Boundaries and roles
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===Conclusion and discussion=== | ===Conclusion and discussion=== | ||
Revision as of 22:26, 6 August 2007
Contents |
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
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 single episodes in which a small group engages in problem solving tasks to longitudinal development of online communities of learning and knowledge building. These different arrangements of human activity 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 become 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 start by outlining the basic concepts of positioning theory, a dynamic lens on the notion of roles which focuses its attention on "dynamic aspects of encounters in contrast to the way in which the use of 'role' serves to highlight static, formal and ritualistic aspects" (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 research and design work.
Positioning Theory
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 set of "rights and obligations" recognized by any competent member of a culture as being the conversational or interactional moves which are open to the interactant being positioned in a particular context (Van Langenhove & Harre, 1999). Co-participants might position each other in different ways throughout an interaction (a.k.a. interactive positioning) or they might attempt position themselves directly (a.k.a reflexive positioning).
As an example, consider the following interaction taken from the dataset fully described in a later section. 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 recognize that MFMod, the facilitator of the session, initiates a sequence of activities in line 106 by position herself as a member of a general collectivity ("we") in charge of tasking the students with what they are supposed to do. This task, in turn, also frames a situation in which students are positioned as being in a world with certain navigation rules. In line 115, MFMod explicitly position all the students present in the online chat at that moment, as those who are to "figure out the math" of such imagined world, and presents a way of doing it: asking a math question that involve two points in a grid. The set of possible options for the students is certainly very varied, both, within the "participation framework" that is being put forward, or within a new one that would need to be presented and upheld in contrast to the current task. 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. This 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 central to positioning theory...
Before presenting our analysis of how positioning theory 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.
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 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.)
Positioning Case I
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?
Session two of Team two. Analysis of how bob positions himself as the one who knows (what was done and the solution to the question), why "being sure" matters to mathfun and how not being sure opens up the possibility of the group taking a different course of action (checking bob's equation in line 151). This new activity has a different alignment of the group members towards participation that what had been established up to that point, so this is a change in positioning within a session.
In addition, we can ask, whether this type of positioning (bob reporting on his knowledge) appeared in session 1 and whether it continues 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).
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.
Harre, R., & Moghaddam, F.M. (Eds.). (2003). The self and others: Positioning individuals and groups in personal, political, and cultural contexts. Westport, CT: Praeger.
Van Langenhove, L., & Harre, R. (1999). Positioning. Oxford: Blackwell.
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.
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.,
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.
