This study investigated patterns of change in children's strategies for sol
ving mathematical equivalence problems. The strategies children expressed i
n speech and in gesture were assessed both before and after an instructiona
l intervention. In the intervention, children received either no input, acc
uracy feedback, or feedback plus instruction about a principle, an analogy,
or a procedure. From pretest to posttest, many children changed both the v
ariability of their strategy use and the content of their strategy repertoi
res. Patterns of change depended on type of instruction and on children's i
nitial level of variability. Children who received instruction were especia
lly likely to generate new strategies, and children with high variability w
ere 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 proced
ure-based instruction and among children with low initial variability.