Teachers Support Students' Construction of Mathematical Understanding and Development of Academic Language

• In Event: Cyber-Enabled Research That Repurposes a Major Video Collection on Students' Mathematical Reasoning

Abstract

One application for a VMCAnalytic (Authors, 2015a) is to assist teachers as they deepen understanding of children's mathematical and academic language development. Teachers can create engaging problem solving tasks where students apply their diverse repertories of mathematics and language knowledge unique to the mathematical tasks at hand. Of key importance is academic language, the disciplinary-specific language characterized by a distinctive voice and patterns of linguistic/discourse features. Students must learn how to integrate disciplinary concepts with unique and complex linguistic/discourse elements to transition from everyday language to the academic stances towards listening, speaking, reading, and writing---specialized in their functions in both the oral and written domains. Comprehending mathematics academic language (register) without adequate support is difficult for all students, but in particular bilingual students, because it consists of highly technical and precise language, densely structured through unique grammatical patterns, specialized vocabulary, and text organizations (Authors, 2015). This challenge is significant for bilingual students, who are learning English; for them, the process should emphasize grasping and solving the mathematical problem at hand by applying all of their resources–both language and non-language. These students will best learn both the mathematics and the specialized language of mathematics in these contexts of understanding (Chan, 2015).

We examined how one bilingual adolescent, Ariel, built an understanding of the linear function concept and represented his understanding of the basic algebra ideas underlying the construction. Our VMCAnalytic was developed originally as a research tool to depict the process of Ariel's transitioning from the everyday oral, conversational language to the academic language that is unique to mathematics: the mathematics register (Authors, 2015a; 2015b). Ariel was a 13-year-old student in grade 7 whose home language was Spanish. He participated, for over 18 months, in a mathematics enrichment experience as he formed algebraic concepts to solve The Ladders Problem using the required oral and written language. Initially, he did not understand the standard way one talks about and writes mathematical discourse (Ravid et al., 2010). Perhaps he was sufficiently fluent with the everyday oral, conversational English, which then masked his underdeveloped mathematical concepts and inadequate storehouse of linguistic/discourse knowledge to talk about mathematical notions, such as the algebraic concept that he was expected to explain. Our VMCAnalytic highlights that informal, open-ended problem solving tasks provide students opportunities to construct their knowledge. Such tasks are explorations at the heart of developing mathematical understanding. Professional developers thus could present our multimedia narrative of Ariel and ask teachers to identify what they see as the critical steps: The goal is for teachers to explain what they see as significant, and why they believe these elements are important in Ariel's construction of both his mathematical understanding and his development of the specialized language of mathematics. This process would be followed by asking teachers how they could envision changing their own practice to both create such problem solving tasks for their students and how they would support students as they construct both mathematical understanding and the mathematics language.

Author

• Louise C. Wilkinson, Syracuse University