Students’ Mathematical Reasoning, Communication, and Language Representations: A Video

Learning mathematics is a complex process, requiring many conceptual lenses and rich data sources to document and understand students’ construction of knowledge. The purpose of this article is both to introduce a unique database on students’ mathematical learning and to describe analytical techniques used to study students’ growth of the knowledge of mathematics and language. Our approach includes the following aspects: First, we describe a unique collection of video-taped recordings of longitudinal and cross-sectional studies of diverse, U.S. students, learning mathematics (Video Mosaic Collaborative, VMC). Second, we introduce our analytical methods, which utilize the database for collaborative study of students’ learning. These methods include video-narrative analyses that display fine-grained examinations of interactions among students who are solving engaging problems that require them to reason mathematically and to represent their understandings with language and non-language forms. These analyses, referenced as VMCAnalytics, demonstrate the accessibility and flexibility of the database to study relationships among students’ mathematics and language learning. The findings generated are illustrated by two examples demonstrating the accessibility and flexibility of the database to study relationships between mathematics and language learning (mathematics register). The contribution of our work is illustrated by describing the rich database; employing a collaborative research approach; and signifying our understanding of relationships among students’ mathematical and language learning