Transcript The Organization of Collaborative Math Problem Solving

The Organization of Collaborative
Math Problem Solving Activities
across Dual Interaction Spaces
Murat P. Cakir, Alan Zemel, Gerry Stahl
Introduction

Dual interaction spaces

Combination of two quasisynchronous online
communication technologies


(e.g. text-chat and a shared
workspace)
Traffic Simulator (Jermann, 2002)
Popularly used in many CSCL
applications
Belvedere + chat (Suthers et al., 2003)
Epsilon (Soller & Lesgold, 2003)
The VMT Chat Environment
Message
to message
referencing
Explicit
Referencing
Support
Chat
Scrollbar
Whiteboard
Scrollbar
awareness messages
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
Data




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

(Session 3)
A team of 3 middle school
students


Hexagonal pattern
Source of excerpts
Collaboratively investigate
geometric patterns made by
sticks
Original pattern
(Session 1)
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
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
Excerpt 2: Where is the hexagon?
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
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
Excerpt 3: Persistence & Mutability of Contributions
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
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)
Excerpt 4: Figurative use of representations
during problem solving work
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
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.
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?
Thank you for your attention
References
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