I’ve made a harrowing discovery. There is a gaping hole in
my understanding and knowledge of mathematics. For most, my statement doesn’t
seem concerning. Mathematics isn’t a popular subject. But for a future math
teacher, like myself, it’s a confession of a big, terrible shortcoming.

My revelation came when my class was asked a very simple question,
“What is mathematics?,” and I couldn’t think of a satisfactory answer. The
confidence I had in the very subject I was preparing to teach was gone. How can
someone teach a subject, when they can’t even define it in words?

Before that question, I believed I knew what mathematics
was. I’ve been doing it for years - adding, subtracting, multiplication,
matrices, algebra, geometry, and proofs! But those words are either what people do
in mathematics or a specific area within mathematics. Not one of them encapsulates
what mathematics is, and listing everything in mathematics does not describe
what it is either. So, what do all those words have in common to help define
mathematics in a clear, precise way?

At first, I thought numbers. Recalling my elementary years, learning
math was learning adding, subtracting, and other operations. But before I could
do or be taught math, I needed to know numbers. To learn numbers, I counted
physical objects before and during kindergarten.

Others in the class shared my view, stating that math is
about describing the physical world with numerical values. Some expanded on
this concept and said putting numerical values in an order is math. Others mentioned
measurement, explaining how trade spurred the use of mathematics, while others
mentioned astronomy and how mathematics was used to find the length of a year
and day. Finding patterns was also mentioned, and a particular person said,
“mathematics is the science of patterns.”

“But is that enough?,” our professor asked and continued to ask with each new claim of what math is. Is having a
pattern enough for something to be labeled math? How about counting? Are people
doing math when they count? How about labeling a quantity with a specific
value, like 4 or 9? Does knowing you have 9 cows make it math? Or could any
conceptual form of measurement make it mathematical? A student used an example
of a stick as an example of the first rudimentary means of measurement - walk 4
stick lengths and then turn left. How about time? Does knowing the position of
the sun in the sky or time of the year make it mathematical? Does assigning
that position with a numerical value like 1:00 pm make it mathematical? Just
because it has a number or value or quantity, does it make it math?

Since the class period, I’ve been thinking a lot about these
questions the professor posed to the class, and I’ve come to the tentative conclusion that yes, just because
something has a number or could be described or substituted with a number, it
is math. To do the simplest math, like adding, numbers needed to exist or at
the very least some form of measurement had to be in place to describe and
order our world. To figure out time, the concept of a start and end needed to
be established, which could then be described more specifically with numbers.
Then operations could have been conceptualized from there. Imagine two people
looking at a sundial. One says to the other, “Meet me in two sun-lengths time
from now.” The other person sees the shadow on the sundial, and then imagines
the position of the shadow in two sun-lengths time. That person has just done
addition. Mathematics started with numbers.

Lastly, I have another confession to make. My knowledge of
the history of mathematics is very and utterly limited to pop culture. Another
embarrassing fact about the math teacher to-be. When asked to think of five top
moments or milestones in mathematics, I could barely think of five at all. The
first one I thought of was Albert Einstein’s E=mc2. My knowledge of that
equation is very lacking. Do not ask me to explain it or tell you what it is
for. My embarrassment is bad enough.

The second milestone was the discovery of the number Zero,
since it took civilizations a long time to create a number to describe nothing.
A student in my group had also mentioned this when we were discussing the “What
is mathematics?” question, and I remembered hearing that fact in high school
when I learned about how certain civilizations influenced others when they
traded or were conquered in war. Again, don’t ask me which civilization came up
with the concept of Zero first.

The third milestone was Sir Isaac Newton discovering or
creating Calculus. The fourth was Alan Turing’s use of mathematical theory (I’m assuming
from the movie) to create a computer during World War II - thank you very much,

*The Imitation Game*! The fifth…didn’t the first woman receive the Nobel Prize in mathematics for something last year? I remember reading an article about it. The math portion was completely over my head.
Luckily, someone acknowledging they have a problem is the
first step towards a solution, and my remedy to fix my lack of knowledge is to
read Clifford Pickover’s

*The Math Book*. According to Amazon.com, the book gives brief explanations to many historical moments in mathematics. Just the book I need.
Thanks, Brooke. I did see this but forgot to or missed bookmarking it. I like the idea of a pop culture history of mathematics...

ReplyDelete