Cod - DD's been doing them this year and seems to have learned them by 'counting in' different numbers. So started in Y1 counting 2,4,6,8... then 5,10,15... Now this year 3,6,9... 4,8,12...
Once they are reasonably proficient at the counting in different bases they then add on the 2*3 = 6 etc etc.
I don't think they have ever chanted in the way we would have done as children. Not least because the whole class is at completely different levels in maths and don't seem to do much whole class work in this subject!