Cognition as Communication: Rethinking Learning-by-Talking Through Multi-Faceted Analysis of Students' Mathematical Interactions

Abstract

In this article we take a close look at the now popular claim that many school subjects, and mathematics among them, are best learned in an interactive way, through conversation with others. Two types of specially devised analytical tools are used to analyze the data coming from a two-month-long series of interactions between two 13-year-old boys learning algebra. Focal analysis gives us a detailed picture of the students' conversation on the level of its immediate mathematical contents and makes it possible to assess the effectiveness of communication. This is complemented by preoccupational analysis, which is directed at meta-messages and examines participants' engagement in the conversation, thus possibly highlighting at least some of the reasons for communication failure. What we managed to see with the help of our special analytic tools led to a two-layered set of conclusions: It changed our opinion on learning-by-talking, and it also forced us to revise some of the basic assumptions with which we began our study. First, while having a close look at the pair of students working together, we realized that the merits of learning-by-talking cannot be taken for granted. Because of the ineffectiveness of the students' communication, the collaboration we had a chance to observe seemed unhelpful and lacking the expected synergetic quality. Second, on the meta-level, we concluded that what can be seen in classrooms does not make much sense as long as thinking is regarded as a self-sustained factor that regulates communication. For us, thinking became an act of communication in itself. This reconceptualization led to the disappearance of several traditional dichotomies that initially barred our insights: the dichotomy between "contents of mind" and the things people say or do; the split between cognition and affect and the distinction between individual and social research perspectives.