1 Introduction
Communication is an integral part of many learning contexts, including tutoring, peer collaboration, and of course, classroom instruction. However, communication some-times break down. Students sometimes fail to comprehend the information their teachers provide, and they sometimes fail to draw appropriate inferences or to construct knowledge, despite teachers’ best efforts to create conditions under which students will learn. One way to conceptualize the difficulties that students and teachers have at such ‘‘trouble spots’’ in the classroom discourse is in terms of a lack of common ground (Clark and Brennan 1991; Clark 1996), or shared understanding among participants in an interaction. Creating shared understanding between teacher and students is crucial in instructional communication (e.g., Vygotsky 1978; Blake and Pope 2008), and indeed, several recent analyses of discourse in educational settings have focused on how shared understanding is negotiated (Paulus 2009; Evans et al. 2011; Nathan et al. 2007). In this paper, we focus on teachers’ efforts to establish and maintain shared understanding with their students during classroom instruction in mathematics.