Are you friends on FB with your childs teacher? Do you expect to be? Does it matter what age your child is? ie: I'll be friends with childs teacher until she is in grade X. I have a kindergardener, and thought contact with the teacher would be pretty easy thru FB. Should I be 'bothering' her through there, or should I be using the email address she provided at the beginning of the school year?
As a teacher, I do not friend my students or their parents. The only exception that I have to this rule is people I was friends with BEFORE I was their child's teacher. Please don't put that kind of awkwardness between you and the teacher. My FB page is for my friends and family, I don't want to be friends outside of school. That is my personal area, I like to keep it that way.
I am FB friends with some of my former HS teachers, just to keep in touch, and some of my former students, but no, I would not recommend friending the teacher. She needs her space, too. I value the continued contact, but there definitely needs to be a separation while she is teaching. Maybe friend her after the year ends, if all goes well.
I would not be friends on FB. You want to keep the relationship separate from the rest of your life. I would just use the email she provided. I guess I would worry if you posted something or someone posted something on your wall that the teacher found "offensive" or "questionable" on how you're raising your child. You never know what people will think.