Just wondering

I can't believe you assume we think.

As for more of a *GASP!* real answer, I look at music as if it's like a table with multiple legs holding it up (where each leg represents an area to be learned:  Music theory, learning an instrument, rhythm, sound processing, mixing, recording, harmony, physical ability & accuracy, ear training, etc.).  You can only go so far on one leg before things are unbalanced and you need to catch up in other areas.
 
The whole process is a very iterative thing.

My Dad's favorite saying when listening to a "musician" who announces "...and I've never had a lesson in my life..." is generally "Yes,  and it sounds like it".
 
I've never had a guitar (or cowbell) lesson in my life, but I have had lessons on piano and trumpet, so I've been taught music theory which I can apply to any instrument.
Learning to play a specific instrument is a mechanical thing like learning to touch type. Learning how to make music with that instrument requires a lot more which is best learned from a teacher in a structured way.

In my opinion, there is a difference between conceptual learning and muscle memory training.  In addition, different people have different learning styles.  A kinetic learner will study concepts in a different manner than an auditory learner.  The nature of the instrument we study colors our understanding of music and music theory.  
 
I'm a drummer, so my approach to studying a piece of music is to hear it in pattern layers.  Even the most complex arrangements can be simplified by breaking them down and examining each layer individually.  Hearing the patterns, I can follow each line and how they interact with one another.  When I write a song, I "hear" each layer in my mind before playing a single note.  Obviously, others take a different approach.  
 
In high school, I started picking out notes on a piano in an attempt to explain parts to other musicians.  A pianist took pity on me and taught me a small amount of theory.  Armed with an insignificant amount of knowledge, I wrote some songs.  The pianist was fascinated.  "How can you write music with absolutely no idea what you are doing?" he asked.  I could only say that I tried to play the notes and chords I heard in my head.  He watched, fascinated, as I slammed the keyboard.  He would interrupt occasionally to tell me that some of my chord combinations should not have worked, but he thought they sounded great.  He explained to me that as a pianist, he thought of music in a certain way and it colored his concepts.  He also told me to stop hitting the keyboard so hard.  I had a lot to learn.
 
I've known musicians who lacked the music theory education to articulate their musical ideas.  I've also known musicians whose vast understanding of theory was not matched with their muscle memory.  For some, playing music is a mental/emotional exercise and the muscle memory technique is merely a tool for the job.  Others I've known enjoy the mastery of the technique more than the conceptual comprehension.  I can see that there is a certain degree of pleasure in both.  
 
When I'm learning concepts, I can't follow abstract discussions of music theory, but I can appreciate explanation coupled with demonstration.  When I'm studying muscle memory, I need it broken down in to simple pieces.  As I master each one at a slow speed, I can put them together and speed it up.  I've always believed as a drummer that if I can think of the part, I can play it.  To me, conceptualizing the layers of the drum part is essential to playing it.  When I'm playing, I'm listening to the layers; how the drum part interacts with the bass, guitar, keys and vocals.  Everything I'm playing shifts to the background, because I've already thought it through, and I'm thinking about what's coming next.  I'm listening for that build into the chorus, the drive into the bridge, opening up space in the verse, etc.  On the way, I'll sometimes imagine some fills that will fit where the song is going.  As I think of them, they are added to the overall pattern, and then I play them.  I never thought about which stick I would lead with, the mechanics of the fill, or even counting the time.  Instead, I thought about the feel of the song, leading the vocal to the climax of the chorus, snapping into the rhythm guitar's hook, nailing that downbeat with the bass, etc.
 
That's just me, though.  YMMV.
 

I didn't post this to question if one method was better than any other. I believe if one has time to
spend with music they're doing alright.
 
However I am questioning;
Can an example for each of the two methods be given?
 
1. Rote
2. Critical
 
And I may mention what I believe to be a third latter...if this makes it that far.
( "believe" because with "music" I'm not sure my understanding of rote vs critical is correct.)
 
 
 

Maybe;
 
Rote= a process such as; Play this chord ( from somebody showing one how to make it and tellin one , "it is a X chord".)
Critical= explain how that type chord is built.
 
Rote= "play this" ( from somebody showing one how to play a major or pentatonic scale)
Critical= learning how a major or pentatonic scale is built.
 
If we agree I can see going into deeper waters LOL.

Well you got me beat then!
 
Then what is next?
 
