Through my own experiences as both a student and a teacher, it has become apparent to me that many times when a student is having difficulty understanding a new concept, it is due to the unawareness of the instructor, not the student. Many times the instructor has assumptions and pieces of knowledge that he/she is unaware of that enable him/her to understand the concept he/she is explaining; bad explanation is the result of the teacher assuming that the student already has this knowledge because it seems so obvious to the teacher. Typically, teachers like this will blame a student for not understanding a subject(not that they do it explicitly, but rather they hold it their own mind that the student is merely lacking in talent when this is rarely the case). But my experience tells me that it is almost always the teacher's fault (if the student is giving effort) and that any reasonably healthy student cannot help but be perfectly logical and perfectly able to integrate new understandings into their present body of knowledge with the proper instruction.
Basically, I see each student as a puzzle to be solved. It takes a great amount of analysis of a student to be able to tell precisely what small pieces of the big picture are missing that have perhaps been glossed over for most of their education without anyone knowing, and I take much pride in my ability to figure out what the student may be missing, or what others have assumed was there because it seemed common sense to them but was clearly missing in the student!
I specialize in both mathematics and musical improvisation/composition, specifically on the guitar. I am three time Arizona All-State Champion on Jazz Guitar and am generally acknowledged as the best, most knowledgeable and most innovative musician (especially among guitarists) in any circle of people I interact with and have ever met. I pride myself on understanding how to develop unique musical voices and have an extreme understanding of improvisational and compositional music theory. I will teach any style but I specialize in Jazz and in developing any unique ideas that the student may have - whether they want to play the guitar with two fingers and a beer bottle or if they want to be calculating math equations in their head to tell them what to play next, I will help them to discover and cultivate skills that will set them apart from all the copycatting that pervades the styles of the afraid and musically unadventurous. I will also impose a very strict and intense curriculum, helping the student to achieve maximum success in minimal time (if the student is ambitious enough to do so), but mostly I will tailor the lessons to the student's level of energy, creativity and ambition.
Mathematics is my second love, and I LOVE teaching mathematics!!! I feel that I always have things to learn even in the most basic mathematics and am always actively engaged in what the student is studying to better both my understanding as well as the student's. What I believe makes me a successful math teacher is that I apply my experience with practicing and developing skills as a musician with acquiring new skills as a mathematician. I find that the same principles that create a well practiced musician apply to mathematics as well! Also, I have the experience that my understanding of basic mathematics far exceeds that of nearly all mathematicians I have ever met, so I feel particularly qualified to teach lower levels of mathematics (high school/college math through advanced calculus) and I always have the highest grade in my math class, I refuse to be beaten!
Either way, I love teaching so much because I love learning so much and I am constantly learning while I am teaching - its perfect fun! And when I'm not teaching or learning math or music, I am talking about it with friends, so this is really what I would be doing anyway and I love it! Also, I love to have my students become awesome at their respective subjects, I think it is the best to watch their skills improve through the years, and I want them to become better then I ever was - sometimes I really wish I had a teacher like me when I was a kid, but I suppose it had to start somewhere. Basically, I love talent and skill and people who do amazing things, and I hope to be one of them and I hope to help fill the world more completely with them so we can see amazing people doing amazing things all the time!
(as a final note, it says in my checklist of preferred teaching subjects that I do not teach alegebra I or pre-algebra, but I was only allowed to pick 10 boxes, so you can consider those checked as well!)