Algorithmically driven systems are now frequently found in educational spaces in the form of adaptive tutoring systems and online learning environments. Previous research has shown that well-integrated technologies can augment good human teaching practices. How such integration is measured, however, is an evolving debate within the field of artificial intelligence for education. Research that seeks to measure equity in these systems often assumes the social categories that are used for comparison, typically by using already existing demographic data such as race or sex. While practical, these assumptions may limit the transferability of subsequent conclusions. This work explores dimensions of algorithmic justice questions through interviews with students. This research engages middle and high school students directly, as the least powerful but arguably most impacted individuals in the algorithmic tutoring ecosystem, about their own identities, their relationship to these technologies, and the way their data are used.