This Chinese proverb is similiar to the English proverb "All roads to Rome". It means that there are many ways to go about things and there is no one right way to do it. This is very relavant when talking about how people learn Mandarin. There are so many different ways to learn, and none is 'one and only correct way' all the different methods are valid.

殊途同归
shū tú tóng guī
different routes to the same destination