Title: Classification of Spoken Discourse in Teaching the Construction of Mathematical Proof
Description: The purpose of this study is to analyze the patterns of classroom discourse when high school students move from performing prescribed algorithms in order to solve problems for which the process and solution are well-defined to spoken proof, in which ideas are discussed and arguments are formulated and formalized. The study uses a modified version of discourse analysis developed by Arno Bellack and refined for usage in a mathematics classroom by James T. Fey. The analysis framework is supplemented by codes borrowed from Maria Blanton, Despina Stylianou, and M. Manuela David (2009), which is in turn a modified version of a coding system developed by Kruger (1993) and Goos, Galbraith and Renshaw (2002). Twelve mathematics lessons involving two mathematics teachers were recorded, transcribed and coded. Eight of the lessons were classified as “proof-related” and four were designated “non-proof-related.” A lesson designated “proof-related” contained more than half activity that was actively concerned with the construction of proof; whereas a lesson in which no proofs were formulated was designated “non-proof.” Using the codes described above and a variety of qualitative and quantitative measures, the transcripts were examined for constructivist behavior on the part of the teachers and modes of participation on the students’ part.

The findings suggest a relationship between a teacher’s beliefs in constructivist principles and the way in which that teacher instructs proof vs. non-proof. More specifically, a teacher who views her/himself as informed by constructivist pedagogical principles may not evince a sharp distinction between her/his teaching of proof vs. non-proof; but a teacher who does not attempt to incorporate constructivist principles on a daily basis may exhibit more constructivist tendencies when teaching proof.