UPDATED: Investigating Changes in Students’ Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra (NSF #1651571)

The main issue our project addresses is how students’ reasoning about concepts that are not new to them changes when learning about a new concept, 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.

One way our project has been innovative is by being the first to use contrasting cases to examine backward transfer (i.e., comparing distinctly different instructional environments). By comparing backward transfer across contrasting cases (e.g., business-as-usual classroom environments, summer math camps), we have gained insights into backward transfer we would not have gained had we examined a single instructional environment alone. Another way our project has been innovative is by being the first to develop and test mathematics activities designed to teach students new concepts, while simultaneously enhancing their reasoning about concepts that are not new to them.