How children change their minds: strategy change can be gradual or abrupt.

This study investigated patterns of change in children's strategies for solving mathematical equivalence problems. The strategies children expressed in speech and in gesture were assessed both before and after an instructional intervention. In the intervention, children received either no input, accuracy feedback, or feedback plus instruction about a principle, an analogy, or a procedure. From pretest to posttest, many children changed both the variability of their strategy use and the content of their strategy repertoires. Patterns of change depended on type of instruction and on children's initial level of variability. Children who received instruction were especially likely to generate new strategies, and children with high variability were especially likely to abandon prior strategies. Gradual change was most common; however, many children modified their repertoires abruptly. Abrupt strategy change was especially prevalent among children who received procedure-based instruction and among children with low initial variability.