There is a whole lot of essential musical information that traditional notation cannot and does not express: time feel, rhythmic placement, tone, gesture , timbral shading, articulation, phrase shape, etc.
And, the most direct way to grasp and internalize these musical elements is through hearing, then emulating. In fact, much of the time, when learning music aurally, we automatically absorb these elements of the music without even trying. It's the analog to learning the cadences, inflections, grammar, and accent of a spoken language.
So, with this in mind, I have all of my students—at every level—learn music by ear from recordings. I also teach them music by ear in our lessons.
Aural learning can be difficult. Here is a helper tool.
But, it's not always easy for students to figure out all of the pitches. And, this part of the process is where most students seem to get hung up. So, inspired by GuitarTAB notation, I've begun using these home-brewed "tablatures" as a small crutch for these students to help them in the learning-by-ear process. (GuitarTAB only shows the user which string to play at a specific fret, in order of the song. Beyond this, the user needs to know how the song sounds in order to make music using this notated tool).
I am finding that the students using these JazzTABs are still absorbing ALL of those other musical elements mentioned above. And, more importantly, they're losing their reluctance to play something else by ear. AND, they're also getting better at picking out melodies by ear. AND, they're having fun!
My former teacher at Northern Illinois University, Ron Carter, who is one of the US's leading authorities on jazz education, told me recently that he advises developing musicians to have 2/3 of their music-learning be aural and 1/3 be notated. It's a natural way to learn music, fostering the student's direct connection between sound and his/her instrument.
I believe that aural learning allows student musicians to tap into their natural, innate musicianship, something we all possess to one degree or another. As students become more engaged in sound relative to their attachment with sight (i.e. "read this note, press these keys and blow"), notation becomes a more meaningful representation of music (i.e. sound).
Try them on for size