Bridging: Interactional mechanisms used by online groups to sustain knowledge building over time

1. Bridging: Interactional mechanisms used by online groups to sustain knowledge building over time Johann W. Sarmiento College of Information Science & Technology Virtual Math Teams @ The Math Forum Drexel University

2. Goal This 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 the teams’ knowledge building over time.

3. Studying Group Cognition in VMT • Mathematics as social practice • The group/team as the unit of analysis • Interactional dimmension: • Micro-level co-construction and management of problem-solving resources • Organization of participation over time and across colectivities

4. Pointers of a Theoretical Framework • The creative construction and maintenance of a “joint problem space” (Roschelle, 1993) • Group Cognition as Interaction (Stahl, 2006) • The interplay between Synchronic and Diachronic Interactions (Sawyer, 2003)

5. Team Sessions * A VMT Case Study Teams • Upper middle school & high school • Across 5 different states • Invited teachers selected students • Groups mixed across schools • Membership varied slightly • Group size: 3-5 students • Four 1hr-sessions, 2 weeks • New virtual rooms for each session • Light facilitation and feedback in-between sessions • Anonymous • Open-ended, creative task partially self-regulated • Data: Text transcripts and Whiteboard animations

6. Sample Trajectory

7. “The Grid World” Pretend you live in a world where you can only travel on the lines of a grid. You can't cut across a block on the diagonal, for instance. Your group has gotten together to figure out the math of this place. For example, what is a question you might ask that involves points A and B?

8. The VMT Collaboration EnvironmentPersistent Chat & Whiteboard, Explicit references

9. Session 1 Session 2 e w d e Team A d g g q i Team B b (A) Case 1 [Session 2, Team 5] 302 gdo: now lets work on our prob 303 drago: last time, me and estrick4 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 mw3: 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

10. (B) Case 2. [Session 2, Team 2] 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

11. (C) Case 3[Session 4, Team 5] fangs: uh... fangs: where'd we meet off.... fangs: i remember gdog: i was in ur group fangs: that we were trying to look for a pattern gdog: but i didn't quite understand it gdog: can u explain it to us again fangs fangs: with the square, the 2by 2 square, and the 3by2 rectangle fangs: sure... fangs: so basically... gdog: o yea gdog: i sort of remember fangs: we want a formula for the distance between poitns A and B drago: yes... fangs: ill amke the points MFmod: since some folks don't remember and weren't here why don't you pick up with this idea and work on it a bit fangs: okay fangs: so there are those poitns A and B fangs: (that's a 3by2 rectangle fangs: we first had a unit square fangs: and we know that there are only 2 possible paths... fangs: ill drwa the square fangs: in a 2by2 square... drago: ok... fangs: there are i think... 6? fangs: so we're trying ot find a pattern here fangs: lemem check on the 2by2 square fangs: i see only 4 actually drago: I see 6 fangs: ken u show me

12. Initial Observations • Specific interactional mechanisms are used by groups in the ongoing construction of a “sustained” joint problem space • These mechanisms underlie the relationship between synchronic and diachronic interaction • This kind of interactional activity seems to combine three basic elements: • Temporal or sequential organization of experience • Management of participation • Creation and management of tasks, problem-solving resources and their corresponding epistemic stance

13. Three aspects of interaction involved in “bridging” work?

14. Further Questions • Can different degrees of “success” be identified across instances of bridging work? How can this be assessed interactionally? • Were the teams that engaged in bridging work “more actively” better able to overcome the instability of their membership and the their problem-solving activity (e.g. as represented by the depth of exploration and number of problems attempted)? • Can these analyses of bridging activity inform further design work?

15. Designing supports for bridging? • Improving Referencing Supports • Revisiting “Persistence” • Longitudinal cross-team collaboration

16. Acknowledgements The Virtual Math Teams Project is a collaborative effort at Drexel University. The Principal Investigators are Gerry Stahl, Stephen Weimar and Wesley Shumar. A number of Math Forum staff work on the project, especially Stephen Weimar, Annie Fetter and Ian Underwood. The graduate research assistants are Murat Cakir, Johann Sarmiento, Ramon Toledo and Nan Zhou. Alan Zemel is a post-doc. The following visiting researchers have spent 3 to 6 months on the project: Jan-Willem Strijbos (Netherlands), Fatos Xhafa (Spain), Stefan Trausan-Matu (Romania), Martin Wessner (Germany), Elizabeth Charles (Canada). The ConcertChat software was developed at the Fraunhofer Institute IPSI in Darmstadt, Germany, by Martin Wessner, Martin Mühlpfordt and colleagues. The VMT project is supported by grants from the NSDL, IERI and SoL programs of the US National Science Foundation. The perspectives expressed in this paper are those of the authors, not necessarily NSF or others.

17. (B) Case 4. [Session 2, Team 2] 323 drago: ok.... 324 drago: so 325 gdo: square root of 45 326 mathwiz: but you have to move on the grid lines, right? 327 gdo: 3^2+6^2=c^2 right? 328 drago: no 329 drago: you can't go diagonal 330 gdo: ok 331 drago: the problem before said so, but you weren't here 332 gdo: so the hypotenuse is not square root of 45? 333 gdo: i was on team 2 334 drago: I mean 335 drago: it is 336 gdo: but moved to team 5 337 gdo: since u guys didn't have enough people 338 drago: but, we can't move diagonally since that would be cutting through the grid 339 mathwiz: the hypotenuse is fine, but for the problem, you have to go on the grid lines 340 gdo: ok 341 drago: so 342 mathwiz: it's like, you can't walk in water, and the lines are dry lines 323 drago: ok....