title: Applying math onto mechanisms: mechanistic knowledge is associated with the use of formal mathematical strategies.
abstract: It is notoriously difficult for people to adaptively apply formal mathematical strategies learned in school to real-world contexts, even when they possess the required mathematical skills. The current study explores whether a problem context's mechanism can act as an "embodied analogy" onto which abstract mathematical concepts can be applied, leading to more frequent use of formal mathematical strategies. Participants were asked to program a robot to navigate a maze and to create a navigation strategy that would work for differently sized robots. We compared the strategy complexity of participants with high levels of mechanistic knowledge about the robot against participants with low levels of mechanistic knowledge about the robot. Mechanistic knowledge was significantly associated with the frequency and complexity of the mathematical strategies used by participants, suggesting that learning to recognize a problem context's mechanism may promote independent mathematical problem solving in applied contexts.
authors.affiliation: Department of Psychology, University of Pittsburgh, Pittsburgh, PA USA.|Learning Research and Development Center, University of Pittsburgh, 3939 O'Hara Street, Pittsburgh, PA 15260 USA.
authors.forename: Allison S
authors.initials: AS
authors.lastname: Liu
authors.affiliation: Department of Psychology, University of Pittsburgh, Pittsburgh, PA USA.|Learning Research and Development Center, University of Pittsburgh, 3939 O'Hara Street, Pittsburgh, PA 15260 USA.
authors.forename: Christian D
authors.initials: CD
authors.lastname: Schunn
keywords: Embodied analogy; Mathematical strategies; Mechanistic knowledge; Proportional reasoning