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doi:10.7282/T32N5096

In his analysis of student-to-student discursive interactions solving a mathematical problem referred to as the Taxicab Problem, Powell (2006) posited the notion of a socially emergent cognition. Powell described this type of cognition as "a process through which ideas and ways of reasoning materialize from the discursive interactions of interlocutors that go beyond those already internalized by any individual interlocutor." With that in mind, the purpose of this analytic is twofold: 1) to highlight the key discursive interactions in the Taxicab Problem sessions that lead to socially emergent cognition, and 2) to identify any observable patterns in the structure of the discourse.

In Powell (2006), the analysis of the student-to-student discourse was carried out using a framework based on work by Davis (1997). That discourse analysis framework contained four categories, defined as follows:

1. Evaluative - interlocution for the purpose of judging the correctness of a statement made by a partner.
2. Informative - interlocution for the purpose of requesting information or contributing information to satisfy a request or need.
3. Interpretive - interlocution for the purpose of understanding or clarifying a partner's statement, thoughts or intentions.
4. Negotiatory - interlocution for the purpose of mutually shaping or recasting a group's shared understanding or meaning of a given idea.

Powell (2006) indicated that negotiatory interlocution was the necessary precursor to socially emergent cognition, with sociomathematical norms (Yackel & Cobb, 1996) playing a significant role in shaping the negotiatory interlocution. However, since the publishing of Powell (2006), additional discourse analysis frameworks have been introduced. One such framework is Accountable Talk(SM) (Michaels, O'Connor & Resnick, 2008), which considers discourse as falling into three broad categories:

1. Accountability to the Learning Community - talk aimed at gaining clarity on what others are saying or thinking.
2. Accountability to Standards of Reasoning - talk aimed at presenting original reasoning or pressing for, challenging or adding on to existing reasoning.
3. Accountability to Knowledge - talk aimed at contributing or recollecting relevant factual knowledge.

In this analytic, a three-phase pattern of interlocution leading to socially emergent cognition is observed and highlighted. This three-phase pattern, referred to as Structured Collaboration (consisting of a preparation phase, a negotiation phase and a closure phase), extends Powell's discourse analysis framework by: 1) incorporating Accountable Talk as a useful norm that enhances negotiatory interlocution, and 2) adding what amounts to a well-defined beginning and a well-defined end to the negotiatory interlocution, thereby making it more visible and, hopefully, more repeatable for other collaborative groups.

REFERENCES:

Powell, A. (2006). Socially emergent cognition: particular outcome of student-to-student discursive interactions during mathematical problem solving. Horizontes, 24(1) 33-42.

Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching. Journal for Research in Math Education, 28(3), 355-376.

Michaels, S., O'Connor, C., Resnick, L. (2008). Deliberative Discourse Idealized and Realized: Accountable Talk in the Classroom and in Civic Life, Studies in Philosophy and Education, 27(4), 283-297.

Yackel, E. & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.

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