When first learning to count, a child counts by rote memorization. This means he/she will likely be able to say the names of the numbers from 1 through 10 simply because they have memorized the order of the words, “one, two, three,….ten”. However, he/she likely does not yet understand that 5 is 2 more than 3. For example, before a child understands one to one correspondence, they will count by rote memorization. When asked to count a small group of objects, they will likely count quickly through the numbers they have memorized and randomly touch the objects being counted instead of touching and counting each object just once.
For example, a child given five beads may automatically count aloud from 1 to 10 when asked to count the beads, pointing to random beads as he proudly shows how well they can count. Counting on allows a child to continue counting objects added to a previously counted group without recounting the entire group.
For example, give your child two apples and ask him to count them. Then give your child three more apples. Counting on would involve your child applying one to one correspondence to the additional three apples by counting “three, four, five” instead of restarting at one and recounting all five apples.
Counting on is an important skill because it is time consuming and impractical to recount a group of items each time additional pieces are added.