Physical manipulatives are commonly used to improve mathematical understanding. However, it is unclear when physical manipulatives lead to significant benefits. We investigated whether understanding the mechanism of a manipulative would affect mathematical use and understanding. Participants were asked to navigate a physical robot through a maze, and to create a strategy that could navigate differently sized robots through the same maze. Participants with a better understanding of the robot’s mechanism were more likely to utilize complex mathematical strategies during the maze task than participants with lower mechanistic understanding. These participants with higher mechanistic understanding also showed greater understanding of the mathematical relationships within the robot. The study provides evidence for a relationship between mechanistic understanding and mathematical understanding, suggesting that mechanistic manipulatives, upon which mathematics can be applied, may be especially beneficial for fostering mathematical understanding
