My question involves education law in the State of: California

Hello, I'm a high school teacher in California. As a new teacher, I want to be able to self-assess after a lesson and would like to videotape a class. I do not plan on posting this video to any internet sites; however, I may submit it as part of a job application where it will only be viewed by other eduction professionals.

What precautions should I take in videotaping in my classroom? Do I need to get consent from parents or students? How about from my administrator? I keep reading that the classroom is a public space and is therefore an okay place to record. I cannot find anything in California's Education Code about this so I figured it is covered under other types of law.