Responsibility for contact tracing was removed from schools on Monday and passed to NHS test and trace, who will now inform parents if their children have to isolate.
Headteachers are only expected to assist in exceptional circumstances, such as an outbreak of more than 10 cases in a school.
Campaign group Us for Them England reported some schools are still sending home whole bubbles to isolate, despite it no longer being their responsibility.
And some parents have been told their school cannot pass details to NHS test and trace “because of GDPR”.
James Bowen, director of policy for school leaders’ union NAHT, said: “The changes are causing confusion. School leaders are working through the practicalities of what those changes mean as quickly and safely as they can.”
Julie McCulloch, director of policy at the Association of School and College Leaders, said: “This guidance was only issued last Thursday and contains a significant amount of detail to be processed.”
She said that guidance says that schools are able to share personal information with test and trace officials without consent under powers imposed by coronavirus legislation.
But it is understood that some schools may have missed or misinterpreted guidance on GDPR. Ms McCulloch added: “It appears that test and trace will mainly focus on contacts that may have happened in social settings away from schools and colleges and that contacts in the classroom will not normally need to self-isolate.”
A government spokeswoman said schools will be contacted by NHS test and trace to offer advice if there is an outbreak of multiple cases.