*Ok this is a interesting question since I teach 4 and 5 year olds?
Yes,I do give homework to the children in my classroom. It is usually the tracing the letter and number of the week. Also we do a monthly book log of the books the parent has read to the child during the month. We also do show and tell once a month and have the child bring in a item that starts with one of the letters we have learned during the month. The only problem with giving homework to the children is the parents want me to send home more home work for the children to do.
We also send home a calander of fun things with their parents during the month. The calander has things on it like making a peanut butter and jelly sandwich together. Hunting for shadows with your parents. Do a treasure hunt for a color (the parents pick the color)item. I know the calander is not homework put it is to encourage the parent to do things with their children. The parents love the calander of things to do with their children.
Homework should never be thought of as a punishment for the parents to use with the child. Homework in the VPK classroom is given to the child to have the parents involved in their childs learning. Chldren get excited when they learn something new and like to share it with everone they can. It is kind of like a adult gets a new car they like to show it off. The child likes to show off what they are learning.
The first time a child learns to do something by themself is a big step for the child. They take pride in themselves and by sending homework home with 4 and 5 year olds gives the child a chance to show off what they are learn at their school. To the child the kind of homework I send home is to the child is a chance to show off to their parents what they are learning in the classroom.