Ensure that you explain the educational benefit to recording the teacher for a lesson. When you record, it's important to make sure that you do not record anybody else apart from the teacher. You are correct in saying it's actually illegal to record somebody without consent (and this is no different in a classroom context, as it's not "public" so to speak). I actually had a situation late last term where a student was recording (without permission) and I had to stop it as it contained other students and the student did not request the consent of the teacher before doing it.
You have to respect the decision of the teacher, however. If they say no (and there are going to be a few teachers that don't feel comfortable with you recording them for various reasons), you have to follow it and seek alternatives to assist your learning (e.g. youtube vids, edrolo).
Even if the teacher provides consent, you cannot record or take photos of any other student. You can get into some serious trouble if you end up taking a video/photo of a student without knowing if there are any restrictions in place (e.g. access/custody issues resulting in photo/video bans in the school environment).
I personally can understand and I get the reasoning behind why you'd want to record a lesson for playback later on.
So key points:
- Consent MUST be sought from the teacher before you even photo or video the teacher, preferably in writing but verbal is fine too.
- Even if you have consent, only the teacher can be recorded. No students should be in your recording (nor should anybody who hasn't given you explicit consent).
- Provide an educational benefit for why you are doing it. Support yourself. If you just approach a teacher and say "can I record you", the answer will most likely be no.
- Some teachers will be happy for you to, but some will not (for varying reasons). Respect the decision of the teacher and move on if they say no.