My son has been learning for 2 years and now has 段. In my opinion, the most effective way to improve is to join a 兒童圍棋學院. They can learn the theory during weekly lesson. There are many theories like 定式. My son learns different things every week and is still improving his "chess strength". There are many kids staying in the academy, especially at weekends, and children can play chess with opponents of comparable strength, and improvement is very apparent. They can also play chess with teachers and during playing, teachers can point out their weak points so as to get improvement.
Playing chess on the web is very important too, because they can do it at home, and it's better than playing other computer games. But the opponents will not comment which step is good and which is bad. Therefore, playing chess with teachers is the most effective way to improve.
Any parents who have kids playing go-chess and joining the many competitions are welcome to share their experience with me.