In the novel Ender's Game, all little kids are protected and closely watched via a 'monitor', a device that sees and hears through them. This happens from around age 1 to about 5 or 6. So my question is, how would being monitored 'round the clock change how people act, from ages of 3 to 12? Please don't say this is too broad: I'm asking how people would act when they know they're being watched, but specifically watched by a thing attached to them by the neck.
I liked Snow's answer, but I feel like I should add my own.
In Ender's Game only a few children were monitored. That idea of the monitor was that these children were special, and had to be watched either to determine their potential, or to safeguard their safety - remember that when a bully attack's Ender and no one shows up to stop him, everyone involved is surprised.
And so, would EVERYONE be monitored, or is being monitored a sign that you're a cut above, and might be groomed for a leadership position later in life?
What is the PURPOSE of the monitoring? Is it to exercise control over people? Keep them under constant watch, afraid to overstep the boundaries of social etiquette, or laws? Could it be that the monitoring device would serve a dual purpose and also tutor children, by speaking to them, and providing them with lessons and knowledge as they interact with the world, thus rendering schools unnecessary?
There's also a logistical aspect to this. In Ender's game a human being is monitoring his feed. However, if you monitor EVERY CHILD it would quickly become impossible to keep track of them all. Would an AI do the monitoring?
And so, we come to the real answer to your question: how would people, and the children, react to being monitored. How would it shape society.
The monitor as a tool for control
If the monitor is constantly reacting to anything it perceives as being "wrong", or "unlawful", you'll end up with a highly indoctrinated society, with some individuals who hate "authority" to a very high degree. It might also affect some people in the sense that the monitor becomes their conscience, and that without it guiding their actions their morality becomes rather ambiguous. Adults who enjoy not being monitored in this fashion might avoid having children, so that their actions are not monitored through their children's devices. (although i find it hard to believe that this kind of society would not also monitor adults in some way)
The monitor as a benevolent teacher and guardian
If the purpose of the monitor is to safeguard and teach children, and not to control/brainwash them, then society would probably see this technology as highly beneficial. Children would probably grow up thinking of their monitoring device as some sort of guardian angel, and maybe even be upset at parting with it, or feel insecure (then again a teenager with a monitor may be seen as "lame", and not willing to "grow up").
In this situation kids would probably not be too anxious about always being "monitored", because the device would not police them, it would only guide them, and mentor them. Some mentally unstable kids who enjoy hurting others, or simply causing mischief/pain would see the monitor as a negative factor, but that would be a minority.
The monitor as an indication of social status
If only kids who are seen as being having high potential are monitored (selected based on a genetic scan at birth, for example), this alters things significantly. Children can be very cruel and vindictive, especially to other children who make them feel "less special" - quite often the smartest kid in class is picked on, and bullied.
Even then, however, it's society's take on what it means to be selected that determines how it all works out for these children. There are really two main scenarios:
a) The Monitored as Nobility
If the monitored reach their potential, they are trained to become part of an elite that rules the world and lives high above the means of "regular" people.
Being "monitored" could become a sort of social stigma among children. Teachers and other adults might regard these kids suspiciously, wondering if they too are being assessed through the monitor. All in all, the monitored individuals would end up feeling very alienated from society.
Furthermore, these kids might regard each other as competition, and develop ways in which to hurt each other (physically, or psychologically, etc) that are not detected by the monitor. They may become highly manipulative, and competitive, because the stakes are very high for them.
Losing their monitor later in life might lead to them feeling incredibly lonely, as their whole identity had formed around being "monitored". What's worse, some of the people who hated them for being special might now commit violence against them, or otherwise bully them mercilessly.
These kids would probably follow one of two paths:
The Chosen Ones who are found to live up to their potential and are taken away to be trained for a higher purpose, and who mostly develop a feeling of superiority to everyone else. Think of it as a "nobility" based not on your ancestors, or family name, but on your genetics. These people might end up looking down on the "unmonitored", even regarding them as genetically inferior.
The Failures who are found wanting, and simply left behind in the general population. These people would probably look at the special treatment of The Chosen Ones with great envy, and grow to hate them. Worse, the general population might react very negatively to them, seeing how The Chosen Ones lord it over everyone else.
b) The Monitored as The Future of Mankind
If the monitored are not meant to "lord it" over the rest of us, but be our benevolent leaders, our top scientists, etc, then society would probably hold these people in very high regard, and see their training and mentorship as a high priority.
I know my answer covers a lot of different scenarios, some of which you won't be interested in in the least, but I hope it helps you none the less!
My first reaction is, at age 5 they'd have very little awareness of the device. But you said you'd have it go to age 12. By that age, kids (especially girls) start to mature, and are likely to resent being watched and controlled.
A big factor here is what feedback the monitoring system gives. If you're a kid and you steal from the cookie jar, do you get an electric shock, or does nothing obvious happen because the system only watches for troublemakers looking to kill someone? You'll grow up with a different attitude toward the surveillance depending on that. Recent experience says that government can apparently get away with a whole lot of surveillance against innocent people so long as it's not openly acting on the information in constant, petty ways. If the gadget rarely rebukes people, they might not care much about it. If it's constantly screaming at them to eat their vegetables, that's a recipe for revolution and worse: people equating all morality with an outside force threatening them. And when they get free of the outside force, Bad Things will follow because they grew up with a corrosive moral training.
How about an in-between level of reaction, where the system doesn't scream at you but you know it's taking notes, building a permanent record that'll affect your future? Then you might get a darkly funny form of gaming the system like some video games with moral choices. Do one 10-point evil deed, then do ten 1-point good deeds and you're back to saint level. For a real-world example of where this might show up, see China's proposals for a "social credit" system where being a dissident or associating with troublemakers cuts you off from good credit and expedited visas and other privileges.
Another thing to ask is how equal/fair it is. If your classmate doesn't get yelled at by his neck-gadget for misbehavior because he's a politician's son, you'll likely see that this system is unfair and resent it.
Something to look at for inspiration for when the device gets removed is the Amish tradition of "Rumspringe" (sic), a time when young Amish are invited to go out into the world and stereotypically party, see that the outside is scary and outside their comfort zone, then return home to be part of their parents' community. The college experience in general is like that too: people newly freed of close parental monitoring change the way they eat, decorate their rooms, study, and so on.