That's what my typing teacher taught me about typing, that by not memorizing all the key+finger combinations I would never type (Owning a computer, I was self-taught and used all the wrong fingers). Twenty years and a law degree later, after authoring literally thousands of pages, I still cannot say which finger is supposed to hit the 'r' key. Somehow I muddled through. The point is that rather than memorize combinations of seemingly random numbers, the same knowledge will come naturally as students learn other aspects of math.

Seems to me that you just spent twenty years to slowly develop muscle memory, when you could have achieved the same results in a few weeks. (I did the same thing.)

> the same knowledge will come naturally as students learn other aspects of math

The key difference here is that being slow at typing for twenty years didn't discourage you from typing. Being slow at math can discourage kids from doing math, and the "twenty years of regular practice later" moment will never arrive.

I can't recall the commands to my text editor. I just look at my fingers to see which keys they hit.

Yes - When someone asks me what a particular key combination is in emacs or Eclipse, I put my fingers out like they're on a keyboard, think about doing the thing, and, look at what my fingers are doing.

To bring it back to the article: It's similar with a lot of things - you sort of need to memorize aspects of it to do it fluently. As part of calculus, you sort of need to know how to do polynomial factorization. Intuition is great and helpful, but you also need to be able to proceed methodically in order to produce or understand proofs. Scales on piano are boring, but you don't just tell kids to feel like they're Bach and they start playing Goldberg Variations. Why on earth we think the intuition is not only necessary but sufficient is unfathomable to me.

Simple. You use the r finger.