Math & Music - Harmony & Counterpoint:
Mathematics and Music share extremely similar positions in the world of education due to popular perception of them. Ability in either field is seen by many as a "natural" talent that one is born with or not. I cannot count the number of times that somebody has told me that they are "not good at math," "not a math person," "not good with numbers," etc. Likewise, many people decide that they are "not musicians", "not musicallyl inclined", "don't have an ear", or "don't have rhythm".  While it is true that various mathematical and musical concepts come easier to some than others, it is rarely the case that someone's learning difficulties are insurmountable. Desire, patience, and willingness to practice are the only prerequisites - not natural talent. I was certainly not a musical or mathematical prodigy, but my love for both subjects guided my study.

For teaching Music over Math, there is one BIG advantage. People like music. Maybe on the planet there are a handful of people that derive no pleasure from at least some form of music, but I have not had the privilege to meet one of them. The learning obstacles I have helped people surmount since I began teaching piano in 2007 have been numerous, but I try as much as possible to tap into each of my student's natural love of whatever type of music speaks to them. Any difficulties can be conquered once the love and the desire are there. I constantly check in with my piano students during lessons. If they're not having fun, then something needs to be adjusted.

Now, for Math... Despite what you may think, I find that Math (as much as music) is an art-form, and there is such thing as "playing" with math. For me, one of the most articulate presentations of this argument comes from Paul Lockhart, a Mathematics teacher at Brooklyn's Saint Ann's School. Check it out: A Mathematician's Lament. Our education system turns a lot of students off to math as a boring and impersonal subject devoid of creativity. On the contrary, the pattern finding, structural organization, and reasoning that comprise true mathematics make for one of humanity's most original and creative pursuits.

One of the many tools I rely on to awaken interest in mathematical thought outside of rote exercises are puzzles. I have been studying and collecting puzzles of several varieties longer than I have been teaching math. Puzzles require of a solver the same sorts of abstractions and organization of thoughts that mathematics demands.

Another way I try to engage students with math is through its history. Math is not just the conclusions of a few elite European men. All the world's people have done some form of math and have written a piece of its history. Very clever people have been doing math for thousands of years before things like Algebra or even our number system occurred to them. Schools dump hundreds of generations of conclusions on our students heads as nothing more than a load of obvious "facts". Routine tasks for middle school math students such as: "find the slope of this line" are as recent as the the 1600's. Calculus is a little over 2 centuries old. Many math teachers refute their students' objections that most of this material is irrelevant or useless. That the material presented as math is largely a bunch of conclusions to be memorized, I AGREE with them! If students were never interested in the process of discovering these patterns or understanding their derivation, they will quickly forget these conclusions as adults and never give them a second thought. If, on the other hand, students gain an appreciation and an understanding of the process of deriving these conclusions, it will stick with them forever.

As a society, we have religiously turned to standardized testing as a measure of knowledge. From state testing of school children, to SATs, to GREs, to various professional examinations, we test, and we have faith that those tests matter. A test can ONLY measure one's ability to take that particular test. I do not believe in IQ. An IQ test measures one's ability to take an IQ test. I believe in multiple intelligences: mathematical, spacial, linguistic, emotional, physical, etc. I don't believe that any of these are static. We can increase our intelligence in any area we choose.

Testing is big business, and unfortunately my business benefits from it. While I think that reliance on tests like the SHSATs, the SATs, and the GREs as gatekeepers to various academic institutions is deplorable, I can and will help you or your child beat the test as much as possible. Again, these test only measure your ability to take these tests. This is a skill that can be learned. The same types of problems appear year after year. The math sections of these tests rely HEAVILY on algebra.

Relevant Quotes:
"Education is not the filling of a pail, but the lighting of a fire."
    - William Butler Yeats, poet

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple."
    - Stanley Gudder, mathematician

"Music is the pleasure the human mind experiences from counting without being aware that is counting."
    - Gottfried Leibniz, mathematician and philosopher

"Geometry is not true, it is advantageous."
    - Henri Poincare, mathematician and physicist

"Nothing of any importance can be taught. It can only be learned, and with blood and sweat."
"Belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence."
- Robert Anton Wilson, author