"Privacy" and "internet" are two terms that go hand-in-hand in that one's existence depends on the non-existence of the other. The internet, inherently, cannot exist with privacy. Yes, one can protect their privacy—to an extent—on the internet. But the internet's purpose and well-being depends on its nature to present information to the masses.
This is somewhat of a double-edged sword. On one hand, there is a certain openness of the internet that makes it appealing. On the other hand, anything posted on the internet is, in almost all cases, permanent. Not that something can't be taken down—it certainly can. But, since almost anything the normal internet-goer would be posting to on the internet would be open, it can instantly be viewed. There is no way to stop this. All those pictures someone else posted on Facebook? No way for you to take them down but ask the uploader. Even if they take them down, the internet has already seen them. People could've saved them, Facebook has them in their records. It's an entirely new concept that is at once exhilarating and terrifying.
On a relevant note is the issue of identity. The internet's innate openness creates a ground for anyone to do anything and say anything. This, of course, leads to such problems as cyber-bullying. This creates a problem for parents: how can they keep their children safe online? There is no easy answer. They can simply prohibit their children from using the internet, though this seems a bit extreme, not to mention they are missing out on a wonderful learning tool. They can limit their child's internet use, or even monitor it through the use of a third-party application. These may be reasonable or even very successful solutions for some; to me, as a teenager, they seem all too
parent-ish. For me, the best approach would be to simply talk about the subject, warn about the dangers, and tell children to not get sucked in to a world where they might put themselves in a vulnerable position to cyber-bullying.
Truth is, most parents don't know a rat's tail about what their child does online. Is this a bad thing? From a parent's perspective, understandably yes. And it is, in most likely the majority of cases, a bad thing. But, as with most things with the internet, it is that all too familiar double-edged sword: the internet has a highly underrated educational functionality. Believe it or not, people learn stuff on the internet. They may be boring their eyes out on Facebook or Tumblr most of the time (this, by the way, is in no way a good use of time and the author is not promoting it in anyway), but there is also a sense of exploration on the internet. It is, after all, infinite: there is a whole world of untouched media and information, ready to be consumed by the hungry individual. It may not always be the most respectable media or information, but at least its something. The trick, then, is to promote this pursuit of this information; spark the curiosity, and put the internet to use in its fullest potential.