Our social image is tougher to discern than our physical one. We can easily see our face in a mirror; it's tougher to see how we come across to different people in different situations. For that I think it'd be interesting to get kids a fiercely reciprocal robot.
One problem with understanding how we come across is that there are different lag times and different probabilities for feedback from people. One person might patiently take our stupid jokes or tendency to volunteer "honest" feedback about how fat they look in that outfit while another will immediately take offense and avoid us later. One will put up with something from us for a couple of months before deciding that it is too much and another will put up with it for life. We don't really know how we come across as social beings and particularly for the young this process of understanding who we are to others can be slow and difficult.
A potential solution to this is the fiercely reciprocal robot. Imagine a robot that a child aged 2 to 14 could interact with. This robot would reciprocate everything from being ignored to telling amusing jokes to giving compliments to insults, handshakes to punches. If the child looked away when the robot was telling a story, the robot would look away; if the child made appropriate noises - the Ooohs and the "oh no's!" to express amazement or alarm, the robot, too, would make such noises. If the child expressed encouragement rather than complaints, the robot would be encouraging rather than complaining. If the child were happy being with the robot then one might safely assume that the average, typical peer would also be happy to be with the child; if the child were miserable with the robot, then one might safely assume that the average, typical peer would be miserable with the child. Whatever the robot made one feel would be a reflection of what the child made others feel.
Of course you would need a "model good form" mode that might inspire the child to new behaviors. It could not be all reciprocity. Sometimes instruction is needed.
The default mode would be reciprocity, though, and this would be a great teacher and predictor. As it turns out, the average person is fiercely reciprocal. If you are kind to strangers they're generally kind to you; if you are rude to them, they're generally rude to you. For the most part, who we are dictates who people are to us. The fiercely reciprocal robot would be unique mostly in the immediacy and the relentlessness of its feedback.