ABSTRACT
An important component of expertise is the rapid pickup of complex, task-relevant pattern structure, yet such skills are seldom trained explicitly. We report initial results applying principles of perceptual learning to the processing of structure in mathematics, specifically the connection between graphed functions and their symbolic expressions. Subjects in two experiments viewed graphs of functions and made a speeded, forced choice match from several equations. Training consisted of many short trials of this active classification task involving examples of a function (e.g., sine) subjected to various transformations (e.g., scaling, shifting, reflection). Experiment 1 used contrastive feedback – the graph for a trial was shown superimposed on the canonical function to accentuate transformations. Subjects showed substantial performance gains from 45 minutes of training and transferred to new instances, new function families and a new task. In Experiment 2, with contrastive feedback removed, subjects showed no transfer to new functions. The results indicate the value of perceptual training in producing mathematical expertise and the value of contrastive feedback in particular.
