A growing number of teaching materials invite students to discuss the complex mathematical, contextual and social aspects of data visualizations. Orchestrating such discussions can be difficult, as this requires teachers to balance a variety of learning goals and student perspectives. This paper examines how teachers interact with data visualization discussion tasks--specifically, those that engage visualizations' social complexities--as they consider using them in their own classrooms. Drawing from semi-structured clinical interviews with six U.S.-based teachers as they reviewed discussion tasks called Data Story Bytes, we explore: How did these teachers envision using these data visualization discussions in their classrooms? And, What mathematical, contextual, and/or social aspects of visualizations did teachers emphasize when engaging with the discussion task materials? We found that all teachers envisioned using data visualization discussions as lesson openers or routine activities, but they differed in their overall emphasis on the visualizations' mathematical, contextual, or social aspects. Despite these differences, certain types of discussion prompts were associated with particular response patterns across all teachers, suggesting these task structures can help guide teachers to address a shared set of intended baseline goals for all three of these dimensions. Our findings represent a first step in understanding whether and how socially-oriented data discussion materials may be enacted in classrooms, and what additional design features and supports may be needed to help teachers do so productively.