdo and mathwiz as a distinct collectivity from estrick and drago, and opens up the possibility for these two collectivities to orient to each other as such (e.g. who should do assessment work and who should do explanation work). Finally, gdo is offering in line 306 a version of that work which he has begun to present as relevant: “you always have to move a certain amount to the left/right and a certain amount to the up/down”. The posting itself has the structure of a rule-like statement which is, in part, signaled by the use of "always". This posting also contrasts in its temporal orientation from those temporal indexicals presented so far in the interaction ("now" and "last time"). Finally, the posting includes a presentation of how one is to (always) move in the grid-world; something discovered by gdo and estrick in session one. With these sequences of postings, it is as if gdo has opened up a third temporal relevance, that of a generalized understanding of the grid-world which makes prior work not only particular to the past but applicable to their present activity (and possibly their future activity as well). Needless to say, this presentation doesn't make the reported past directly intelligeable to others and the work of assessing its intelligibility, its relevance and usefulness is something that the team has to engaged with subsequently, as a present matter. (See also how this idea was developed by gdo and estrick in session one)

The reply posted by gdo in line 307 (“what?”) and the subsequent elaboration attempted by drago suggest that the posting in 306 may have required additional work for it to be fully sensible for the team. In the subsequent lines we can see the beginnings of an instance of the kind of interactional work necessary to constitute prior work as relevant and useful. Even without a thorough understanding of the mathematical task at stake, one can appreciate the fact that drago elaborates on his initial posting by providing additional task references (308, “for the shortest path”) and adding further references to elements of the past problem-solving activity (310-312, “since the problem last time stated that you couldn’t move diagonally or through squares”). In this way, drago continues to use a variety of resources to organize a potential starting point for the present problem-solving task of the team and, in doing so, he attempts to project that past history onto the current interaction. Other instances of similar activity identified in the work of the teams in session two will allow us to expand this initial characterization of "bridging" activity

"we already did that yesterday:" Bridging three dimensions of interaction to manage the "joint problem space"

As we mentioned before, the setup of the activities in which the teams engaged in was expected to be propitious for them to make issues of continuity of their activity relevant. Two aspects of these design, in particular, were expected to become relevant in the interactions: the existence of multiple teams participating in the same problem-solving activities and the sequential aspect of the four tasks provided with were presented as building on each other. During the analysis of the recorded interactions, we found a series of instances were these aspects played a significant role as relevant concerns for the problem-solving work that the team was engaged in. Here we review a second of such cases in a attempt to contrast it and compare it with our previous case and expand, that way, our description of the central elements involved in these kind of activity.

The following excerpt comes from the second session of team two. Team two was the most stable team in the dataset with three of the four participants from session one returning back. Towards the end of session one, the team discussed a question proposed by mathis: How many (shortest) ways are there to get from A to B? Bob1 offered an answer that applied to the particular arrangement of points A and B that they were considering but there was not significant discussion on why bob1's answer could work. Since this question was included in the list of questions collected by the moderators from all the teams and provided to the team in session two, they see it as a valid task to revisit it for this session.


144  mathis:   letz start working on number 8
145  bob1:     we already did that yesterday
146  qw:       we did?
147  mathis:   but we did it so that there was only right and down
148  bob1:     i mean tuesday
149  mathis:   i guess we will do it with left and up?
150  qw:       It would be almost the same.
151  bob1:     it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1)
152  bob1:     try it if you like
153  mathis:   nah
154  mathis:   if you are so sure...
155  bob1:     i'm not
156  bob1:     actually
157  bob1:     take out the -2 and the -1
158  mathis:   then letz check it

