Recordings of a class clearly show the lecturer and students (either moving or still). You need permission (tacit or otherwise) to make such recordings as individuals may always choose not to be included. Once a recording has been made, those appearing in it can only object to the recording's disclosure if they have a reasonable interest in doing so.
Furthermore, the GDPR prohibits the use of personal data about an individual’s race, religion, health, sexual orientation, criminal record or membership of political parties and trade unions. If class recordings reveal someone’s race, religion or physical deficiency, for example, this is a problem. In that case, it is safer to ensure express permission for the use of these recordings in a contributor declaration. If the pupils are minors, this declaration must be signed by the parents.
At some schools, the parents are informed during enrolment that the school may record some have classes and it is assumed that the parents have no objection to this without further notice. Especially when pupils/students are clearly shown or playing an important (main) role in the video recordings, you are advised to ask them (or their parents) to sign in contributor declaration clearly stating their permission to use their image in all the video's intended forms of exploitation.