How a student conceives the nature of a subject they study affects the approach they take to that study and ultimately their learning outcome. This conception is shaped by prior experience with the subject and has a lasting impact on the student's learning. For subsequent education to be effective, an instructor must link the current topic to the student's prior knowledge. Short of assessing their students, an instructor relies on their subjective experience, intuitions, and perceptions about this prior knowledge. These perceptions shape the educational experience. The current study explores, in the context of undergraduate mathematics, the alignment of instructors' perceptions of student conceptions of mathematics and the students' actual conceptions. Using a version of the Conceptions of Mathematics Questionnaire, instructors of lower-year courses were found to have overestimated, while upper-year course instructors underestimated, their students' fragmented conceptions of mathematics. Instructors across all years underestimate their students' cohesive conceptions. This misalignment of perspectives may have profound implications for practice, some of which are discussed.