I believe music is valuable both to an individuals' enjoyment of life and to culture as a whole. I also believe that in both cases, the musical rewards are dependent on the level of skill and experience that has been acquired. Musical skills not only enable the creation and performance of music, but also the appreciation of it. Studying the piano provides an opportunity to acquire these skills. Therefore, it is my aim to help my students acquire as many skills and as much music and musical experiences as I am able. My hope is that when they leave, they will take with them not only an interest in music, but also the resources needed to continue to explore that interest for the rest of their lives.

Studying music, and particularly the piano, has been shown to benefit learning in general, but especially math. It has often been said that music is a form of math. This is apparent in rhythm, where time signatures are expressed as fractions (4/4, 6/8, etc.) and a beat is simply a unit of time that is divided or multiplied in various ways to create the rhythms that engage us. Music is math in many less obvious ways as well. Mathematical relationships are embedded in the very sounds of which music consists, the sounds we experience when our ear drums vibrate. When one plays or sings music, one is constantly experiencing these complex relationships.
This, I believe, is where an important part of music's unique value to the developing mind lies: Unlike math as we usually think of it, where patterns are revealed by working out problems according to formulas, in music, the patterns (and relationships between patterns) can be experienced; the abstractness of mathematical relationships can be felt concretely. A child will not learn algebra from playing the piano, but they will have experienced and familiarized their brains with many of the building blocks on which a thorough understanding of algebra can be built. 

More directly, learning to play the piano cultivates many valuable skills. Among the abilities required to play the piano are finger dexterity, mental and physical coordination of many kinds, pattern recognition, analysis, awareness and control of sound, memory and various practice techniques. Playing the piano means exercising these skills daily. Moreover, there are the lifelong rewards of the music itself. As the parent of one of my students said, "I've talked to a lot of people who have regretted quitting piano, but not one who regretted not quitting."

Simply put, the study of classical music provides the best foundation. One reason for this has to do with music history.

The keyboard instruments and the ways in which they could be played were developed and explored during the evolution of European classical music. The keyboard music of the Baroque, Classical and Romantic eras was written in part to explore and expand playing techniques. Composers approached writing for the piano partly in the same way a gymnast would choreograph a routine; to demonstrate (or perhaps to challenge) the gymnastic feats of which the gymnast is capable. In many classical pieces, the composers were seeking to highlight certain finger feats (this was often true not only of pieces intended for learning, but of pieces intended for concert performance). As a result, the pianist often has only to deal with a few technical difficulties. These difficulties are challenging to overcome, but they are relatively simple to understand.

Popular music and Jazz (as well as "classical" of the 20th century), on the other hand, developed long after traditional playing techniques had been expanded to the point of breathtaking feats of virtuosity. Partly as a result of, and reaction to this, pop and jazz composers have tended to be more concerned with energy, mood, style and creativity. They have often used a variety of difficult rhythms and complex harmonic/melodic patterns to achieve this. Jazz and pop music has also been influenced by the music of other cultures, particularly those of South America and Africa whose musical traditions are rich with rhythmic complexity. Jazz and pop music also is rarely composed for piano alone. For these reasons, pop and jazz are often very difficult for students to learn in their original forms and, when simplified, are often unsatisfactory. It's just the nature of things that classical music often sounds and looks difficult to play, but it is usually easier to fully understand than other types of music.
 
Another reason for studying classical music is that virtually all the harmonies, rhythms and compositional procedures that pop and jazz composers use (and have used) have their origins in classical music. In fact, many pop and jazz artists have strong classical training. A classical foundation gives the student the ability to go in any musical direction they choose and it makes possible a deeper appreciation of most of the music one is likely to hear today.

Having said all that, all students are not created equal. They all have different strengths & weaknesses, different interests and different backgrounds. 

I like to give my students exposure to a variety of musical styles. I feel that a true appreciation of classical music comes only through familiarity and maturity. Classical music is sophisticated and is, in truth, the music of another time and culture. What we commonly call "classical" music evolved according to the cultural values of the European countries, roughly during the 17th through 19th centuries.  Much classical music evolved from dance forms and singing styles that were common at social events and celebrations of the time. For example, a Bach minuet (heard only in recitals now) might have been played at an aristocrat's ball, viewed by the party-goers in much the same way that music at a prom is viewed now.

Kids are generally not exposed to such dancing and singing and so can't grasp this aspect of classical music. It seems to them like something in a vacuum or something they are "supposed" to like; with the exception of those very popular pieces such as "Für Elise." I want my students to eventually understand this aspect of classical music. I believe that including music in their piano study that is a part of their daily lives helps to create a foundation for that understanding. 

In classical music, one finds levels of skill and comprehension that match the inherent abilities and skill development of children. Classical is very important for this. But in pop and jazz, one finds levels of emotion and fun that match children's inherent perspective and daily experience. That, I believe is important as well.