I think there is considerable confusion between what the government are proposing and mass testing which is what teachers want. So...
Let's give an example showing the 3 options. In my example I'm going to use y9 from my school, there are about 300 students in the year split into 11 teaching groups - they stay in these classes for all lessons but mix with the wider year group in social spaces at break and lunch. They share toilet facilities and space on buses with their year group.
Current scenario: y9 student tests positive, close contacts are sent home to isolate, these are determined by the seating plan and who the student stays they spent social times with - usually around 15 students are asked to isolate.
Government scenario: these 15 close contacts wouldn't isolate, instead they would attend school and be tested each day using a test that only picks up 50% of positives. If positive they get sent home and their close contacts commence testing.
Mass testing scenario that I and other teachers would like: 15 close contacts sent home, others in class (or better still, year group) tested to pick up other cases allowing better control of spread.