Students learning language and learning to reason mathematically

The focus of this chapter is on applying language learning concepts and approaches to understand how students use language to reason mathematically. Airey and Lindner (2006, cited in Bailey & Heritage, 2019) referenced disciplinary discourse practices as “shared ways of knowing that make up a discipline” (p.27) and the “unique ways of understanding that involve actions, tools, specialized vocabulary and genre, and representations for the purpose of efficient communication (p.7). Despite highlighting language, we recognize that mathematical proficiency includes a blend of understanding the use of mathematical symbolism and disciplinary language, everyday language and visual displays, so that students are offered multiple opportunities to make connections among all three semiotic systems, each having its own conventions and each posing specific challenges (O’Halloran, 2005). That is to say, mathematics is a multi-semiotic discipline (O’Halloran, 2015). It is important to note, therefore, mathematics is unique among the disciplines, since representations of knowledge do not depend uniquely on linguistic representations. Linguistic representations, however, generally are privileged as forms of representation in standardized assessments of mathematical knowledge. Mathematics learning and teaching involves mediating complex relationships among linguistic, symbolic, visual forms of knowledge representation. These relationships are interwoven and evolve throughout schooling. We propose a synthesizing framework that is both adequate conceptually, and also offers a firm basis from which implications for practice can be drawn. In addition, we can consider the ramifications of the work presented here. By extension, such a conceptualization can be applied to the specific registers for each discipline including each of the sciences, history, social studies among others, since each discipline is characterized by specific language conventions.