The main issue our project addresses is how students' reasoning about mathematics concepts that are not new to them (e.g., linear functions) changes when learning about a new concept (e.g., quadratic functions), and we call this phenomenon backward transfer. We specifically focus on mathematics, but believe our backward transfer research is highly relevant within and across STEM content domains more broadly. For instance, this research is relevant to how learning about the relationships between position, velocity, and acceleration in physics could influence students' reasoning about derivatives and integrals in calculus, and vice versa. Recent results show that students with different incoming ways of reasoning about a concept that is not new to them are influenced in different ways when learning about a new concept.