The view of mathematics education as an activity that involves participants in social interaction challenges what it means to know and learn mathematics, as it reveals a connection between experience and language, more specifically between words and actions. Brown (2001) argues: "spoken words are always part of some sort of action" (pp. 69-70) and raises questions such as: "How do we share our thinking with other people? How do language and symbols mediate this?" (p. 9). Habermas and Gadamer ask whether it is possible to frame all experience in language. My research analyzes the non-verbal communication of second-grade bilingual students. I argue that the richness of bilingual students' mathematical understanding requires an investigation of forms of meaning making that transcend language. The flexible use of two languages in bilingual classrooms suggests that bilingual learners may use alternative forms of communication (e.g., nonverbal communication) as equally flexibly as language. The various levels of linguistic proficiency that characterize bilingual classrooms constitute an opportunity for exploration of non-verbal communication as a way to expand what it means to communicate mathematically.
Literature Review
The literature, which explores the intersection of language, experience, and meaning, highlights beliefs such as: "knowledge that has been made explicit-that is, languaged knowledge-is only a tiny fragment of knowing" (Davis, 1977, p. 115); "it is not useful, nor even possible, to represent all aspects of human experience in natural language…[and]… there must be representational systems not involving words which humans use to encode information" (Huttenlocher, 1993, 1976, as cited by Alibali & Goldin-Meadow, p. 514); "speech and gesture together can often provide a clearer and more accurate picture of what children really know about a given concept than either modality alone" (Kelly et al., 2002, p. 21). This literature also presents empirical evidence on how the correlation between language and gestures is mediated by meaning and on the role of gestures as supporting verbal comprehension.
Methodology
Seven second-grade bilingual students participated in this study. Half of the participants were proficient bilinguals, and half were less proficient bilinguals. On three occasions, students were given two addition and subtraction problems. To analyze the students' nonverbal behavior, I used an interpretive research approach. According to Lampert (1990), "The purpose of interpretive research is not to determine whether general propositions about learning or teaching are true or false but to further our understanding of the character of these particular kinds of human activity" (pp. 36-37).
Results
Student understood problems and explained solutions using both verbal and nonverbal communication. In general, the bilingual students demonstrated that language does not constitute an impediment for bringing meaning to their mathematics learning; rather, gestures supported their own meaning making and the communication of this meaning to other people. Examination of nonverbal behavior may reveal important information about the students' conceptual understanding that is otherwise not available in their verbal explanations. Attention to diverse forms of communication is essential in bilingual classrooms given that students in these classrooms often come from environments in which extra-linguistic factors may be prominent in cultural communication patterns. Also, the emphasis in mathematics education on understanding adds importance to the exploration of all forms of meaning communication by bilingual students. I hope this study will broaden our understanding of bilingual education as multi-resourced education.