Muffling drums is technique used to dampen the 'ringing effect' which is sometimes heard after a drum is played and is used to improve the sound. It is a very common practice to do this and can be done in many different ways to reach your desired drum sound. I am often speaking to students of mine in lessons about muffling and they have had some great results with it. See the video below for more information.
Wearing ear protection while drumming
As I'm sure you are all aware drums can be a very loud instrument to play and it is absolutely necessary to take the required precautions to protect yours or your child's ears. There are many forms of ear protection on the market from foam ear plugs you can find in the travel section of a supermarket, to industrial ear defenders to custom made earplugs where a mold or your ear canal is taken to create the plug. See the video below for to explain this in more detail.
Using Silencer pads on an acoustic drum kit
Acoustic drums are as we know very loud so it can be helpful to practise drums with something called Silencer Pads. These are made from a heavy rubber material to add weight on the drumhead and reduce the sound considerably to avoid disturbing family members or neighbours. See the following video.