Think primarily in terms of fingers and keys rather than arm.
What happens at the end of the fingertip is what is important.
The greatest finger activity is in the knuckle joint. The fingers are prepared for both the black and white keys by the first two finger joints.
Practice is arranging things in your mind until they become automatic.
An article in The American Music Teacher in 1939 quoted Petri regarding practice: A pedestrian who was on his way to Athens met a peasant working by the roadside and asked him "How far is it to Athens?" The peasant replied, "Walk!" The man said "I know I have to walk, but tell me how long will it take me to get there?" The peasant repeated, "Walk!" When the third inquiry drew forth the same information, the traveler, giving the peasant up as a hopeless idiot, walked away with great strides. After a few seconds the peasant called out: "Half an hour!" Greatly surprised, the man turned back and said: "Why did you not tell me that at once?" Whereupon the peasant replied, "How could I tell you before I saw how you walked?" So what would be the use of telling a pupil how long to practice without knowing how he practiced? You can't help being your own teacher and pupil when you practice. If you learn quickly and incorrectly, that's bad. If you learn quickly and correctly, that's good. If you learn slowly and correctly, that is also good. But is you learn slowly and incorrectly, that's the worst. If you do the exercises right, you don't need them. If you do them wrong, they may do you harm.