When student devices are off of the school network their web traffic is still being monitored.
If you would like to setup filtering on your home internet connection, there are multiple services that can do this. The service below works well and ranges from free to $20/year. The free version automatically blocks adult content. The pay version allows sites to be allowed through the block, reports, etc.
You can find information on how to setup OpenDNS FamilyShield here: https://www.opendns.com/setupguide/?url=familyshield