Moon in Gemini suggests a strong need to be heard. Such a person must pronounce all his emotions. In addition, it is very important for him to hear and know, what you feel. Without certainty in the emotions and feelings the young Gemini will feel lost.
In addition, the Moon in Gemini is suggesting the need for diversity and communication. Without the inflow of a fresh information and without enough chances to talk to someone, Gemini will become nostalgic and depressed. Without diversity in everything, they just can not sit still, creating a storm in their own souls or in the environment, to somehow avoid the monotony.
Be sure to listen to your child. Surround him with a lot of sources of information (books, pictures, etc.) - and you will not need to exert much effort to develop him, he instinctively chooses all the information and absorb it faster than any other kid. Be sure to spend more time outdoors, and talk to your child about everything you see. And try to avoid any ambiguous situations.
The child with his Moon in Gemini must feel that the parent is clearly confident in what he does. This will provide his inner comfort.