In this sequence, we recognize that the team is also engaged in defining a new current task for themselves and also that some prior activity has become relevant in this process. What that prior activity was, how it relates to the proposed current activity and how the participants are related to it, all seem to be relevant concerns for the team. The way what is reported is framed in this instance, however, seems to contrast with our previously analyzed case. In this case, bob1's posting in line 151 is framed as a problem answer, or a final state of problem solving ("it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1)") and is used by bob1 to explicitly "task" the team with a particular activity: "trying" his formula; a typical activity that one can pursue after producing a candidate solution for a problem. In contrast, in our previously analyzed case, drago's rule-like posting (line 306 "you always have to move...") was presented without explicitly offering any particular activity that the team could pursue based on such report of prior work. Instead, drago's presentation left it for the group to decide how to orient to it and produce the uptake of his report. In contrasting these two cases, it seems as if these are two variants of the same type of bridging activity. In one, a particular task is framed based on a participants re-presentation of a past problem-solving resource (i.e. a prior answer). In the other, no current task is presented explicitly with the re-introduction of a prior resource (i.e. a rule or conjecture). This contrast seems to indicate that the teams are actively engaged with constructing and monitoring the problem-solving task and that part of this work might involve the use of prior resources, which, when introduced might directly or indirectly participate in such aspect of the interaction.

One other contrasting aspect between the two cases seems worth mention. In this exchange, there is no explanation or rationale for why line 151 could be a correct answer but instead the decision to task the group with the testing of that answer seems to be based on how sure bob1 is of "his" answer. In this case, mathis seems to be using the asymetry between bob1 as the one who is reporting a prior answer and the rest of the team, to position's bob1's understanding as sufficient for the team to be satisfied with. In reality, bob1 is not as sure of his answer and his doubts make it relevant for the team to engage together, in a more peer-to-peer manner, with the checking of the proposed formula, as a the current task at hand. In the initial case we analyze, drago as the presenter of the discovery made by him and estrick in the previous session, is positioned as the one who is to respond to questions and assessments about it and as a kind of expert or the one who knows how a particular aspect of the grid world works. The relationship between the presenter and the reported past seems them to be an important aspect that determines how the team organizes its subsequent participation.

In our analysis of the entire dataset we found a few more instances that seemed to belong to the same interactional category as the ones we have presented here (See some other examples: case 3, case 4, case5. ). The deciding criteria that defined such instances included the re-introduction by participants of prior team problem-solving activity as a resource to initiate some new current activity. Although we certainly found fewer instances than we expected and numerous ones where no significant problem-solving activity was initiated out of references to prior doings (see an example), we do not believe that this makes the interactional phenomena behind bridging less interesting.

Once we identified all the instances that seemed to fit the defining criteria, we proceeded to analyze them in order to describe the interactional methods at work. In general, the instances seem involve methods related to collective remembering, narrating or reporting past doings as resources for constructing a new task. These kinds of activities, however, have a level of complexity in the context of sustained collective problem-solving that we want to pursue further. One way to describe what the teams are engaged in, might be to say that they are concerned with what Roschelle and Teasley (1995) described as the construction and maintenance of a "joint problem space." Originally this space was theorized as a "shared knowledge structure" that integrated goals, descriptions of the current problem state, and the awareness of available problem solving actions. Different participants may have asymetrical relationships with these resources but their relevance for the problem-solving task is taken as a collective concern. We have seen that all of these three elements are relevant resources of the interactions we have analyzed but in paying attention to the ways that the participants construct that joint problem space as an interactional space that integrates past doings we also see three basic interactional elements that seem to be at play:

  • Temporal or sequential organization of experience (e.g. what was done in a different episode of activity or at a different time, how does one action relates to something done before, what possible actions might be available at a particular moment, etc.),
  • Management of participation (e.g. who was and was not involved in an activity, who can or should speak about a particular matter and how, what activities such as assessing and responding to assessments are allocated to participants), and
  • Creation and management of tasks, problem-solving resources and their corresponding epistemic stance(e.g. what is the problem and which resources are relevant to it, how to create a current task, what is known and unknown about different relevant resources and by whom, etc.).

