I am a teacher for third grade boys. Over the year there were some times when I got upset and embarrassed a student in front of other children even though I could have done it privately; is there any effect in their mechilla now, or do I need to wait until they are Bar-Mitzva to ask for forgiveness?
Regarding your question, you do not have to wait until the child is bar mitzvah. Although regarding money matters the mechila of a child doesn’t count , and even if he mochel he can take back his mechila, however regarding personal hakpada or resentment, a child can be mochel. Therefore someone who hurt or embarrassed a child may and should placate the child and make the child feel better and be mochel him even when he is still a katan, and it is considered as if he was mochel. Often people think that they can’t ask a katan mechila, therefore they feel that they have to wait until his bar mitzva, but by then they are too embarrassed to ask, or they forgot about it, and the issue goes unresolved. Therefore they should know that they can ask a katan mechila.
Tosefos Baba Basra 143b D:H V’im, that when the child doesn’t have a loss by being mochel that his mechila is valid. Also see Chut Shani (MIli D’nekizin) pg. 348, Hayomim Hanoraim pg. 344, Reyacha Kmocha 3 pg.346-347, Shut Even Yisroel 8-52 (15) regarding asking a child mechila for not answering him shalom. Also see Tosefos Kesubos 107a D:H Ktana, that for small things ( even money) a katancan be mochel. On the other hand there is a famous story with the Steipler ztl brought in Toldos Yackov pg. 162 and other places that he once came special to a bar mitzva in order to ask the boy mechila because he couldn’t ask him beforehand since he was a katan. The story was that the Steipler saw the boy learning during from what appeared to be gemora during Rosh Hashana davening and he closed his sefer. Afterward he realized that the boy was looking in his machzor. See Doleh U’mashke pg. 380, who asks on this story from tosefos, and R’ Chaim shlit”a answer that there it was also considered a loss. However it is brought in Derech Sicha pg. 174, and Ashrei Ish 3-pg. 126, that they cannot be mochel. Nevertheless, there are plenty of poskim to rely on that one may ask a katan mechila.
There are numerous stories of gedolim that went to children to ask them mechila. R’ Eliezer Turk shlit”a told me a story about the Chazon Ish that he heard from R’ Movshovitz zt”l (Rosh Yeshiva of Novarhodok) that the Chazon Ish once pinched a child on his cheek, and after wrds he felt that maybe it was too hard, so he went all the way to Yeshivas Ponovez to ask the cild mecila. Also Sarfei Kodesh pg. 318. Also see Pele Yoetz (Hak’aah) who brings a story of someone who took care of an orphanage and when he died he asked that they ask mechila from the small small children. (However Shut Aderes Tiferes 4 pg. 319, that over there it could be that he had no other choice) .