After one-to-one counting, students move on to the concept of cardinality, which is when students can tell how many things are in a set. In the link above, there is a video of a child who struggles with the concept of cardinality, as he recounts the same objects, one at a time, over and over again when he is asked how many of them that there are.
I like Ben Smith’s suggestion, in the comments section on G Fletchy’s page, on how too teach cardinality to children. He asks the following 3 questions:
“Let’s each eat 4 jelly beans. Can you get four for each of us?”
“How many jelly beans did you just eat?
How many did I eat?”
I also like the idea of having kids count the items that go into a bucket, but having them tell the teacher how many items are in the bucket without counting them again.