Children who ignore you at home often comply at school
Parents told by a teacher that their child is co-operative and attentive tend to hear it as an accusation. It is more useful as data.
What classrooms have
A classroom supplies an enormous amount of structure invisibly: fixed sequence, visible expectations, peers doing the same thing, and instructions delivered once, to a group, from the front. Homes supply almost none of that, and are not supposed to.
The same child therefore faces a much harder compliance task at home — ambiguous timing, competing activities, and an adult usually doing three things at once.
What transfers
Two things from classrooms transfer well: doing the same sequence in the same order daily, and giving instructions from within arm's length rather than across a room. Neither requires making home more like school in any way a family would notice.
What does not
Group-management techniques — charts, public tallies, whole-class rewards — generally land badly in a family, where the audience is a sibling and the relationship is permanent.