There is a lot of documentation that examines the correlation between musical training and mathematical ability. When I Googled “Math & Music,” I found over 2 million entries. You can watch a quick overview of some of the connections between the two disciplines here: http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=1373
There is also a connection between music and language. There has been ongoing debate about whether music actually IS language, and there is evidence that learning to play music enhances a person’s ability to learn new languages. http://misschrista.wordpress.com/2007/03/22/article-from-ny-times-musiclanguage-connection/
Music, math and language all have systems, rules, equations, and formulas. To play a musical instrument is to stimulate the areas of the brain that make use of those concepts. The concepts become familiar to the brain, which makes it easier for the brain to assimilate new information based on those familiar patterns and structures.
Another valuable aspect of musicianship is the importance of practice. One crucial factor that predicts any level of success with an instrument is regular practice. A hidden benefit of regular practice is that It allows a student to observe the connection between working at something on a daily basis, and achieving a desired goal. The discipline that a student learns because he or she wants to make music is a discipline that can easily be applied to academic study.
A bonus benefit is that practicing an instrument can be an amazing study aid. The brain is able to absorb new information for approximately 20 minutes at a time. If a student alternates 20 minutes of academic study with 5 or 10 minutes of practicing an instrument, the brain thinks it has been on “vacation,” and is able to refocus on the academic study with renewed concentration.
A music instructor’s job is to broaden students’ minds, and teach them about the phenomenal results that consistent effort can bring -- all while the student thinks he or she is simply having fun. It’s important to teach them to play music by ear, to build their abilities to read and write music fluently, and to help them develop a strong foundation in music theory. Each of these facets of playing music will augment and broaden a student’s total learning capacity.