A Framework for Mathematical Knowledge for Undergraduate Mathematics Tutors

Most institutions of higher learning offer undergraduate mathematics tutoring, yet little is known regarding the work tutors do or the knowledge needed to enact that work. We explore the mathematical knowledge needed for the work of undergraduate peer drop-in mathematics tutoring. The data consists of transcripts from eight stimulated recall interviews, two each from four tutors, during which each tutor reflected on six of their recorded tutor sessions per interview. We first summarize and synthesize different conceptualizations of mathematical knowledge for teaching, with particular attention to definitions of knowledge types and their use in teaching. We examine the applicability of conceptualizations of the mathematical knowledge of teaching to tutoring to answer the following research question: How do frameworks for mathematical knowledge for teaching appear in the undergraduate peer drop-in tutoring context? Our findings indicate aspects of mathematical knowledge for teaching frameworks apply to the tutoring context; however, it is not a perfect match. In particular, aspects of mathematical knowledge for teaching which are used in planning tasks are not relevant for the work of drop-in tutors. By understanding the knowledge required for tutoring, future research can explore how this knowledge develops. This understanding may ultimately lead to improved tutor training which focuses on both mathematical knowledge, different from content knowledge gained in the math classroom, and pedagogical knowledge specific to mathematics tutoring.