In this episode we meet Haynes Miller, Professor Emeritus of Mathematics, who in his 35+ years of active teaching at MIT has done much to shape the institute’s math curriculum. Prof. Miller’s special focus is algebraic topology, but his teaching has encompassed a wide range of other topics from differential equations to number theory, and he has a special interest in teaching undergraduates. Join us as Prof. Miller discusses math education with guest host Paige Bright, a current MIT third-year student who was one of his students in a first-year seminar and who has since acquired teaching experience of her own as the instructor for the course Introduction to Metric Spaces during the Independent Activities Period in January 2022 and 2023. Among the topics they cover in this discussion are the importance of communication in mathematics, Prof. Miller’s use of computer manipulatives (which he calls “mathlets”) to engage students more actively, what “lab work” means in the context of pure mathematics, how instructors from different institutions have come together online to discuss ways to improve undergraduate math education, and what happens when you ask students to switch roles and become teachers.Relevant Resources:MIT OpenCourseWare The OCW Educator Portal 18.03 Differential Equations on OCW 18.821 Project Laboratory in Mathematics on OCW 18.915 Graduate Topology Seminar: Kan Seminar on OCW Paige Bright’s course Introduction to 18.S097 Metric Spaces on OCW Prof. Miller’s faculty page Prof. Miller’s “manipulatives” at mathlets.org Online Seminar on Undergraduate Mathematics Education (OLSUME) Music in this episode by Blue Dot Sessions  Connect with UsIf you have a suggestion for a new episode or have used OCW to change your life or those of others, tell us your story. We’d love to hear from you! Call us @ 617-715-2517On our site On Facebook On Twitter On Instagram  Stay CurrentSubscribe to the free monthly "MIT OpenCourseWare Update" e-newsletter. Support OCWIf you like Chalk Radio and OpenCourseware, donate to help keep these programs going!  CreditsSarah Hansen, host and producer Brett Paci, producer  Dave Lishansky, producer Show notes by Peter Chipman