I know this is a super old thread, but considering how many times it has shown up in a thread or been referenced, I imagine a lot of people are still reading it regularly. So I'll add my two cents.
I am currently writing a book using very similar methods to what both Carol Kaye and Jeff Berlin do and the first thing I will say is that, while I agree with the majority of their ideas and approaches, they are both fairly horrible when it comes to communicating them. I think part of it is that they are so smart that they say too much, but I suspect that they also don't just want to give away all of the the goods for free....and they shouldn't.
I would take lessons with Carol in a heartbeat because I suspect she is quite different in a one on one context. She lives too far away though. Jeff and I would be butting heads over a few points that would make it not worth the effort or money even though his school is driving distance from me.
Just keep all that in mind when reading this thread. People are arguing against points Carol doesn't make or at least interpreting the ones she does the wrong way.
There are two main points of contention Varol is speaking to in her statement:
The first is regarding the order that a student learns and the second is the thinking that happens when approaching a chord progression.
The reason you learn chord tones first is two fold:
First off, they are the strongest tones and the ones that you (normally) resolve to, and therefore MUST be addressed as a special category rather than seen as of equal value with the rest of the notes in any particular scale, so you are, first and foremost, training your ear to be familiar with these tones.
Sure, many people with figure this out on their own playing scales, but many will not and many clearly have not. Learning them first guarantees that you do.
Second, you are able to play meaningful parts sooner. It may not be the hippest approach, but you can play a whole lot of music, including jazz, with nothing more than an elementary understanding of how cords are formed and decent familiarity with the Major 7th, minor 7th, Dominant 7th, and minor 7b5 chord tone fingerings. You will always be hitting the "in" notes.
A scale first approach will require much more information just to get to this basic level of performance. It's not even close.
In regards to thinking through changes it is again a question of getting more for less most of the time too.
Now assuming we are playing a genuinely diatonic progression, which eliminates all jazz, blues, and a bunch more, we could indeed just use the major or minor scale of that particular key and just move the root as we progress. The problem, of course, is that you have only one note that you KNOW is a good starting and resolving point for each chord, unless you know all of you diatonic modes. This will work for those with a great ear, but that is not many and it doesn't help develop an ear if you lack it.
Now if we are playing a more complex progressions, the scale player has to decide what function the chord is playing and then match the scale with that function. This can be pretty hard in jazz. Things modulate all over the place.
Is that D minor 7 the ii, iii, or the vi?
Is that major 7th a I or a IV chord?
In Carol's system the student has learned the major scale (the harmonized major scale) in order to practice the chord tones, so they are also able to play within a truly diatonic progression freely, even with notes outside the chord tones. The difference is they have been trained to recognize them, emphasize them on the strong beats, and to resolve to them, rather than just hoping to get lucky of rely on the movable 1 approach the noob scale player in stuck with.
Carol actually teaches some very simply passing tone choices, but the truth be told, you can throw in almost any note on the weak beats (2 & 4) and sound ok in may contexts. As Victor Wooten says "you are only a half step away from a right note." Ironically he is only right in the context of weak beats, but........................
Both groups are going to learn riffs and we all know players who know NOTHING about scales or chord tones, yet know lots of riffs. Scale knowledge or chordal tone knowledge is less important when learning them.
Riffs aside, the scale student will always get the 1 right, but has 6 other notes he might blow with the wrong scale choice where Carol's student will, with much less thinking involved and much less knowledge acquired, only have a change of missing the notes not specifically explained in the chord itself. The other difference being that Carol's students mistakes will be on the weak beats, and thus, less consequential.
I personally take a slightly different approach than Carol.
Two of my overriding rules are that you are what you practice and understanding is useless without familiarity with the sounds.
In other words, we would never play a scale Root to octave because we will likely never play it that way in a song and knowing that you can play the b5 is of little help if you are not comfortable hearing the b5.
After the student learns the notes on the fretboard, I move right to playing all of the intervals of the chromatic scale. They are not played as a scale, because that doesn't teach the ear the distinctions. Instead, each type interval is played around the cycle (b2: C-Db, F-Gb, ect) so the student is learning the sound, the fingering, and relationship to the root. They are also learning to play in various intervals through progressions because of how the cycle works.
Ear training, fretboard knowledge, and progressions all in one simple exercise. The student is immediately able to recognize these same intervals in songs, knows where the notes are for them, and can transpose without even knowing how many sharps or flats are in a particular. Actually, they are not even thinking in terms of note names except for the 1. They are learning them via that process, but I am concerned first with fingering, interval, and sound.
Next I teach Root only and R-5 movement because it is easy, reinforces the strongest resolution, and lets us focus on time and notation stuff.
Chromatic half steps at chord changes come next. Easy and super useful.
By now the intervals are becoming familiar. The progressions as well. And the chromatics are teaching the simplest form of playing "out" and creating movement.
The student is also learning specific melodies, learning to label them as intervals, and then transposing them to all 12 keys.
Next we move to chord tones. Instead of learning the major scale and then essentially reverse engineering them to build chords, ("Dm is from D major scale, except the F# is now a F natural.........") we just use the intervals we learned through the first exercise. Major is 1-3-5, minor 1-b3-5, and not a scale though of thus far.......and nobody misses them.
The student now learns chord tone only riffs in various styles to inspire them to make and find their own. They also learn the diatonic keys via learning ii-V-I & I-IV-V progressions.
After this they learn to add more notes via riffs and walking lines. The order is based on going from what would be thought of as scales/"in" tones and moving towards ways of playing more chromatic/"out tones.
First we add the 2 & 6 to major and dominant chords and the 4 to minor chords. Yes, these are from the pentatonic scale in some people's mind, but we still do not pay scales yet. We think only in intervals.
Second we add the "blue" notes of b3 and b5 to major chords.
Next is chromatic runs and enclosures.
Lastly we learn chord substitutions (vi for I, b5, ect.). This is when we start regularly using notes other than the I as a starting point as well.
By now the student has a great ear and is able to play things that would require learning tons of scales, but has not played a single one and only uses the chromatic scale as a reference point to build chords and find notes on the fretboard. They have a huge vocabulary and the potential to deal with most of western music without any more melodic or harmonic knowledge, but simply by becoming better at what they already have learned.
Now we finally start using scales for what they are needed for: limiting the students palette for certain situations and genres they are not familiar with.
Certain modal and unfamiliar genres are simply easier to play if you have a particular scale as a reference point. The scale then serves as a sort of chord chart. There is still no running up and down scales and in fact there are ZERO exercises that I ever teach that do now also have a musical element, wwhich is why the interval exercise is always played using the cycle or some progression.
Outside of this purpose I have no use for scales. They are an analytical tool that, outside of a very narrow purpose or situation, SUCK as an improvisational tool. Too much thinking and rote memorization are needed.
The reality is that the primary reasons they get so much love is because:
1- People don't know better.
They think because they are popular that they are the right tool.
2- It makes teaching lessons easy.
My wife's viola teacher would have her run through scales every practice. Are you kidding me? She played in the orchestra. All she had to do was memorize what was on the page. They didn't even work on improve, but they are easy to teach (particularly for bass and guitar) and they eat up lesson and practice time, so people FEEL productive.
3- People expect them.
It's like tabs. Even the books I have which don't rely on scales to teach still throw them in because people expect to see them. It is no harder to teach notation than tabs, which still require notation for rhythm anyway, and everyone knows that different fingerings work better for different people, but we all know most students will put the book back on the rack if there's no tabs. It's pretty much the same with scales.