It's already been settled that schools can not legally require a child to recite the pledge of allegiance in the United States of America, in fact they can't even require a child to stand up for it, per a separate case.
So lets say that two students in a classroom, who sit next to each other, have chosen not to stand or participate in the pledge of allegiance. During the pledge of allegiance the two students continue an unrelated whispered conversation while the rest of the kids are reciting the pledge of allegiance.
Can the school prevent these students from having this conversation?
On the one hand forcing students to maintain a respectful silence feels similar to forcing a child to stand during the pledge as an indirect method of supporting the pledge. However, schools have the right to prevent talking and disorderly conduct from children in general.
If the children in question were speaking quietly, not loud enough to be overly disruptive to those participating in the pledge, would these theoretical students have a right spend the time talking, since they refuse to support the pledge, or would the school be legally justified and forcing them to stay silent during it?