They may be more productive after going outside because they will probably be more content then they were before they went outside. Maybe the mere sight of being outside can in some ways inspire one to want to work hard and study so they can be happy after they graduate.
Change is good. It wakes people up, and gives them a reason
to pay attention. For this reason, letting students go outside for a while is a
good teaching technique. Field trips give students motivation, and stop their
minds from drifting off into daydreams. Trips outside can also be used as rewards
for good behavior, and as learning experiences. When it comes to studying
topics including biology, architecture, and ecology, nothing beats a trip
If Students were given the chance to go outside, they would only become hyper with the possibility to leave. The only way to make them productive would be to let them out for insane amounts of time, which would make the school day an excess of 10 hours just to have students feel ready to do work.
Another is that going outside can be abused as students would do ANYTHING to go, or stay outside.