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Getting Over Math:
Learning Math in the Real World
By Anna Hoffstrom
A few months ago, I found myself on a shopping trip
in Helsinki. Finland – where I live – is a pretty small country, all things
considered, and Helsinki is the only decent place to get some good clothes.
Even more importantly, it’s the only good place to buy some good books.
The garden shelves caught my attention first, but not for long. I moved
onward, skipped the math section, and looked at books on literature, then
business, then history. I browsed almost every shelf, and enjoyed every
minute of it. But I still didn’t look at any of the math books. Good riddance,
I thought. I didn’t need them anyway.
I was browsing the paperback science section when
I found a book I thought I would buy. It was about Nature’s symmetry, something
I’ve always found fascinating. It’s something we’ve all come across: You
find it in starfish, snowflakes, the seedpods of an apple, leaves, and even,
perhaps especially, in ourselves. Even our brains are wired to find symmetry
beautiful. It took me a minute to realize I was reading a math book. After
another, I realized I didn’t mind reading about math after all.
Why Math Matters
Conventional schooling tells us every child deserves
an equal opportunity, and I agree. Children do deserve equal opportunities.
School just has a funny way of showing it, especially when it comes to math.
When I was in school we had math almost every day,
even in elementary school. It was a fifty-five minute block of the day for
six years of my life, and it quickly became my least favorite subject. The
numbers we practiced and counted and learned about were so detached from
everything else that it seemed pretty pointless.
“Everyone deserves an equal opportunity,” the teachers
would parrot out. “You might need this math if you want to become a scientist
someday.”
Sometimes the profession they mentioned would change,
but otherwise the message was the same: You might need this, and so we’re
giving everyone an equal opportunity by teaching everyone the same thing.
Yeah. Right.
Math does matter. It just isn’t because every child
deserves an equal chance at becoming a scientist. Or a doctor. Or a lawyer.
Or whatever profession your teacher liked to tell you about. Math matters
because it isn’t arbitrary. If you asked me, schools wouldn’t suffer at
all if math was dropped completely from the curricula and integrated into
other subjects.
I’m life learning now, so school curriculum doesn’t
matter much to me anymore. But all of a sudden, I find that math does. After
I came home with my shiny new book on Nature’s symmetry, it felt like a
dam had been broken. I finally opened my eyes to the fact that everything
I am interested in, from cooking to electronics, is related to math. In
real life you don’t have to worry about integrating math into other subjects.
In real life, math already is integrated into everything else.
Math in the Real World
After I saw that math isn’t anything like school
makes it out to be, I realized I had gotten a very short end of the stick.
School had gone about it all wrong, and I had missed out because of it.
I have to ask, what if a different topic was taught
in schools the way math is taught? What if, for example, art class was?
Try to imagine it. It would be difficult to enjoy art if all you learned
about was color theory and artist biographies, never created your own art,
and never saw the masterpieces you read about. What if art class was nothing
but repeating the same brush strokes and shading techniques over and over?
What would you tell someone who thought that was
all there was to art? I’d have to tell them that they didn’t know about
art at all. So I have to ask another question: What makes math so different?
And yet, despite the unrealistic way math is presented in schools, so many
of us find ourselves respecting those methods and believing that’s how math
is. Instead of thinking that math is being presented in the wrong way, we
blame ourselves for not understanding it.
There are so many examples that make it obvious that
art is much more than brush strokes and shading techniques. Luckily for
us, math also has its own real world examples that show us just how beautiful
math can be.
One example is symmetry, as my new book showed me.
It’s a subject that is all math, even if Nature’s way of showing it is pretty
visual. When I look at starfish or the perfect proportions of a shell, I
don’t think about math. Reading a book on Nature’s symmetry has yet to make
numbers dance around in my head when I look at the world around me, but
I still appreciate things just a little bit more. The math part is just
there, a small part of my whole understanding.
Symmetry is just one thing on a long list of real
world examples of math. Looking back at that shopping trip last fall, I
realize now that all the books I looked at had some bit of math in them.
And if nothing else, I had to count out how much everything would cost.
Even now, as I sit at my desk and write this, the
things that are within arm’s reach are related to math in some way or another.
My computer, for one, wouldn’t work without all the mathematical equations
making sure it works right. My desk itself wouldn’t be so sturdy without
the math that it took to design it. Even my body, something I usually take
for granted when everything is working right, can be described and explained
with numbers.
And that’s just the start. Here are a few real-world
examples of math that we come across every day:
Color and Light: Electromagnetic
radiation is a form of energy that moves in waves as it travels through
space. Radiation can be a scary word, but visible light and the colors that
it produces is a form of electromagnetic radiation. Different colors are
determined by the different frequencies and wavelengths of the electromagnetic
radiation.
The visible color spectrum ranges from violet, blue,
cyan, green, yellow, and orange, to red. From left to right the frequency
of the waves decreases as the wavelengths increase, and that’s what changes
our perception of color. Humans are most sensitive to green light, which
is smack dab in the middle of the visible spectrum. A great example of our
sensitivity to green can be found in green laser pointers: In the dark,
the entire beam of a green laser pointer is visible. A red laser pointer
of the same strength would only show up as a dot as it hit a solid object.
Gravity: We all learn from a very
young age that when you drop something it will keep falling until a solid
surface stops it. Gravity is the word used to describe the rate of acceleration
near or on a body’s surface, and Earth’s gravity accelerates falling objects
at a rate of 9.81m/s2. This explains why objects fall, why falling from
a greater height hurts more than from a shorter one, and why different objects
fall at the same rate. It also explains why our weight would be different
on other planets and moons, since their gravitational forces are different.
