That's how I was taught in 1977. But I took lessons off-and-on for 6 years and only got through the 2nd year book!

As I'm learning a song, I think about musical "phrases." For example, a chromatic run of eighth notes, or maybe even a few sixteenth notes thrown in. In order to play a run like this "a tempo," I've come to realize that I have to have my hand positioned correctly at the beginning of the phrase. So after a few fumbling attempts, I might annotate the paper score. For example, on an ascending phrase I may write "1" (or "thumb") next to the first note, so I know to reposition my hand at that point. If I remember to do this, I can usually play the remainder of the phrase by feel, and without moving my hand.

Sometimes I'll do something similar with the chords. If it's a slash chord that has to be played in a certain inversion, I'll write the word "shift" and draw an arrow so I know to reposition my hand. This is best done on a whole note, or tied notes when you have plenty of time to get situated. I may or may not write finger numbers above the chord. More so than the melody, the chord fingering has slowly become natural, at least in the familiar keys.

Now I'm not above transposing a song to improve the playing comfort or ergonomics- for example, I prefer to use my longer middle fingers on the black keys. Also, for memorizing chord sequences, there's a lot of value to playing in a familiar key such as C, F, or G.

Despite all this I still make plenty of mistakes, late notes and late chords, etc. I pretty much have to play a song over and over until it's ingrained in my "muscle memory." I'm no musician and I don't want to spread heresy. So if I'm wrong in the way I'm going about this, please counsel my ignorance!!