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For EARLI members only. Not for onward distribution. Social practices of group cognition 201 • An acceptance is made by someone else (Avr in line 22) on behalf of the group: (“Right!”). • There is an elaboration of the proposal by members of the group. The proposed work is begun, often with a secondary proposal for the first sub- step (such as Sup’s new proposal bid in line 23). But here the pattern breaks down. It is unclear to us as analysts what Sup’s proposal bid, “Proportions” is proposing. Nor is it responded to or taken up by the other group members as a proposal. Avr’s lines 24 and 25 ignore it and seem to be reporting on Avr’s efforts to work on the previous proposal to draw the altitude. Breakdown situations are often worth analyzing carefully, for they can expose in the breach practices that otherwise go unnoticed, taken for granted in their smooth execution. Our analysis of Sup’s “failed proposal” (in Stahl, 2006d) helps to specify – by way of counter- example – conditions that promote successful proposals in math chats: (a) a clear semantic and syntactic structure, (b) careful timing within the sequence of postings, (c) a firm interruption of any other flow of discussion, (d) the elicitation of a response, (e) the specification of work to be done, and (f) a history of helpful contributions. In addition, there are other interaction characteristics and mathematical requirements. For instance, the level of mathematical background knowledge assumed in a proposal must be compatible with the expertise of the participants and the computational methods must correspond with their competencies. We call the three- step pattern described above a math proposal adjacency pair. It seems to be a common interaction pattern in collaborative problem- solving of mathematics in our chats. We call this a form of “adjacency pair” in keeping with conversation- analysis terminology, even though in chat logs the two parts of the pair may not appear adjacent due to the complexities of chat postings: e.g. line 22 responds to line 20, with line 21 intervening as a delayed response to line 19. As we see in other chats, however, not all student groups adopt this method of making math proposals. Deictic referencing and threading The more we study chat logs, the more we see how interwoven the postings are with each other and with the holistic gestalt of the interactional context that they form. There are many ways in which a posting can reference elements of its context. The importance of such indexicality to creating shared meaning was stressed by Garfinkel (1967). Vygotsky also noted the central role of pointing for mediating intersubjectivity in his analysis of the genesis of the infant- and- mother’s pointing gesture (1978, p. 56). Our past analysis of face- to- face collaboration emphasized that spoken utterances in collaborative settings tend to be elliptical, indexical and projective ways of referencing previous utterances, the conversational context and anticipated responses (Stahl, 2006b, ch. 12). So we provide support for pointing in chat.
For EARLI members only. 202 G. StahlNot for onward distribution. We recently adapted VMT- Chat (Mühlpfordt & Stahl, 2007), a chat environment that not only includes a shared whiteboard, but has functionality for referencing areas of the whiteboard from chat postings and for referencing previous postings (see Figure 12.1). The shared whiteboard is necessary for supporting most geometry problems. Sharing drawings is not enough; students must be able to reference specific objects or areas in the drawing. The whiteboard also provides opportunities to post text where it will not scroll away. The graphical references (see the blue line from a selected posting to an area of the drawing) can also be used to reference one or more previous postings from a new posting, in order to make the threads of responses clearer in the midst of “chat confusion” (Herring, 1999). In one of our first chats using VMT- Chat, the students engaged in a particularly complex interaction of referencing a figure in the whiteboard whose mathematics they wanted to explore (Stahl, 2006c). Here is the chat log from Figure 12.1: 1 ImH: what is the area of this shape [REF TO WHITEBOARD] 2 Jas: which shape 3 ImH: whoops 4 Imh: ahh! 5 Jas: kinda like this one [REF TO WHITEBOARD] Figure 12.1 Screen view of VMT- Chat with referencing. Line 12 of the chat is selected
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Learning Across Sites: New tools, infrastructures and practices - Earli

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