Classroom interactions that shape the nature of students’ appropriation of a complex mathematical practice

Scholars continue to emphasize the importance of fostering proficiency with mathematical practices as an educational outcome. As teachers attempt to support students in developing these practices, they communicate subtle messages about their nature. However, researchers lack a detailed understanding of the classroom interactions that communicate these messages. To begin to address this gap in the literature, we investigated the relationship between the types of classroom interactions around the mathematical practice of imposing structure and the ways students subsequently engaged in that practice. This led to the identification of three types of classroom interactions that shaped the nature of students’ appropriation of imposing structure: (a) engaging students in the practice, (b) providing different representations of the practice, and (c) reflecting on different instantiations of the practice. Our examination of the nature of these interactions suggests teachers must attend to details as they support students to appropriate mathematical practices in formal learning environments.