Double counting. Double counting is an advance over the more basic direct
representation because it required more abstract processing and involves integrating two counting sequences. Double counting occurred only in division. When
children used a double count strategy for measurement division, they used physi-
cal objects but did not begin by representing the dividend with a set of objects. The
dividend was used to signal when to stop the action of forming groups. From the
start the children kept a running count of the total number of objects in the groups
while also counting out the objects to form groups. When the count of the total
reached the desired dividend, the child stopped and reported the number of groups
formed as the answer. ‘For partitive division the double count was done while
dealing objects one by one.