On Earth’s moon, which has a force of 1.63m/s2, we weigh only 16.6 percent
of our “Earthly” weight. Someone who weighs 150 pounds on Earth would weigh
just short of 25 pounds on Earth’s moon. No wonder astronauts bounce so
high!
Games: All of us have played some
game or another and, whether we’re talking about Monopoly or World of Warcraft,
games have always had a deep connection with math. We give points to the
winners, compare weapon damage, budget our money, and work for experience
so we can level up. The list is endless. In games like World of Warcraft,
the entire digital world is based on math, much like our real world is.
The more complicated the game, the more math there is.
Music: Music and math have the reputation
of being the world’s two international languages. No matter where you are
or what language you speak, math and music are understood without translating
musical notes or numbers. To make it even more interesting, music can be
analyzed with math. There’s even an entire branch of study behind the physical
properties of music, called musical acoustics. Some composers have gone
as far as using math to help compose their music. A prominent example is
the French composer Erik Satie, who used the golden ratio in many of his
pieces.
Cooking: Not all of us are cooks,
but all of us eat. Even if you’re a raw foodie, your food relates to math.
The math of food doesn’t stop at pie fractions, either. It can be as complicated
as explaining the chemical reactions in yeast or the nutritional requirements
for an individual, but we come across the simple equations of food every
day.
We keep our freezers and refrigerators and our pantries
at the right temperatures. We have best before dates on our food because
of the rate food starts to break down. We have to cook certain foods, especially
meat and eggs, at the right temperatures in order to kill bacteria and break
down proteins to an edible degree. A sweet cookie is only so many numbers
away from being sourdough bread. Aren’t you glad math makes it easier to
know the difference?
Gardening: If you’ve ever set up
your own garden, you’ll know that quite a bit of math can be involved. The
area of your garden plot is calculated, you have to space your seeds correctly,
and troubleshooting the problems your plants face can relate to anything
from hours of sunlight to the amount of nitrogen in the soil. Even better,
I’m sure all of you have heard about photosynthesis. That’s quite an equation
in itself, and without the photosynthesis in plants, we wouldn’t have oxygen.
It’s harder to get more mundane than the very air we all breathe!
Unschooling Math
It doesn’t take much to see that math is all around
us. It’s in the air we breathe, the food we eat, everything that we can
see and hear and smell, and even the things too big or too small for us
to appreciate. Math isn’t just theory, it’s life. It’s there whether we
notice it or not.
Having said all of that, let me remind you that math
was never my favorite subject in school. When I started life learning, I
relished the fact that I didn’t have to think about it if I didn’t want
to. For a long time, I ignored it completely. I knew the basics, I had a
trusty calculator, and I didn’t need anything else.
I had been life learning for two years when it finally
clicked that math wasn’t as pointless as I had thought it was, but math
hadn’t magically disappeared for the two years I ignored it. Math was always
there in the background. I didn’t have to deliberately focus on math in
order for it to be part of my life. Math affected it all the same. A lot
of new life learners, and even some people I know have been out of school
for a while, worry about math. After my experience, I’ve stopped worrying
about it. I want to let you know you can, too.
If you’re worried you can’t learn math informally,
I have a simple exercise for you. You don’t even need to get out of your
chair to try it:
Step One: Look for math in the things you normally
enjoy doing.
Step Two: Ask yourself if the math part of what you
enjoy doing makes any difference. For example, does the insane amount of
biological symmetry in a starfish make it any less interesting to look at?
You don’t have to change the way you spend your day
in order to come across math. If you look for it, you’ll realize it’s already
there. In my opinion, knowing more about the math that has been lurking
behind the scenes makes the things I enjoy even more awe-inspiring.
Unless you have a math phobia, I don’t see many of
you changing your everyday lives just because there’s a bit of math involved
in your favorite foods or the games you like to play. But here’s the big
question: If you can find math in your everyday life, why is math any different
from any other “subject” encountered by life learners? That’s just the thing.
It isn’t.
We all learn at our own pace, and math will make
itself known to all of us one way or another. So take a deep breath, and
don’t worry. Math is as much a part of everyday real life as anything else
and no child will be able to ignore his or her curiosity about numbers for
long.
Getting Over Math
Math doesn’t have to be a big purple polka-dotted
elephant in the living room that we’re all doing our best to ignore or tolerate.
It isn’t math that’s the problem; it’s our general attitude about it that’s
all wrong. And only we have the power to change that attitude in ourselves.
The most fascinating thing about math, in my opinion,
is that we didn’t make it up. Brush techniques are something humans developed.
Instruments are something we invented. But math is something that already
exists, and we’re doing little more than discovering it. It’ll always be
there, and it always has been. It’s like a treasure hunt, and the prize
is a better understanding of the world around us. As a life learner, I find
that pretty hard to resist.
A lot of us have a bad relationship with math. I
used to, but I got over it. Real life can’t be divided into subjects. You
can’t ignore math without missing out on everything else. Without getting
up, look around you. Can you find something within arm’s reach that isn’t
related to math in some way or another? Neither could I.
Anna Hoffstrom is a writer and was an
eighteen-year-old unschooler living in Finland when she wrote this article.
She went to public school until the age of sixteen.
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