Instructors' Orientation on Mathematical Meaning

Students often ask "when is this ever going to be useful?", "why are we doing this?", etc. when speaking about mathematics. If we take this as a question about 'meaningfulness', how can instructors respond and how do they even understand the terms 'meaningful' and 'meaning'? My dissertation looked at how college instructors see their instruction as meaningful or not. Drawing on social and cognitive perspectives of learning, I define four ways to think of what's 'meaningful' about mathematics. From a cognitive perspective, instructors can understand 'meaningful' as mathematical understanding versus understanding the significance of mathematics. From a social perspective where meaning is taken as the experiences of everyday life within communities, teachers can understand 'meaningful' as anything that engages students in practices the mathematics community engage in versus practices non-mathematics communities engage in (e.g. pushing computation or critical thinking as a means for maintaining social hierarchies). Using these four conceptions to categorize instructors' goals, this work focuses on how four undergraduate mathematics instructors thought of their instruction as meaningful and contextual and background factors that influenced those views.