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
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.
& Music - Harmony & Counterpoint:
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.
IV. MATH: HISTORY AND RELEVANCE?!
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.
V. TESTING CULTURE
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.
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.
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
"Geometry is not true, it is
- Henri Poincare, mathematician and physicist
importance can be taught. It can only be learned, and with blood and
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