Negative Instances in Mathematical Concept Acquisition: Transfer Effects between the Concepts of Commutativity and Associativity

The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. 2 treatment levels for commutativity (positive instances only, or positive and negative instances) and the same treatment levels for associativity were crossed to form a 2 × 2 factorial design with 16 ninth-grade subjects per cell. Criterion variables were numbers of correct responses, stimulus intervals, and post-feedback intervals. The results favored the treatments containing both positive and negative instances and supported the hypothesis that the effects for negative instances transferred from one concept to another. Near-significant time differences weaken effects observed for negative instances.