Dual dimensions of productivity in cross-community mathematics teacher dialogue

Abstract While scholars have been calling for cross-community teacher dialogue, it remains relatively rare, both in research and in practice, and its potential productivity is unclear. We propose a dual framework distinguishing between pedagogical productivity and boundary productivity. The former dimension relates to the advancement of instructional reasoning and pedagogical judgment and the latter to articulation, negotiation, and transformation of professional boundaries. We conceptualize these forms of productivity as emerging through processes of reflection, understood as the collective examination and reinterpretation of instructional practice and professional perspectives in interaction. Drawing on four cases from a secondary-tertiary video-club setting (M-Cubed), we show that these dimensions are analytically distinct and variably related. Cross-community deliberation may stall along both dimensions (boundary-avoidance deliberation), advance pedagogical reasoning without boundary reflection (boundary-mediated deliberation), clarify professional differences without instructional advancement (boundary-reflective deliberation), or integrate both forms of productivity (boundary-integrative deliberation). We further show that these configurations are shaped by distinct reflection mechanisms, including problematization, defamiliarization, avoidance, and translation. These findings provide a framework for analyzing the generative force of cross-community teacher deliberation and clarify the conditions under which dialogues between secondary and university mathematics teachers advance pedagogical reasoning and judgment, boundary reflexivity, or both.