Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn

There has been significant growth in the literature base exploring questions of teaching undergraduate mathematics. In this paper we synthesize on proof-based mathematics, drawing 104 published reports from a range countries and research traditions. We primarily differentiate papers into those which explore lecture-based pedagogy student-centered pedagogy. For each type instruction, focus three categories findings literature: description instructor beliefs rationales, relationship between instruction students (cognitive, participatory, affective, equity oriented). Much is known about enactment teaching, including instructors’ cognitive affective goals. The focuses tensions challenges implementing curricula with greater participatory Overall, there are few studies that attempt to link classroom activity students’ learning. Similarly, attention relatively lacking extant research.