While Hall Cross Academy in Doncaster told pupils who had been on a skiing trip to northern Italy to isolate themselves for 14 days, a number of others in the area have said that it not necessary.
Bradfield School in Sheffield told pupils to carry on as normal as the trip did not go near the quarantined part of Italy.
And McAuley Catholic High School in Cantley and Don Valley Academy have both issued warnings but have not advised self-isolation.
NHS dentist Sheffield: Patients wait months for appointments, travel for miles or go private due to shortage
Sheffield man prepares to jump from plane in memory of beloved mum wanted to be by his side
The best and worst dentists in Sheffield according to NHS patient reviews
Baby Ultrasound Clinic: Sheffield scan centre given warning notice over safety concerns
New data reveals the number of Covid-related deaths in Sheffield care homes
Public Health England has confirmed it is not advising that schools shut in an attempt to stem the spread of coronavirus.
The organisation's medical director Paul Cosford told Radio 4's Today programme: "Schools have to take difficult decisions given the complexity of issues that they are facing.
"What I would say is that our general advice is not to close schools.
"What we are clear about is if you have been in the area of northern Italy of concern and you have symptoms - it is a cough, shortness of breath or fever - then you do need to self-isolate, you need to phone NHS 111 and await advice for further assessment or testing.
"Of course if you've been to one of the specific towns that are identified by the Italian government and essentially closed down, then our advice and requirement is to self-isolate anyway."
He said Public Health England was available to talk to schools about their "specific circumstances" and "help them make the right decisions for them".
Earlier this week Greg Fell, Director for Public Health in Sheffield, said that Sheffield residents should ‘not be overly worried’ about coronavirus after it was announced that two patients with the disease are being treated in Royal Hallamshire Hospital’s Specialist Infectious Diseases Unit.
The two patients were flown to the unit after they contracted coronavirus while on board the Diamond Princess cruise liner in Japan.