Experts say it is perfectly fine to look up your child's teacher on social media, but you shouldn't go on a deep dive.
As a professional, the teacher should be aware of public access and should post accordingly. The onus is on the teacher to ensure that he or she has a professional presence online.
Do not dive deep into an investigation; a casual lookup should have its limits. If the profile is private, do not request to be the teacher’s friend; this is an uncomfortable request for a teacher.