What is Browser History?
Every web page that anyone visits and when they visited it, while using a web browser is stored in the browser's history (except when the browser is in private browsing mode). Although it can easily be erased or prevented, it is a great tool for monitoring internet activity on your computer.
Above all, healthy communication with your children is the only thing that will achieve the desired results. Tools to monitor or control access to the internet should be used as a secondary mechanism to help prevent stumbling into dangerous territory by accident.
Your child will likely know how to erase the browser's history at a young age. This functionality is used for other things besides trying to hide your child's questionable activities. They should know how to do this. Do not rely on the browser history alone to track your child's Internet activity.
Here are some suggestions for alternatives to logging their activity.