Undergraduate peer drop-in mathematics tutoring is a common form of support at the university level, yet research regarding how to train this specific group of tutors is underspecified. This paper aims to describe a training program for this population that is grounded in mathematics education research. It serves as a first step in conducting a design experiment on how training impacts tutor behaviours. This paper addresses the research question: How can mathematics education research inform tutor training design? First, the specific context for the training program is characterized, followed by challenges to training programs. Then, ways in which research on mathematics classroom teaching and learning can apply to tutoring are discussed. Finally, the training program is described in detail, including the research which informed the design, as well as the learning outcomes, activities, and feedback mechanisms. Broadly, the goals of the training program are to promote productive beliefs regarding tutoring and learning mathematics, to increase the use of NCTM's [(2014). "Principles to action."] teacher/student actions in tutoring practices, and to develop reflective practitioners. To guide the development of these skills and dispositions in tutors, tutors engage with tutoring scenarios, excerpts, and case studies. Tutors are also provided with opportunities to reflect on their own tutoring practices.