1) Although for all other biblical laws a boy does not become an adult until he reaches the age of thirteen years and one day, and a girl until she reaches the age of twelve years and one day, as regards the laws of vows and oaths this is untrue. As regards these laws, a boy who reaches twelve years and one day, or a girl who reaches eleven years and one day, who make a vow or an oath, and understand fully the vow or oath, the vows or oaths take effect. (Kitzur Shulchan Aruch 67).
2) A child younger than the above ages, however, even if they understand exactly the consequences etc. of their vows or oaths, is incapable of effecting a vow or oath. One should nevertheless become angry with them and teach them not to become accustomed to using expressions of vows or oaths, and if their vow was for an easy thing without any physical distress, they should be made to fulfil their oath. (ibid).