


Jessica M. Walker University of California, Los Angeles, Los Angeles, CA, USA Patricia W. Cheng University of California, Los Angeles James W. Stigler University of California, Los Angeles
U.S. students consistently score poorly on international mathematics assessments. One reason is their tendency to approach mathematics learning by memorizing steps in a solution procedure, without understanding the purpose of each step. As a result, students are often unable to flexibly transfer their knowledge to novel problems. Whereas mathematics is traditionally taught using explicit instruction to convey analytic knowledge, here we propose the causal contrast approach, an instructional method that recruits an implicit empiricallearning process to help students discover the reasons underlying mathematical procedures. For a topic in highschool algebra, we tested the causal contrast approach against an enhanced traditional approach, controlling for conceptual information conveyed, feedback, and practice. The causal contrast approach yielded remarkably greater success, especially on novel problems, across students with varying levels of mathematical competence.
Equations Are Effects: Using Causal Contrasts to Support Algebra Learning (395 KB)