Participation Frameworks and Decision-making in Problem-Solving Chats

1
Participation Frameworks and Decision-making in
Problem-Solving Chats

• Progress Report
• January 12, 2005

2
Problem Solving

• We have observed in the chat transcripts that
  problem-solving is a set of mathematical actions
  whereby actors come to constitute the problem as
  the activities performed to produce a solution.

3
Problem Solving

• This notion of the problem is different from the
  problem posted on the website.
• With an interactional approach, the problem
  participants are concerned with is their own
  emergent sense of what they are doing.
• In this view, the problem emerges by working to
  discover what the problem is.

4
Problem Solving

• The discovery of the problem may or may not occur
  during the chat as a collective achievement.
• Participants in chats who have engaged in this
  discovery off-line typically report their
  work in ways that do no implicate the
  participation of recipients in the performance of
  the math activities described in the report.
• Alternatively, participants may organize
  themselves to collectively discover the problem
  by inviting and allocating the participation of
  actors in and as the discovery of the problem.

5
Problem Solving

• Whether they do the discovery offline or with the
  participation of chat participants, the problem
  is something that actors must produce for
  themselves using the resources afforded them by
• their individual (and, when appropriate
  distributed) competence to recognize what
  mathematical actions may be appropriate to
  perform and to actually specify and perform those
  actions,
• the problem information posted on the website,
  and
• the technical affordances of the chat environment
  itself.

6
Problem Solving

• In the next slide, we see an example of how an
  actor works to produce the extra problem as a
  collectively endorsed interpretation of the
  posted text on the website.
• What is apparent in this excerpt is that whatever
  is posted as the problem text is not what
  participants take to be the problem, but serves
  as a resource by which they come to constitute
  the problem in terms of projected or achieved
  mathematical activities.

7
(Powwow 2-2)
8
Problem Solving

• In the next example, AVRs encounter with the
  problem text leads to the formulation of a
  first problem for participants, i.e.,
  determining the area of each triangle referenced
  in the problem text.
• This excerpt also shows that in certain
  circumstances, problems emerge in the
  interaction.
• One method actors use in problem solving
  situations is to use available resources to
  produce an initial problem in terms of
  projected mathematical activities.
• In other words, a problem may actually consist
  of a sequence or series of problems constituted
  by an actor or by actors each of which is made
  provisionally relevant by prior problems, math
  activities and produced results.

9
(PowWow 2-1)
10
Participation Frameworks

• Close inspection of the chat transcripts has made
  evident that chat participants organize their
  participation to achieve what they consider to be
  the task at hand.
• The task at hand is not the same in all chats,
  or even in the same chat at different times or
  locations in sequence of postings (What was it
  Heraclitus said?).

11
Participation Frameworks

• While actors may engage in a wide variety of
  activities, there are two kinds of participation
  frameworks, which appear to be characteristic
  features of PowWows, to which participants in
  chats appear to be oriented
• Expository participation framework is one in
  which an actor reports on mathematical actions
  that have yielded relevant and meaningful results
  in ways that do not implicate the participation
  of other actors in the specification of or
  performance of these actions or the production of
  these results.
• Exploratory participation framework is one in
  which actors iteratively
• participate in decision-making regarding what
  mathematical activities to perform,
• specify and perform decided-upon mathematical
  activities, and
• assess these activities and the results obtained
  through them.

12
Expository Participation

• An actor reports on the sense he or she has made
  of a problem.
• Reporting is done through a sequence of multiple
  postings in which a sequence of mathematical
  activities that produced a relevant result is
  described.
• Such reporting has many of the characteristics of
  storytelling or news reporting (Sacks, 1992
  Jefferson, 1978).

13
Expository Participation

• In the next excerpt, AH3 produces a report using
  an organization remarkably similar to the
  organization of a story as described by Jefferson
  (1978)
• Storytelling can involve a story preface with
  which a teller projects a forthcoming story, a
  next turn in which teller produces the story, a
  next in which a coparticipant aligns himself as a
  story recipient, a next in which teller produces
  the story, and a next in which story recipient
  talks by reference to the story. Further, the
  story preface can have consequences for the
  storys reception, and thus a rather extended
  series of turns at talk can be seen as a coherent
  conversational unit. (Jefferson 1978, p. 219)

14
(PowWow 2-2)
15
(powwow 18)
16
(powwow 18)
17
(powwow 18)
18
Exploratory Participation

• Actors may engage in what is recognizable and
  observable as problem-solving and
  decision-making, in which
• Candidate projected mathematical activities are
  identified (to some degree of relevant
  specificity) and put forward for consideration by
  others in the chat.
• Decisions are made with respect to uptake of
  (i.e., allocating participation in) these
  projected mathematical activities.

19
Exploratory Participation

• In the next example, AME invites recipients to
  consider a projected set of math activities.
• The matter is considered but is identified as
  possibly problematic by AZN.
• Rather than abandon the projected course, AME
  modifies his proposal and suggests a different
  allocation of participation in which he takes up
  the projected set of activities while other
  participants continue with the activities in
  which they were engaged.
• LIF, on the other hand, offers an alternative set
  of math activities for recipients to consider.

20
(PowWow 9)
21
Exploratory Participation

• If and when a projected set of mathematical
  activities is endorsed (i.e., decided upon,
  usually through a consensus-like set of decision
  procedures), actors
• Specify and engage in the activities that had
  been projected, and
• Assess their ongoing actions and any results
  obtained in performing these actions for how they
  constitute members sense of the problem.

22
Participation Frameworks

• Both exploratory and expository participation
  frameworks may occur in the same chat.
• Which framework members elect to deploy is a
  members matter that is worked out in situ and is
  independent of the prior accessibility or
  availability of the problem information as
  posted on the website.

23
Next Steps

• Examine the way decision making is done in these
  chats, especially with respect to the
  organization of participation in the chat.
• Continue to detail how purportedly solvable math
  problems emerge in terms of
• inviting participation in projected math
  activities,
• specifying of what both the math activities and
  participation consist, and
• assessment of participation in math activities in
  terms of results and their relevance for
  subsequent action.

24
Next Steps

• Continue to detail how reports are produced.
• Continue to examine the chats for the
  interactional basis of observed statistical
  results.