1. Murat P. Cakir, Alan Zemel, Gerry Stahl
The Organization of Collaborative Math Problem Solving Activities across Dual Interaction Spaces
Murat P. Cakir, Alan Zemel, Gerry Stahl

2. Introduction Dual interaction spaces
Combination of two quasi-synchronous online communication technologies
(e.g. text-chat and a shared workspace)
Popularly used in many CSCL applications
Traffic Simulator (Jermann, 2002)
Belvedere + chat (Suthers et al., 2003)
Epsilon (Soller & Lesgold, 2003)

3. The VMT Chat Environment
Message
to message
referencing
Explicit
Referencing
Support
Chat
Scrollbar
Whiteboard
Scrollbar
awareness messages

4. Research Questions
What are the affordances of dual interaction spaces?
How do participants coordinate their actions across dual interaction spaces?
How do actions performed in one space inform the actions performed in the other
How do both spaces work together? Is our main interest
The first question highlights our participant centered approach
We will focus on sequences of interactions in which group members co-construct and use semiotic resources distributed across dual spaces
How does the whiteboard compare to chat in terms of its affordances?
The message: actions performed in both mediums set the context in which future actions are made sense of in relation to
Whiteboard objects have a more persistent interactional status as compared to chat content

5. Data Source of excerpts Math Task A team of 3 middle school students
Hexagonal pattern
(Session 3)
Source of excerpts
A team of 3 middle school students
Qwertyuiop, Jason, 137
Third session (3/4)
4 excerpts that sequentially follow each other
TeamC.jno
5/16/06; 7:08 – 7:26
Math Task
Collaboratively investigate geometric patterns made by sticks
Original pattern
(Session 1)

6. Excerpt 1: Co-construction of the stick-pattern
The point: availability of the productions process in chat versus in whiteboard
The sequential unfolding of 137’s initial drawing seemed to have informed Qwertyuiop’s drawing
But Qwertyuiop uses some elements of 137’s drawing strategy in a selective way, as he takes up on 137’s request to draw a grid of triangles
just a grid? ok
Qwertyuiop
137
Jason
Great. Can anyone m ake a
diagram of a bunch of triangles?
yeah

7. Noticings
The whiteboard affords an animated evolution of the shared space that makes the visual reasoning process manifested in drawing actions explicit
can be a very important interactional resource for mathematical sense making

8. Excerpt 2: Where is the hexagon?
How do participants make sense of indexical expressions such as ‘hexagonal pattern’, ‘this’, ‘it’?
Here we observe some of methods they enacted for referencing objects on the whiteboard from chat
Explicitly mark the object on the board
2. Use the pointing finger tool to highlight a section on the shared drawing
Jason’s request is interesting since it projects a response on the whiteboard
Jason’s uptake to 137’s drawing actions comes in when the drawing reaches this stage
After he acknowledged 137’s actions as an adequate response, Jason also demonstrates his understanding of the hexagonal pattern;
he does that by pointing to the first stage of the pattern. Qw
137
Jas
wait– can someone highlight the
hexagonal array on the diagram?
I don’t really see what you mean…
hmm…okay
so it has
at least 6
triangles?
in this, for
instance

9. Noticings
Bringing relevant mathematical objects referred by indexical terms such as “hexagonal array” to other members’ attention often requires a coordinated sequence of actions in both spaces
Participants use explicit and verbal references to guide each other about how a new contribution should be read in relation to prior content

10. Excerpt 3: Persistence & Mutability of Contributions
as we move to the next excerpt in the presentation we see new chat messages, but whiteboard content is pretty much the same except some annotations
chat messages scroll out of the shared visual field, as new postings are contributed.
Moreover, most chat messages respond to immediately prior messages
Yet, the hexagon made by triangles remain on the whiteboard as we moved to the third excerpt
Unlike chat postings whiteboard objects remain on the shared visual space until they are removed by the participants
There is a temporal referential locality between chat messages, whereas drawing are available for referential use for a longer period of time
It might be easier to see it as the 6 smaller triangles
Like this?
yes Qw
137
Jas
so… should we try to…
Input side length; output # triangles
yup

