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Participation Frameworks and Decision-making in Problem-Solving Chats. Progress Report January 12, 2005. Problem Solving.

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

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**Participation Frameworks and Decision-making in**Problem-Solving Chats Progress Report January 12, 2005**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.**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.**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.**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.**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.**Problem Solving**• In the next example, AVR’s 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.**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?).**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.**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).**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): “[S]torytelling 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 story’s reception, and thus a rather extended series of turns at talk can be seen as a coherent conversational unit.” (Jefferson 1978, p. 219)**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.**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.**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.**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 situand is independent of the prior accessibility or availability of the “problem information” as posted on the website.**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.**Next Steps**• Continue to detail how reports are produced. • Continue to examine the chats for the interactional basis of observed statistical results.

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