Dramatic changes to the transparency, rigor, reproducibility and replicability of research practices have occurred in the last decade. Despite considerable progress towards the adoption of open science practices by researchers in many disciplines, developing pedagogy to train students in open and reproducible scholarship has received much less attention. Engaging students with the multiple dimensions of open scholarship is crucial to embedding sustainable change: it enables the future generation of researchers to practice open scholarship themselves, fosters lasting engagement with research, and allows them to better understand findings in light of epistemic uncertainty. Teaching students about open scholarship also helps it become a public good, thereby reducing knowledge inequities in academia and beyond. We address the lack of an infrastructure for open scholarship education by introducing the Framework for Open and Reproducible Research Training (FORRT). FORRT is a community-driven infrastructure for educators that advances research transparency, reproducibility, rigor, and ethics through pedagogical reform. FORRT encompasses multiple initiatives and tools to provide educators with guidance and resources to easily embed open and reproducible practices into research training. In addition to fostering a wider ecosystem for resource-sharing and discussion, FORRT has developed a wide range of initiatives, including a seven-part roadmap to the open scholarship literature, a curated database of open scholarship materials and pedagogies for customizable adoption by teachers, and a self-assessment tool to help educators evaluate the integration of open scholarship tenets in their own teaching and mentoring. FORRT actively works towards principled teaching and mentoring, an underappreciated dimension of the scientific endeavour.