The latest data from the Health Protection Surveillance Centre showed that 40 outbreaks of Covid-19 in schools last week.
An outbreak is when two or more related cases are identified in a setting.
There were 34 outbreaks in primary schools, three in secondary schools and three in special schools.
The outbreaks related to a total of 191 cases of the virus.
It compares to just 12 outbreaks recorded in schools the week before last, but schools had only just reopened at that stage.
In 2020, the weekly number of outbreaks in schools fluctuated widely depending on various factors, from low numbers after holiday periods to as high as 60.
Last year, 92% of outbreaks in schools involved ten cases or fewer. Just over a third of cases involved two or fewer cases.
Also today, teachers' unions expressed disappointment at confirmation that the delivery of 10,000 C02 monitors to schools will be delayed for some weeks.
The first data showing how schools are faring in relation to Covid-19 since they returned has been published by the Health Service Executive.
It shows a positivity rate in schools of 4.5%.
Before the summer, the positivity rate in schools' testing hovered at around 2% or up to 3%.
15 cases of the virus were detected among students at second level.
However the HSE has warned that the data as it relates to primary and special schools is incomplete "due to testing organisational difficulties through the schools processes". It says its figures do not take into account "significant testing that was undertaken through self-booked tests".
The figures find that 54 cases were found among primary school children, and one in an adult working in a primary school.
These cases relate to testing that took place in relation to 378 schools in the first full week of schooling this month (5 to 11 September).
They included 242 primary schools, 131 post primary and five special schools. No cases of the virus were detected at the special schools.
The tally of positive cases, as always, does not include the so-called index case, which is the original case that would have prompted the school testing in the first place.
This positivity rate of 4.5% is higher than the rate encountered in schools before the summer, but it is lower than the rate for the school-going age group in the wider community, which currently stands at 6%.
Last week saw a total of 3,583 cases of the virus detected among under 18-year-olds, according to the HSE. This compares to 4,057 in the last week of August, and 4,064 in the second last week of August.
The bulk of last week's cases - 1,922 - were detected among primary school age children. 691 cases were found in those aged four and under, while 960 cases were detected in those aged between 13 and 18.
Additional reporting Emma O Kelly