One-To-One Correspondence
Young children LOVE to count! Are they counting or just saying memorized numbers? You are correct if you said they are just saying memorized numbers. This is developmentally appropriate and the first stage of acquiring number sense. In TK, the teacher models counting by touching each object that is being counted. There are many opportunities to practice 'counting' during play!
Number Sense
Number Sense is the ability to understand that one means one of something. Higher level math skills can be taught when a child begins to understand number sense.
The images below are links to articles and videos discussing number sense.