11. Noticings Mutability of contents Persistence
Object-oriented design of whiteboard allows subsequent modifications, which is not a possibility for already posted chat messages
Persistence
Chat area grows linearly, and its contents gradually scrolls off
Chat messages are likely to refer to visually (and hence temporally) proximal messages, and objects visible on the whiteboard
Whiteboard objects remain on the shared visual field until they are removed
This qualifies the whiteboard as the more persistent medium as an interactional resource, (although both spaces are technically persistent)

12. Excerpt 4: Figurative use of representations during problem solving work

13. Noticings
The drawings on the whiteboard have a figurative role in addition to their concrete appearance as illustrations of specific cases:
The particular cases illustrated as concrete, tangible marks on the whiteboard are often used as a resource to investigate and talk about general properties of the mathematical objects indexed by them.
The group’s drawing represents the 3rd stage of the hexagonal pattern, yet they used it as a resource to investigate the properties of the nth stage

14. Conclusion
Actions performed on both interaction spaces constitute an evolving historical context:
What gets done now informs the relevant actions to be performed next, and what was done previously can be reproduced/modified depending on the circumstances of the ongoing activity.
As the interaction unfolds sequentially, the sense of previously posted objects may be modified or become evident.

15. A methodological question
How to systematically pick an excerpt?
This is more challenging than it sounds!
Each excerpt is embedded in a broader interactional context
Some postings are hard to make sense of without access to the broader content
E.g. Qwertyuiop: “each polygon corresponds to 2-sides” thing we did last time does not work for triangles
How to decide upon the length of an excerpt?
Micro-level analysis focuses on sequences of postings that span a few minutes
Problem solving chats span around 2hrs
Some groups discussed the same problem in multiple sessions
How can we get to the macro-level organization of collaborative problem solving activities without loosing the interactional perspective?

16. Thank you for your attention

17. References
Dillenbourg, P., and Traum, D. (2006). Sharing Solutions: Persistence and Grounding in Multimodal Collaborative Problem Solving. The Journal of the Learning Sciences, 15(1),
Garcia, A., and Jacobs, J.B. (1999). The eyes of the beholder: Understanding the turn-taking system in quasi-synchronous computer-mediated communication. Research on Language and Social Interaction, 34(4),
Goodwin, C. (2000). Action and Embodiment Within Situated Human Interaction. Journal of Pragmatics, 32,
Hanks, W. F. (1992). The indexical ground of deictic reference. In A. Duranti & C. Goodwin (Eds.), Rethinking context: Language as an interactive phenomenon (pp ). Cambridge: Cambridge University Press.
Livingston, E. (1995). An anthropology of reading. Bloomington: Indiana University Press.
Mühlpfordt, M., & Stahl, G. (2007). The integration of synchronous communication across dual interaction spaces. Paper presented at CSCL 2007, New Brunswick, NJ.
Stahl, G. (2006). Group Cognition: Computer Support for Building Collaborative Knowledge. Cambridge, MA: MIT Press.
Stahl, G., Zemel, A., Sarmiento, J., Cakir, M., Wessner, M., & Mühlpfordt, M. (2006). Shared referencing of mathematical objects in chat. In S. A. Barab, K. E. Hay, and D. T. Hickey, (Ed.), Proceedings of ICLS2006, the 7th
International Conference of the Learning Sciences, volume 2, pp , Bloomington, IN: Lawrence Erlbaum Associates.
Suchman, L. A. (1990). Representing practice in cognitive science. In M. Lynch, S. Woolgar, (Ed.), Representation in Scientific Practice. Cambridge, MA: MIT Press.
Zemel, A., Shumar, W., & Cakir, M. (2007). The disembodied act: Copresence and indexical symmetry in computer-mediated communication. Paper presented at CSCL 2007, New Brunswick, NJ.