Many studies have documented the challenges facing teachers who use digital technologies in their classrooms. This is especially true for digital technologies that offer new models or representations of school mathematics concepts. In this article, we report on a collaboration between teachers and researchers around the use of a novel touchscreen application called "TouchTimes" (TT) designed to provide new models of multiplication. Taking the application as a boundary object, we study the emergence of new meanings of multiplication that arose in group meetings during which the teachers explored TT and reported back on their classroom experiments with TT. We show how these new meanings emerged from a series of disruptions that involved not only mathematical considerations, but also material, political, social and bodily ones.