I know from personal experience that many parents asks themselves whether monitoring the time their kids spend on the Internet is the right thing to do. The answer to this question is not that simple and usually depends on a situation.
In my opinion, the younger a child, the more monitoring should take place. As a child gets older, there should be less and less monitoring to allow a child for more privacy.
As I have already said before, it is not easy to answer the question whether monitoring your child while he spends time online is the right thing to do. It all depends on various factors like for example how close your relationship with your child is.