The internet is a great resource for your child to get all of the information they need on the various projects they complete. The question many parents have is about how much access they should give their child to the internet. Some parents allow their children to have un-tethered access to the internet with laptops. Others simply have a computer set up in their room. Others still have a computer which is set up inside the home in a central location.
It is understandable you would want to control the exposure your child has through the internet. It is also important to not cause them to challenge you in regards to the computer. Depending on the age of the child, it may be a good idea to sit down with them and talk. Explain why you limit access in certain directions. When children feel they are being treated unfairly, they will act out by rebelling. This is a dangerous game when it comes to the internet.
The best idea is to allow your children to access the social networking sites all of their friends are using, but restrict the usage to a reasonable amount of time. This will allow them to get what they want while you get what you want. You can always set up parental controls on the computer to keep your children from accessing sites with pornography, or reputations for linking adults with minors. When your children know the restrictions are to help them, they will not challenge you.
In extreme cases, it is possible to set up programs which will track the usage of any computer. This will show you exactly what your child is doing with the computer. This should only be done when you suspect your child is at risk. It is not a good idea to use this as a normal monitoring tool as it is a violation of privacy. Children have a right to a certain amount of privacy as long as they are not doing anything which is dangerous.
In the end, your child needs to understand the importance of the internet as a research tool. Viewing the computer as nothing more than a toy is dangerous for their development as a student. It can cause them to waste time they should be studying by playing games, or socializing with friends.