Image:BridgingTriangle.gif
Figure 3. Three Interactional Dimmensions Involved in Bridging


Each one of these three dimensions of collective problem-solving interactions play very important roles individually. In each one, a wide array of different methods are used by the groups. The temporal and sequential organization of experience allows the participants to interlink different bounded elements of their interactions within one interactional episode or across a set of them. In this way the participants construct sequences of moves and activities that can be built upon, combined or contrasted as with the turns of a conversation. This sequential unfolding of a single episode of interaction makes problem-solving work a sequencing of creations and manipulations of problem resources which allow a team to collectively structure the exploration of a problem space and develop their understanding of it. Actions are not just immutably sequenced but instead participants engaged in an active structuring of their experience by building linkages about events and activities when relevant. In the case of multiple interactional episodes, the sequentiality and temporal organization of experiences might also require explicit work by the participants so that the interdependence of relevant activities is made relevant to all participants. This particular aspect seemed to come across very centrally in our datased through the participation of the moderators who repeatedly prompted the teams to considered what they had done in previous sessions, to expand ideas they had started to explore or reconsider prior solutions.

Interaction among the members of a group and between them and the resources they create and have access to constitutes the central dynamic that characterizes participation in joint problem solving. Inevitably embedded in their moment-by-moment interaction is the participants' management of their own stance or position (and that of others) by constructing and playing out specific participation frameworks (Goffman, 1981). In these frameworks co-participants situate each other as peers, experts, explainers, audience, and many other positions that more than simple typologies are the outcome of the collective activity in which participants engage. Sometimes these frameworks are directly related to the sequential or temporal structure of activity leading to activities such as an old-timer assisting a newcomer in catching up on current activity. These frameworks are created and recognized through the doings of the participants, and although they might be influenced with past doings or possible future activity, they are primarily a current concern of the interaction. The collective actions that open up and maintain a framework of participation produce a contingent alignment of the participants towards each other and towards the resources of the current activity that can be abandoned, reframed, or sustained as the interaction continues.

Finally, problem-solving interactions usually involve the production, assessment and use of a set of problem resources that are considered relevant, in one way or another, for the collective task of the team. These resources include noticings about specific aspects of the task, references to potentially relevant principles or strategies, manipulations of existing resources, and many other "artifacts" that constitute the material problem space to which the team members have access in different, sometimes asymmetrical, ways. It is through the manipulation of these artifacts, in interaction, that the team sets to do problem-solving. In doing so, participants are engaged in sense-making activity geared towards their own understanding of certain pieces of the problem and also trying to understand how others are seeing, creating and manipulating problem resources as well. It is through the achievement of degrees of coordination that the collective creation, assessment, and manipulation of problem resources can be managed so that the group can function jointly.

After reviewing the entire dataset, we found these three dimensions to be relevant in numerous instances of interaction. In some instances the teams themselves made one of these dimensions the relevant concern for their interactions (See some examples). In a few instances we recognized that the three elements appeared to be interwoven together in a unique way that we have tentatively labeled as “bridging activity.” Although the importance of these individual aspects of collective problem-solving interactions is undeniable and their interdependence obvious, the ways that teams made their intersection relevant for their problem-solving activity seemed to to engage them in unique problem-solving activity which, at the moment, we can only hint at. Sometimes these three aspects of the interaction involved some of the participants but not all of them, sometimes there was a noticeable asymmetry of participation among the parties involved and such "distribution" seemed clearly a condition that participants managed, but in all cases the bridging of prior problem-solving activity was the central focus of attention of the collectivity.

Summary and conclusions

The analysis presented in the previous sections has defined bridging activity as the interactional constitution of a present task using resources from prior interactions. The presence of this type of activity supports the idea that the discontinuities in time related to the sequencing of multiple problem-solving episodes are sometimes relevant resources for small groups engaged in collaborative knowledge building. In particular, bridging activity is associated with the continuity of a team's work. Three main elements appear as the structural components of bridging activity: temporal references, management of participation, and management of problem and task resources. These three aspects of the teams' interactions are interwoven together through a set of members’ methods that allow the teams’ to interlink their knowledge building activity over time. As we have presented it, bridging is not an individual undertaking but the concerted and situated achievement of collectivities.

