How a Virtual Math Team Structured its Problem Solving

To develop a theory of small-group interaction in CSCL settings, we need an approach to analyzing the structure of computer-mediated discourse. Conversation Analysis examines informal face-to-face talk in terms of a fine structure of adjacency pairs, but needs to be adapted to online textual interaction and extended to analyze longer sequences built on adjacency pairs. This paper presents a case study of students solving a math problem in an online chat environment. It shows that their problem-solving discourse consists of a sequence of exchanges, each built on a base adjacency pair and each contributing a move in their collaborative problem-solving process. Structuring Group Cognition at Multiple Levels A year ago in my opening keynote talk (Stahl, 2009a) at the International Conference of Computers in Education (ICCE 2009) in Hong Kong, I claimed that the discourse of group cognition (Stahl, 2006) has a hierarchical structure, typically including the following levels, as illustrated with a particular case study from the Virtual Math Teams (VMT) Project (Stahl, 2009c): a. Group event: E.g., Team B’s participation in the VMT Spring Fest 2006. b. Temporal session: Session 4 of Team B on the afternoon of May 18, 2006. c. Conversational topic: Determining the number of sticks in a diamond pattern (lines 1734 to 1833 of the chat log of Session 4). d. Discourse move: A stage in the sequence of moves to accomplish discussing the conversational topic (e.g., lines 1767-1770—see Logs 1-10 below). e. Adjacency pair: The base interaction involving two or three utterances, which drives a discourse move (lines 1767 and 1769). f. Textual utterance: A text chat posting by an individual participant, which may contribute to an adjacency pair (line 1767). g. Indexical reference: An element of a textual utterance that points to a relevant resource. In VMT, actions and objects in the shared whiteboard are often referenced in the chat. Mathematical content and other resources from the joint problem space and from shared past experience are also brought into the discourse by explicit or implicit reference in a chat posting. The multi-layered structure corresponds to the multiplicity of constraints imposed on small-group discourse—from the character of the life-world and of culture (which mediate macro-structure) to the semantic, syntactic and pragmatic rules of language (which govern the fine structure of utterances). A theory of group cognition must concern itself primarily with the analysis of mid-level phenomena—such as how small groups accomplish collaborative problem solving and other conversational topics. The study of mid-level group-cognition phenomena is a realm of analysis that is currently underdeveloped in the research literature. For instance, many CSCL studies focus on coding individual (microlevel) utterances or assessing learning outcomes (macro-level), without analyzing the group processes (midlevel). Similarly, Conversation Analysis (CA) centers on micro-level adjacency pairs while socio-cultural Discourse Analysis is concerned with macro-level identity and power, without characterizing the interaction patterns that build such macro phenomena out of microelements. Understanding these mid-level phenomena is crucial to analyzing collaborative learning, for it is this level that largely mediates between the interpretations of individuals and the socio-cultural factors of communities. The analysis in this paper illustrates the applicability of the notion of a ‘long sequence’ as vaguely suggested by both Sacks (1962/1995, II p. 354) and Schegloff (2007, pp. 12, 213). A longer sequence consists of a coherent series of shorter sequences built on adjacency pairs. This multi-layered sequential structure will be adapted in this paper from the informal face-to-face talk-in-interaction of CA to the essentially different, but analogous, context of groupware-supported communication and group cognition, such as the text chat of VMT. I will show how a small group of students collaborating online constructed a coherent long sequence, through which they solved the problem that they had posed for themselves. Methodologically, it is important to note that the definition of the long sequence—like that of the other levels of structure listed above—is oriented to by the discourse of the students and is not simply a construct of the researcher.