Based on the performance on the number-conservation task, kindergarten children were divided into conservers and nonconservers. They learned the identity relation on the task with number or form dimension and then transferred from the number to the form task or vice versa. For the number task the conservers learned faster the identity relation anal used more frequently the win-stay strategy than the nonconservers. The findings suggest that the relationship between the conservational level and the identity learning is task-specific rather than general in nature. The number of the subjects who showed perfect transfer suggests that the conservers acquired the identity relation more strongly than the nonconservers.