One of the mothers at the primary school where my kids went told me that when her first child started school she took the morning off work so that she wouldn't be panicked about dropping her off, and so that she could be there if her child needed her. She walked her child to their class, and looked around the room in a mild state of panic lest her child would not cope with the new environment. When the bell went, the other kids sat on the mat, as did hers, who turned around, beckoned her mother over with her hand, and then whispered in her ear - 'what are you still doing here, don't you think you should go now?'
She left the room, got into her car and promply bawled her eyes out!
The school my youngest now goes to have a rule that parents are not allowed in the classes after the bell goes, unless they are parent help. They have found that the kids get clingy and play up if the parents are there, and they settle quicker if they are not distracted.