Would it be "symbolism" ? ( reading music)
 
 
 
If you're interested in kicking this around Mike...PM me.
 

 I have never heard the term "rote" before.
 
 If rote is a less complex way to pick up music I'm all for it. If rote means one learns from broad concepts and is allowed some personal flexibility. I love the concept. Chord charts, number systems etc. I guess these would all fall into that category.
 
 If this is true then, critical must be mostly the opposite. Diatonics, chord inversions, what things mesh well with other things musically.
 
 If you're asking for examples on critical, probably almost anything classical, and this kind of thing lends itself well to midi. Maybe the composer feels there is an emotional element in their music but it is all distilled down into notes on a page and parts in exact keys and placements. Learning from this persuasion is all about learning your scales, chords, keys and musical relationships on paper.Lots of emphasis on technique. How things are supposed to sound by the rules.
 
 OTOH an example of rote might be a few pickers sitting on a porch in West Virginia somewhere. Neither of them had any "trainin". Other than maybe someone in the family said that this is how you do this and that and they picked it up. No one would say these guys can't play, but if a classical piano player on vacation came along and wanted to join in he had better be a pretty good ear player too.
 
 Years ago when I took trumpet I was told how I was supposed to hold the instrument. Then I saw Miles Davis breaking every rule in the book but he was famous and holding the trumpet the wrong way.He could hit notes I never dreamed of. 
 
 I certainly fall into the rote direction. I don't like all those rules. I have had some formal training but I seldom use it. I played a special number on piano this past week that I didn't really know what I was going to do until I did it. I played with something for about a half hour before I went on. I took something structured and added some stuff to it here and there. It went off without a hitch. I took a song written in a major key and I made an intro in the same format in a minor key, then I merged it into the major key and added some other stuff to that. It all seemed to fit together. The week before that I played  a song using a looper and an acoustic guitar. I added a rhythm guitar part, a bass part and some vocal backups on the looper. I switched certain parts on and off and added a harmonica part. I learned guitar by "rote". Still have a lot to learn but it's fun. We had a pretty full house that day and I got a standing O. One of the few I have ever gotten. I really wish I could concentrate long enough to let someone teach me, but I usually end up learning what I can and learning the rest by trial and error.
 
 If I'm not playing right that's ok. I'm having a lot of fun doing it the wrong way.

drewfx1
To throw a wrench into things: I find that a lot of people seem to learn theory by rote. 

So true. I was working towards this in that other thread.

I believe most try to learn and use most any method they can get satisfaction from. Some just
don't get anything from some methods.
 
One method that hasn't been mentioned- mocking. Well, one may think learning by ear is the same
and I won't dispute it but I think of it differently.
I really enjoyed it years ago when I had a friend that I picked quite a bit with.
The way we worked it in the beginning....we would limit the selection of notes to one scale.
One would play a lick, keeping the other from seeing what was played, and the other would try to "mock" it.
 
I later learned that it was (or maybe still is) a common way for parents to teach their children in Africa.
I'm not sure today- maybe it's common practice everywhere.
I do know that it was fun and I believe it helped us become better players.
Of course the most important thing IMO was that we had fun so it kept guitars in our hands.
 
 

 
"I later learned that it was (or maybe still is) a common way for parents to teach their children in Africa."
 
My first thought upon reading this is that it seems like it might be a precursive form of "call and response" 

But has any learned the critical theory behind rote?

I'm waiting until we can learn Matrix style.
 

Studing music is a mix of several learning styles:
Below simplified how learning works.
 

1. First you learn the 7 basic scales. (Dorian, Frygian, Lydian, etc) Learn to play them on your instrument. (fingering) This is rote learning.
2. If you study these scales you will learn that there is a system behind the scales. This involves critical thinking. Now can play nicely within key.
3. Third step is that you experiment. You will learn that a combination of notes in a scale played to  a certain chord, within a certain key can have an effect on you and the listener. So you can convey your emotion. That is creative learning.

 
Then the cycle will begin again, because it frustrates you that you have not learned enough to be creative.
 

1. So you listen to other musicans and learn note by note what they play. (rote learning)
2. You will notice in what context they play these notes and for example that it is in some cases ok to play a blue note or a chromatic scale.  This involves critical thinking.
3. You can apply this yourself and you have acquired new tools to convey your emotion. (creative learning)

Don't forget the most overused method: Abject failure!