Islamic laws permit beating a child ONLY if all the  following conditions are fulfilled :-

1. Child must NOT have reached buloogh ie. boy must be less that 15 yrs old and girl less than 9 years ,as per hijri calendar.

2. Only the father or grandfather can do so ( wali).any other person including mother or teacher must have permission of either of the Wali

3. It must be with the intention of correcting the child and not to vent ones own anger.

4.Hitting is permitted only thrice ,not more times .( some rare exceptions exist tho)

5.Beating is the only way of correction & there's no other better way.

6.It should not be hard so as to leave marks on skin as a result.

In case there are marks on skin then diyat becomes payable to child as per rules .
Marks on face skin ;Redness is 1.5 gold Dinar, Blue/Greening 3 dinars and Blackening 6 dinars.
if marks on other than face then half this amount
1 dinar is =3. 5 gms gold

Source : Shaikh Ehsan sadiq 2nd khutba atMasjid Rasool on Friday 1 Jan 2016