We investigated what high school mathematics teachers and their students noticed about students' mathematical engagement to develop a framework for teachers' and students' noticing of mathematical engagement. This framework offers clarity about the complexity of engagement, and it includes three elements: evaluations of the valence of engagement (whether students were engaged or disengaged), descriptions of dimensions of engagement (affective, behavioral, cognitive, instrumental, social, or relatedness), and features of engagement (interpretations of what took place in the classroom to support or constrain students' engagement). We interviewed 30 sets of high school mathematics teachers and focus groups of their students and asked them to reflect on students' engagement during a videotaped lesson from their classrooms. Results illustrate cases of how noticing of engagement between teachers and students can be shared (or not), from strongly shared (agreement on all three elements in the framework), partially shared (agreement on two elements), and minimally shared (agreement on one element). Cases of partially and minimally shared noticing of engagement suggest opportunities for teachers to learn about their students' perspectives or how to communicate with students about their intentions for engaging them.