Speer, Smith and Horvath published a research synthesis in 2010 examining the undergraduatemathematics education research literature. They argued that we know relatively little, systematically,about the teaching and learning of undergraduate mathematics. Even though there are relatively fewstudies of the form that Speer, et al called for, I argue that the literature in many areas is now quiterobust, especially in describing and characterizing instructional practices. In this presentation I will focuson proof-based mathematics courses and attempt to give an overview of the field. Essentially: Whathave we learnt from research about teaching and learning in proof-based mathematics courses andwhat more might we want to know? I will briefly describe some of my own research and how it fitswithin the field. I will conclude with a description of what I think are interesting directions for the fieldand some methodological challenges in addressing the more pressing questions. To give away the point,it’s that ‘measuring learning is hard.’

Bio: ​Tim Fukawa-Connelly​ is an Associate Professor of Teaching and Learning at Temple University andpreviously held tenure-stream positions in the School of Education at Drexel University and in theDepartment of Mathematics and Statistics at the University of New Hampshire. He is currently anAssociate Editor of the Journal of Mathematical Behavior. He has written extensively on the teaching andlearning of undergraduate mathematics and mathematics for teaching, especially in proof-basedmathematics courses. Overall, he is trying to explore and characterize what happens inside and outsideof mathematics classrooms and the relationship with student learning. Early in his career, this meantexploring lecture-based pedagogy and what opportunities to learn students might have. Lately, he hasfocused on how students interpret lectures, and how miscommunication between students andprofessors might occur. He has 2 cats, adopted a #pandemicdog, and built a campervan in which heloads up the dog and spouse (the cats stay home) and drives around the country. He has aspirations todrive it to and around Canada.