I like your analogy with learning a language, and I would use that analogy to say the current education system is only teaching grammar rules. Imagine sitting for hours a day for an entire school year conjugating verbs without ever reading a story, listening to a conversation, or trying to pronounce words.

There is so much more to mathematics than calculation. Proofs, number theory, and simulations can all be understood by children and are much more important to their education than long division.