Are children to be educated to wash their hands after the above mentioned actions?[1]
Children above Chinuch: Children that have reached the age of understanding are to be educated to wash their hands after the above actions are performed. The teachers [and parents] of the child are to take special care to ensure that the children do not learn Torah and say blessings after scratching their heads or touching the covered areas.[2] Nevertheless in order not to disturb the order of the class it suffices for the child to clean his hand on his desk and the like, and washing is not required at that moment.[3]
Children below Chinuch: Children that are below the age of understanding [i.e. below Chinuch] are not obligated to have their hands washed after the above actions. See Chapter 3 Halacha 5 for further details on this matter.
[1] Ashel Avraham Butchach [Mahadurah Tinyana] 5; Piskeiy Teshuvos 4:18 footnote 184
[2] Kaf Hachaim [Falagi] 8:31
[3] Based on Teshuvah of Gaon of Ragatchav in Salmas Yosef 25.