Ok, I don't think you have my point at all, either with Reading or Math. I thought it was obvious I was referring to writing not spoken language, as the learning of either skill differs quite substantially.
My kids went to a french immersion school and their spelling was awful for years. So believe me when I tell you I'm not a stickler for perfection, but eventually, kids do become able to write coherently, obviously some better than others.
So let me clarify. It's difficult to read if you don't know the abc's, but you can speak without reading.
We memorize letters, how words are put together but how we do this differs. I have no doubt your daughter hated learning by rote. Even three years olds, who may love watching the same movie over and over, would get bored soon with flash cards.
We learn language by repetition, by mimicking sounds, by pointing to our nose or belly button for the umpteenth time. We learn to pronounce letters or groups of letters, in varying ways, depending on the word or accent.
Most people love music, can listen to it, hum along with a song. It doesn't mean they could sing an opera. I'm a big proponent of learning to play music by ear. That doesn't mean, I don't believe musicians shouldn't learn to read music. The basic building blocks... the fundamentals of both music, speaking and math are similar. (Edited to say: But to become a proficient musician, practicing the same piece or scale is necessary, just like solving the same types of math problems ad nauseam.)
Creativity, whether it be in the sciences or the arts, is not diminished by learning the basics. How one person learns may not be consistent within a classroom, so I think its more important to cater to learning styles rather than one set method. Regardless, every student must understand the same material, however they learn it.
I think it is important to learn the basics, I didn't say problem solving wasn't one of them. Most people learn to read by reading, that is not unusual. If you don't understand a word, you flip through a dictionary. The same with a mathematical problem, if I wanted the area of a circle, I would use a formula.
Maybe your daughter will figure out another way to do it and that would be awesome, but for me π • r² works.