I've been avoiding commenting on this topic, seeing the debates on the merits of James Stamp and Claude Gordon. With any teacher, it is difficult to describe the experience in a few words. However, I've been asked privately to comment on Bill Adam, so here it goes.
Mr. Adam teaches in a manner quite different from virtually any other trumpet pedagogue. He would rarely talk about the mechanics or physical aspects of trumpet playing, and even his most advanced students and grad assistants had to really nag him to ever get him to discuss his thoughts on such subjects. Mr. Adam repeatedly would say that trumpet playing is 90% mental concentration, 9% air and everything else ( horns, mouthpieces, tongue arch, teeth, pivots, etc, etc,) constitues less than 1% of trumpet playing. Many players limit their abilities and even get into trouble when they let their minds wander from making beautiful music to that 1% area.
When I first heard Mr. Adam say that the physical aspects of trumpet playing count for less than 1% of trumpet playing, I, like many, was sceptical. Back then, getting a G on top of the staff out of the horn was a struggle and I sounded like something was stuck inside my bell. It seemed obvious to me that my embouchure was wrong but the more I worked on correcting my problems the worse I got. Bill Adam took me into his studio, simplified my daily routine down to jr. high/ high school level assignments and worked with me to change my concept of playing, to focus my mind on the results I desire and allow my body to do whatever was necessary to reach that goal. (This is a bit of a simplification, but essentially how he works. To get a greater idea of this concept, read the book PsychoCybernetics by Maxwell Maltz). Now I play trumpet professionally and am using the same horn and mouthpiece I had back then. Looking in the mirror, my embouchure looks about the same. The primary change is that I now focus my mind upon playing music with a rich, resonant sound and have developed proper motor responses in relation to the sound I hear in my head.
In the lessons, Mr Adam would play every exercise/solo/etude and the student would be instructed to match his sound. In this manner the student becomes more aware of sound quality and strives to change his or her sound in whatever way Mr. Adam desires. Mr. Adam would actually change his sound so that when the student tries to match that tone, physical changes in the embochure would have to take place to make that sound occur. The student is never made aware that this is what he is doing. I've heard that when he would go home, Mr. Adam would imitate the sounds made by his most troublesome students, creating the very same problems in his playing then correct his playing. In that manner, he knew what sounds to play in order to cause the proper changes in the student's playing when the student imitated him.
A case can be made that it is more efficient to just tell the student "Move the mouthpiece here...do this with your tongue....etc" but Mr. Adam's approach has a much more profound effect on the student. Mr. Adam works on the entire Gestaldt of playing the trumpet, tying all aspects to the sound the player desires. After years of studying with him, a student merely hears the music in his or her head and it comes out the bell. Every aspect of trumpet playing is keyed to sound, or one could say that sound is the only aspect of playing trumpet.
I have to stress again that Mr. Adam played in every lesson, no matter who the student was. When I first arrived in Bloomington, I use to go hang outside Mr. Adam's office and secretly listen to him teach others. I remember checking out a lesson by a woman named Vicki Hastings, and orchestral trumpet player with a huge, glorious Herseth-like tone. Standing outside the door, I heard this overwhelming trumpet sound playing an orchestral excerpt then Mr. Adam's voice saying "OK, young lady! Play it just like that". I was dumbstruck when she sounded enemic in comparison. Another time, Jerry Hey came into town for a few lessons. Several of us sneaked up to Mr. Adam's door to check out what he would teach him. We heard a screaming G above high C followed by Mr. Adam saying "Alright, young fella. Play it like that!". Jerry has since told me that Mr. Adam could put every player in L.A. out of business if he ever moved out there. The last lesson I had with Mr. Adam, he had just returned from L.A. He told me that Charlie Davis wanted a lesson, so he had been practicing to get his range up to a G above double high C so that he could teach Charlie. Some of the things Mr. Adam use to do to keep himself in such amazing shape was to play through the entire Charlier book without taking the horn off his lips and he once played the Brandenburg #2 on the big Bb trumpet with the faculty chamber orchestra, with proper blend, tone and style.
This barely covers the approach to teaching used by Bill Adam. If anyone has questions about his approach, I'd be glad to comment either via tpin or privately.