You might also see it with "how to drum", but it's not necessary.
I wonder if the version without "how" gives, strictly speaking, the same meaning as the version with "how." In my experience, there is normally a "should" meaning associated with the "how"-less construction: "She taught me to breathe"; "He taught me to think." Sometimes we even add things that make the "should" meaning unmistakeable: "She taught me to breathe deeply"; "He taught me to think before acting." Such sentences aren't about technique or about the imparting of a new ability.
Here's an interesting contrast:
"They taught me how to speak proper English."
"They taught me to speak proper English."
Those two sentences are both grammatically correct, but do they have the same meaning?