Applying Math onto Mechanism: Investigating the Relationship Between Mechanistic and Mathematical Understanding

Manipulatives are commonly used to provide concrete bases for abstract mathematical concepts. However, it is unclear when concrete experiences benefit abstract thinking. We investigated whether understanding a manipulative’s mechanism would affect mathematical use and understanding. Participants completed a robotics task that could be solved with either mathematical or non-mathematical strategies. Participants with higher mechanistic understanding were more likely to utilize complex mathematical strategies during the task, and understood the mathematical relationships within the robot better than participants with lower mechanistic understanding. The study provides evidence for a relationship between mechanistic and mathematical understanding, suggesting that mechanistic manipulatives, upon which mathematics can be applied, may foster mathematical understanding.