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{\huge \bf Conclusion \\ \bigskip Math Education \par}
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Despite dozens of examples, mathematical literature is not a very well-known
genre. Very few people are able to name any examples of such literature, and
many are uncertain as to what is even meant by mathematical literature. In
fact, the idea that someone would write or read such literature is a novel
(pun intended) idea to most people. This is because there is confusion
surrounding mathematics, including two common prejudices: that math is
non-literary and that math is non-fun. The ``problem'' --- the source of the
confusion about mathematics --- is that people don't know what mathematics is.
Mathematics is not just about computation; it is not simply a tool. Math is
more
than skills to be applied to science or to mundane tasks such as balancing a
checkbook. Pure mathematics (in contrast to applied mathematics) is an end
unto itself. Pure math is the exploration of math for the sake of math,
just as art is often appreciated for art's sake.
I envision my thesis as a tribute to pure math, a text that
encourages math appreciation. Mathematics is an art in which clever
insights lead to beautiful results, such as the proofs Alice learns from
the Yellow Pig and the works of M.C. Escher.
Math is also a language or mode of communication; it is a way of expressing
ideas clearly and rigorously from hypothesis to conclusion. Mathematics is a
way of thinking, a kind of logic. It is a way of telling a
story. The mathematical story is not just one of numbers, but of problems,
of knowing how to interpret, approach, solve, and understand them. It is
also a story of mathematicians, questions, methods, contemplation, and
beauty.
Most people are not interested in reading math for fun, probably because
they do not view mathematics as fun. The idea that math, its patterns, and
results, are beautiful is a foreign one.
This is largely a result of two intertwined problems: the poor math
education received in schools and the societal view of mathematics. Primary
and secondary schools have attempted a number of approaches to math
education, ranging from stressing computation and exact solutions to
de-emphasizing answers and focusing on problem solving approaches. Neither
approach has been successful, and
thus colleges are finding that students have an extremely weak mathematical
background and instead of requiring them to take challenging math
classes, are offering simplified classes at a much lower than college level.
A large part of the societal problem has been coined ``mathphobia'' ---
the fear of math. People are more afraid of math than of other subjects, in
part because math is neither well-taught nor emphasized in schools, thus
making it difficult for students to discover the intellectual pleasure that
can be found in mathematics.
Just as important and perhaps more disturbing than mathphobia itself, is the
fact that mathphobia is caused by mathphobia; that is to say mathphobia is a
self-fulfilling prophecy. And this fear of math leads directly to
mathematical illiteracy.
Because mathphobia and math illiteracy seem to be socially acceptable, they
become part of a vicious cycle. An intelligent or cultured person is
perhaps considered to be one who is well read, familiar with
the great works of literature, and knowledgeable about history and current
events. The definition may vary, but it very rarely includes mathematical
understanding. While most academicians would not want to admit to never having
read William Shakespeare, there is no sense of embarrassment, or even
discomfort, in not having studied calculus. Mathematical illiteracy
(innumeracy) and mathphobia are not considered shameful. When parents and
educators are lacking mathematical background and don't recognize the
importance of mathematics, it is easy to see why math gets pushed aside.
Even at the ``best'' schools, students are taught not only that math is
difficult, but also that understanding math is not a necessary qualification
for success. With this kind of example, it is no wonder that mathematical
ignorance continues. And so math illiteracy becomes accepted, ignorance
remains, and standards of excellence are lowered to those of mediocrity.
In summary, there are two problems to be addressed: that people don't know
what math is and that people are afraid of it, believing it to be too
difficult. One solution is to increase math awareness and make math fun.
Mathematicians know that math can be fun, but most non-mathematicians do
not because math is too often not made accessible to them. Math needs to be
made accessible to everyone. One way to do this
would be to have more works such as this thesis and the many examples of
mathematical fiction mentioned in the introduction. These are all attempts
to expose non-mathematicians to math and to encourage exploration in
mathematics. Mathphobia must be addressed in schools and in the general
society. The notion that math is difficult needs rethinking, and the
expectations of math educators and the culture as a whole must be raised.
Math books need to be enjoyable to read, and they need to be read.
The goal of these books should
not be merely to instruct, but to provide opportunities for the enjoyment of
mathematics. Only by changing the negative perception of mathematics can we
reasonably expect math education to be successful in creating a society that
enjoys math and is math literate.
As a junior-high and high school student, I was fortunate enough to both want
to learn math and to find, at both the national MathCounts competition and
the Hampshire College Summer Studies in Mathematics, groups of individuals who
were also interested in math. These people are represented in my thesis by
the character of the Yellow Pig. They are a minority in our society.
I wrote my thesis to demonstrate that creative mathematical writing exists
and that math can be made accessible to non-mathematicians. I want to
introduce people to mathematical concepts, share the beauty and pleasure I
find in mathematics, and show that math can be enjoyable. I hope that my
thesis has succeeded in convincing you that math can be fun.