We generally advocate using a fixed camera at the back of the classroom or focused on a particular group of students. If the camera is fixed on a tripod, then there will be no need for anyone to attend to the camera once it is switched on. An extra microphone can be very useful (e.g., with a Bluetooth connection to the camera) in order to ensure good sound quality.
There are significant ethical issues around filming in lessons. Gaining ‘informed’ consent from students and their parents is important and every country will have its own guidelines, the UK’s British Educational Research Association (BERA) publishes ethical guidance for this kind of situation. If clips are only to be used for the purposes of professional development and never shared beyond a close circle of teachers, this goes a long way to mitigating concerns. There are video recordings of lessons in the public domain that have become quite widely associated with “bad teaching” – no doubt participants gave their ‘informed’ consent to these recordings, but what has happened to these videos raises the question of how informed any consent can ever really be? We prefer to think of the ethical dimension of video recording as an on-going conversation that extends beyond the gaining of informed consent and where participants have the right to withdraw consent at any time.
There are several publications that deal in depth with issues around video recording in classrooms (Jewitt, 2012) and in mathematics classrooms in particular (Maher et al., 2010).