This article synthesizes ideas that emerged over the course of a 10-week symposium titled "Teaching Reproducible Research: Educational Outcomes" https://www.projecttier.org/fellowships-and-workshops/2021-spring-symposium that took place in the spring of 2021. The speakers included one linguist, three political scientists, seven psychologists, and three statisticians; about half of them were based in the United States and about half in the United Kingdom. The symposium focused on a particular form of reproducibility--namely computational reproducibility--and the paper begins with an exposition of what computational reproducibility is and how it can be achieved. Drawing on talks by the speakers and comments from participants, the paper then enumerates several reasons for which learning reproducible research methods enhance the education of college and university students; the benefits have partly to do with developing computational skills that prepare students for future education and employment, but they also have to do with their intellectual development more broadly. The article also distills insights from the symposium about practical strategies instructors can adopt to integrate reproducibility into their teaching, as well as to promote the practice among colleagues and throughout departmental curricula. The conceptual framework about the meaning and purposes of teaching reproducibility, and the practical guidance about how to get started, add up to an invitation to instructors to explore the potential for introducing reproducibility in their classes and research supervision.