Learning language is part magical process, have you noticed how kids catch up on grammar without actually learning the rules on speaking a language, Whatever language we use at home kids just start conversing in it with perfection.
Same goes for learning the second language too, in our case it is English. It only makes sense therefore to start speaking to them in both the languages, before we teach them the tools that make up these languages.
I was never rigid with the teaching methodology, kids learn in thousand different ways. We bought little kids first big book of Dinosaurs by National Geographic, even before my son started on alphabets.
He learned letter recognition from that book, and it helped that dinosaur names are complex and big, in our effort to read the names of dinosaurs we covered all letters of English Alphabet.
The point is we don’t have nor should aspire for a set method of teaching, I think learning happens when we make sincere efforts to enable our kids to know and learn about things, and just as they learn, we too learn how they learn :).