This study explored the unique integration of mathematics tutors in teaching high school mathematics in a Virtual mathematics school (VMS). The tutors were three excelling STEM students who did not have any formal preparation for teaching before their work in the VMS. The goal of the study presented in this paper was to design a model of proficiency for these tutors. The model was designed using multiple case study methodology by tracking the learning through teaching of the tutors. Activity theory (Leontiev, 1978 ) framed the design of the study and led to a “goal-action” model of the tutors’ proficiency in the VMS. The goals part of the model is rooted in the construct of students’ mathematical potential (Leikin, 2021 ), and the action part was unraveled using the construct of a Teaching Triad (Jaworski in For the Learning of Mathematics, 12 (1), 8–14, 1992 ). In this paper, we illustrate how our model can be used to analyze changes in the tutors’ proficiency, and how it can be applied to descriptive, explanatory, and analytical power.

The changes are as follows.