Bridging activity as we have described it, although very similar to the offering, discussion and advancement of problem-solving proposals within one single interactional episode, seemed to bring a different qualitative dimmension to the team interaction. Other researchers have pointed out that the management of attention and knowledge proposals as well as the roles of the co-participants in establishing join attention are consequential for the collective achievements of small groups (Barron, 2000) (Stahl, 2006b). In the instances we have analyzed we have seen how these interactional processes are especially important for the establishment of continuity of knowledge building over time. The uniqueness of bridging activity appears related precisely to problem-solving proposals that have a "history" and also to the ways that such history becomes a resource for interaction by positioning the teams in a participation framework that shapes their alignment and their standing towards the current task. These factors, as many aspects of any human interaction, are contingent on the moment-by-moment unfolding of the activity which can quickly oscillate between "reported-past" and "current-activity."

Although we have used a few instances of bridging activity to guide the presentation of our analysis, the systematic review of our dataset indicates that this type of bridging activity is common, although not pervasive. The changes in team membership and the sequential nature of the problem-solving episodes and tasks in our data provided a propitious setting for this type of activity in our experiment. Other factors may trigger bridging work as well. All teams in our experiment exhibited this orientation to continuity in different degrees but those that engaged in bridging work more actively were able to better overcome the instability of their membership and the sustainability of their problem-solving enterprise (as represented by the depth of exploration and number of problems attempted). This preliminary observation points to the consequential aspect of bridging work in long-term collaborative problem solving. Different degrees of success can be inferred across instances of bridging work, an aspect of this type of work that remains to be more fully investigated. Interestingly, bridging was repeatedly attempted by moderators when trying to inform teams of other teams’ work and provide feedback, but such attempts were often taken normatively by the teams resulting in a framework of participation that appears to be more driven by the authority of the moderators than by the self-directed agency of the team. In other cases, moderator-initiated bridging attempts appeared unsuccessful because the knowledge claims made were assessed as inappropriate by the teams. This assessment prevented direct engagement with the alleged prior work being presented.

In an attempt to use the observations derived from this initial analysis of bridging activity to inform the design of tasks and computational supports, our subsequent work has attempted to use an additional interactional space implemented through a Wiki. With this strategy we are trying to explicitly encourage and support continuity of the work of an individual team and also cross-team knowledge building. Preliminary results of this work indicate that such bridging spaces do in fact promote the continuity of knowledge building across teams by engaging them in activities such as discovering, exploring, testing, and advancing other teams’ ideas as well as reporting projecting their own ideas towards future action. We expect these findings to help expand the scope of analyses of long-term collaborative interactions and enhance our understanding of collaborative knowledge building in naturalistic settings. In fact, in a recently proposed framework to assess the quality of collaborative processes in single-episode encounters (Spada et al., 2005), some of the proposed dimensions (e.g. “sustaining commitment,” “sustaining mutual understanding,” and “time management”) appear to be amenable to expansion in order to accommodate the long-term dynamics of cross-team collaboration.

Finally, we would like to offer a few reflections regarding the collaboration supports used by the participants while engaged in the activities that we have presented. For the experimental design used, the virtual room that the teams used for each session was not available either to the same team nor to other teams who were working on the same problem (despite the potential usefulness of these cross-team interactions). However, even if these resources would have been made available, it seems to as as if special interfaces are needed so that “raw” recordings of interactions can be effectively used in promoting and supporting bridging work. The reappearance of findings across sessions of teamwork, expressed in text or through pictorial diagrams, could suggest that computational supports for the teams to annotate and mark their own resources for future work and for others to inspect them might be useful, but the structure of such resources needs to be carefully consider. The three elements of bridging work identified (temporal structure, management of participation, and knowledge claims) might provide a tentative framework for such annotation mechanisms. Further research is needed to develop our understanding of how continuity of collaborative knowledge work is achieved by multiple participants and how to translate such 8 knowledge into design principles. This theoretical and applied enterprise would contribute significantly to the pressing need to better understand how the power of virtual distributed teams and online communities can be harnessed to realize the potential of these new forms of interaction to generate and advance learning and knowledge in organizations, communities of interest, academic disciplines, societies, and other types of collectivity.

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