But there is a warning that this does not mean a return to “sleepovers or birthday parties”.
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Wales’ education minister says she is confident more primary school children will be able to return to face-to-face learning from 15 March, if Covid cases continue to fall.
Children aged three to seven start a phased return on Monday, along with some students on college courses.
Kirsty Williams said it could not be a “return to sleepovers or birthday parties” to help keep Covid cases down.
She also said high school pupils may eventually return on a phased basis.
Meanwhile, Plaid Cymru has called for teachers to be given Covid vaccinations as a priority.
Public Health Wales said although Covid case numbers were falling, the rates in north Wales were nearly double the average and there have been small increases in other areas.
Most pupils have been learning from home since December and Ms Williams told BBC Radio Wales’ Sunday Supplement: “If the public health situation continues to develop as it has been doing since the lockdown in December, then I am as confident as I can be that we will be able to return more children to face-to-face learning on 15 March.
“Please don’t misinterpret this as a sign that things can go back to normal.
“Schools are highly-regulated settings, school staff are working really hard to make them as Covid secure as they can be.
“But it is behaviour around school – on the journey to school, at the school gate, on your way home and at the weekend – that will help us keep the public health situation improving which will allow more children to go back.”
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Ms Williams said trials regarding vaccinating young people against Covid were under way and Wales would be “ready to move forward” if approval was granted by regulators, along with the “get-go” from expert advisers.
UK government scientific adviser Prof John Edmunds, an infectious diseases expert, told the BBC’s Andrew Marr programme “there is an argument for turning to children as fast as we can” when it comes to vaccination.
More than 860,000 people in Wales have been given a first dose of the Covid vaccine among the top priority groups, including the over-70s and health workers, according to the latest data.
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All schools and colleges in Wales were told to move to online learning before the start of this term in an effort to “suppress the virus”.
Schools and colleges have remained open for children of critical workers and vulnerable pupils, as well as children who needed to complete essential exams or assessments.
On secondary schools returning to face-to-face learning, Ms Williams the situation was more “complicated” due to the risk of transmission because coronavirus “behaves much more like it does within adults”.
“Our priority will be to use whatever headroom we have to maximise face-to-face learning for years 11 and 13, and many head teachers that we’re consulting with would like some flexibility to get some year 10 and year 12 students in as well.
“But we might have to do that on a routine basis, allowing us to cut the number of children in the class down, helping to keep those schools as Covid-secure as possible.”
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Ms Williams also said some university students were due to return to campus this week so they “can undertake the practical assessments and the practical elements of their work”.
She said the Welsh Government was working with universities “to bring back students when it’s safe and appropriate to do”.
Plaid Cymru education spokeswoman Sian Gwenllian renewed her calls for vaccinating school staff.
She told Radio Cymru’s Dewi Llwyd programme that any “spare” vaccinations should be offered to school staff as a priority.
Welsh Conservative Senedd leader Andrew RT Davies welcomed the moves to reopen schools but was concerned that not enough was being done for businesses.
Schools in England and Northern Ireland are set to return from 8 March but Scotland’s youngest are to restart face-to-face learning from Monday, as well as some senior pupils.