"Minor American English quibble: if the children were three or four year-olds, then over here it's a "nursery school". Kindergarten is (generally) for five year-olds, the class just before first grade."
Thanks. AFAIK, nursery school here in the UK is until they start "proper" school, which may be as young as 4 in a reception class, normally 5. That can vary from town to town, but there's nothing in between.