Exploring variation in students' correct traces of linear recursion

There has been a wealth of education research focused on recursion. This research has documented students' persistent difficulties with recursion, a variety of pedagogical approaches, and students' correct and incorrect mental models of recursion. This paper explores the variation in students' successful attempts to trace linear recursion. The findings go beyond correct and incorrect mental models to show how each of four modes of tracing linear recursion may require or facilitate a particular understanding of recursion. Additionally, the current study shows how knowledge of algebraic substitution can be applied to tracing linear recursion, and identifies a potential difficulty in students transferring this knowledge.