Talk Plus Inscriptions: How Visual Representations Ground Meaning in Mathematical Discussions

• In Event: Complicating Accounts of Oral and Written Discourses in the Teaching and Learning of Multilingual Youth

Abstract

This presentation uses a situated and sociocultural perspective on mathematical language and communication (Moschkovich, 2002; 2015) and a view of mathematical discourse as the complex interaction of three semiotic systems---natural language, mathematics symbol systems, and visual displays (O’Halloran, 1999) to analyze discussions among bilingual students and illustrate how learners coordinate talk, writing, and visual representations. The analysis highlights the complexity of classroom mathematical discourse that involves multiple modes (oral, written, etc.), representations (words, symbols, tables, graphs, etc.), and written texts (word problems, student explanations, etc.).

The data—discussions among bilingual eighth graders as they interpreted a distance-time graph for a written story of motion—is excerpted from a larger data set collected during a study in an eighth-grade bilingual mathematics classroom. Classroom observations and videotaping were conducted during a Connected Mathematics Project unit titled Moving Straight Ahead (Lappan et al, 1998). The analysis uses the following questions: What modes and sign systems did students use to communicate mathematically? What were situated meanings of words and phrases? How were students coordinating talk, writing, and a visual representation?

The examples illustrate how students coordinated talk, writing, and a visual representation as they participated in mathematical practices and used hybrid resources—multiple modes of communication and sign systems. The examples also show how mathematical discussions, like other conversations, involve situated meanings for utterances—rather than static meanings for words—and that these situated meanings are coordinated with multiple views of the visual representation, a graph. Meanings for utterances and written text were grounded in talk coordinated with a visual representation and were situated, depending on where and how participants focused joint attention (Rogoff, 1990) and viewed inscriptions (Goodwin, 1994).

A shift to a view of mathematical discourse as the coordination of multiple modes and representations is particularly important for multilingual youth. A simplified view of mathematical discourse as competence in developing meaning for isolated words treats oral and writing modes separately and independently of the visual representations that ground mathematical meanings and can have dire consequences for multilingual students. It is essential for teachers of multilingual students to consider when and how to connect talk to written work and visual representations. Instruction to support participation and competence in mathematical discourse for multilingual learners needs to shift from focusing on students acquiring static meanings for words provided by the teacher or a textbook to supporting learners as they use and explore mathematical meanings. These meanings are situated, negotiated, and grounded in activity that includes not only talk but also writing and visual representations. Instruction can support mathematical discourse by providing opportunities for students to negotiate and refine meanings grounded in mathematical activity that includes talk, writing, and visual representations.

Author

• Judit N. Moschkovich, University of California - Santa Cruz