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The Organization of Collaborative Math Problem Solving Activities across Dual Interaction Spaces

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Collaboratively investigate geometric patterns made by sticks. Original pattern (Session 1) ... the 3rd stage of the hexagonal pattern, yet they used it as a resource ... – PowerPoint PPT presentation

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Title: The Organization of Collaborative Math Problem Solving Activities across Dual Interaction Spaces


1
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)
Epsilon (Soller Lesgold, 2003)
Belvedere chat (Suthers et al., 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

5
Data
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
  • 5/16/06 708 726
  • Math Task
  • Collaboratively investigate geometric patterns
    made by sticks

Original pattern (Session 1)
6
Excerpt 1 Co-construction of the stick-pattern
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?
Qw
137
Jas
wait can someone highlight the hexagonal array
on the diagram? I dont really see what you mean
hmmokay
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
It might be easier to see it as the 6 smaller
triangles
yes
Like this?
Qw
137
Jas
so should we try to
Input side length output triangles
yup
11
Noticings
  • Mutability of contents
  • 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 representationsdurin
g 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 groups 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), 121-151.
  • 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), 337-367.
  • Goodwin, C. (2000). Action and Embodiment Within
    Situated Human Interaction. Journal of
    Pragmatics, 32, 1489-1522.
  • Hanks, W. F. (1992). The indexical ground of
    deictic reference. In A. Duranti C. Goodwin
    (Eds.), Rethinking context Language as an
    interactive phenomenon (pp. 43-76). 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 716-722, 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.
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