As already mentioned free coloring pages are a great way to teach your child all sorts of things, numbers for example. There are different ways this can be done, one way would be to simply have the number somewhere on the page, such as the number 10, and then somewhere else on the page would be an object or animal cleverly twisted into that number. There could also simply be 10 of something on the page, you can get your child to color the page in and then count out how many apples for example there are, which will obviously correspond to the number on the page.
The last benefit I would like to discuss, actually consists of two advantages. Coloring allows your child's creativity to blossom, but it also provides insight into a child's emotions, and often child psychologists will utilize this tool to learn more about a child's feelings or frame of mind at a particular time. This is another great benefit of coloring for children, it can help you to understand how exactly your child feels at any given time.