Promoting conceptual thinking in four upper-elementary mathematics classrooms

Informed by theory and research in inquiry-based mathematics, this study examined how classroom practices create a press for conceptual learning. Using videotapes of a lesson on the addition of fractions in 4 primarily low-income classrooms from 3 schools, we analyzed conversations that create a high or lower press for conceptual thinking. We use examples of interactions from these fourth- and fifth-grade lessons to propose that a high press for conceptual thinking is characterized by the following sociomathematical norms: (a) an explanation consists of a mathematical argument, not simply a procedural description; (b) mathematical thinking involves understanding relations among multiple strategies; (c) errors provide opportunities to reconceptualize a problem, explore contradictions in solutions, and pursue alternative strategies; and (d) collaborative work involves individual accountability and reaching consensus through mathematical argumentation.