Poetic lines in mathematics discourse: A method from linguistic anthropology

Abstract

The hills my brothers & I created never balanced, & it took years To discover how the world worked. We could look at a tree of blackbirds & tell you how many were there, But with the scrap dealer, Our math was always off. ('Believing in Iron', Yusef Komunyakaa) [1] In many contemporary mathematics classrooms, students discover how the world of mathematics works by talking about it. Creating linguistic meanings helps students create mathematical meanings. However, if communication is a central process for mathematical learning, we must account for the linguistic processes that allow students to construct mathematical ideas. While linguistic meaning is often considered a property of words, significant mathematical ideas - arguments, inferences, and relationships - can also be expressed through discourse structure. At times, the form of a student's statement can convey meaning as much as the isolated definitions of the words themselves. The fields of linguistic anthropology and poetics offer a method of analyzing knowledge construction in discourse that involves the repetition of words, grammatical features, intonations or rhythms. Repetition creates ideas that transcend the sentence; the repeating elements are said to form lines. Revoking, when a teacher paraphrases a students' comment and speaks it back to the class, is a type of repetition that is familiar in mathematics education research (O'Connor & Michaels, 1993), but repetition can occur in discourse in more complicated ways. Repetition can occur in student discussions that do not involve a teacher, within the speech of a single student, and it can rely on sentence and paragraph structures that are more complex than typical instances of revoicing. Poetic structures in classroom discourse have been identified as a priority for research in the linguistic anthropology of education (Wortham, 2003). In this article, I outline the academic history of repetition and I discuss examples of mathematical thinking that can be expressed through poetic structures. Because repetition requires attention to speech structures beyond words and sentences, I describe methods of representing repetition in transcribed discourse. Analyzing repetition can help researchers deal with transcripts more delicately and to perceive processes of meaning construction that go unnoticed in traditional forms of transcription. Representing poetic lines