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Mathematical Functions Describe the World
by Jacqueline O’Donnell
Whether or not you know it, I guarantee you’ve done math today.
Did your alarm go off and you calculate if you have enough time for one snooze button? Maybe even two…
Did you wash your hair with a one-to-one ratio of shampoo-to-conditioner or did you do two washes and one condition today in a two-to-one ratio instead?
Or if you escaped DOING math this morning, I’m confident you encountered it so many times already just on your morning commute.
Did you use a mascara wand this morning? By design, a logarithmic spiral helped with that smooth, even application.
Did you stop at a four-way intersection? Those streets were most likely perpendicular lines meeting to form right angles.
Oftentimes when I tell people that I’m a mathematician and that I founded a math tutoring company, I get one of two responses:
“Omg you probably could have tutored me back in the day, I’m so bad at math,”
or,
“Oh that’s awesome! I was really good at math in school.”
That’s it, it goes no other way. (But also, if someone introduced me to a chemist, I’d probably share similar sentiments about me being terrible at chem in high school.)
What has mainly stood out to me in these conversations is this duality of being “good” or “bad” at math. I think most people base this judgment of themselves on either a grade or an adult in their lives deeming them as “good” or “bad” early on, which sometimes carries the tone of “smart” and “dumb.” An incongruent comparison, in my opinion. (Pun intended.)
And while math at the surface is obviously numerical and we, as mathematicians, love to measure things in all sorts of ways, it’s not just in the percent grade earned or the grade point average that makes a mathematician. It’s the ability to recognize, reason with, and interpret patterns. It’s about understanding the behavior of functions, being able to manipulate them in a controlled environment, and to make predictions based off of these findings.
For example, we can look at this quadratic function and describe it by its roots, its vertex, its horizontal and vertical stretch, its shifts, its periods of increase/decrease, negative/positive, etc. All very advanced algebra topics, and we would have a solid description of this quadratic. Someone could take this “description” and reproduce this exact quadratic based on those stats and understand the essence of the same graph we’re looking at here.
We can also look at the behavior of this quadratic function and contemplate how it mimics human behavior, maybe our own behavior. Have you felt the way this graph looks, increasing rapidly and hitting the highest point before returning to where you came from? Do we all, at some level, have a shared understanding of what that feels like? This graph (a negative quadratic function) strives its whole life for the top, only to fall down. A tale of tragedy or fortune?
Or exponential growth functions which are defined by their slow increase in the beginning, followed by rapid growth.
How often have we experienced this feeling of coming from nothing but gradually getting higher? How do you measure your progress? Where in life are you currently on this journey? Are you in the beginning stages or about to pop off?
What about this set of lines? Two lines meeting to form right angles with slopes which are negative reciprocals of each other means we have perpendicular lines.
You probably skimmed all that math jargon, which is fine because do you know what else we can look at? The fact that perpendicular lines meet once and never see each other again.
On any given day, how many times do we meet people in passing on line at Kru Coffee, in the grocery store, in the waiting room? How do we behave in those seemingly small encounters? If we knew this person only has one chance of meeting us in both our lifetimes, would we change how we handle these situations?
*Also important to note this set of lines is an example of a non-function. Is there perhaps a lesson to be learned in that?
With a mathematical mindset, we can see life as a symphony of mathematical functions. We can use mathematical patterns and relationships as a way to see the world and describe our experience. So if you are a human being in this human experience, you are experiencing the wonders of mathematical principles!
It’s this fresh approach to mathematics education that we take at Math Refresh. We teach the conceptual understanding of these patterns so our students develop strong analytical skills, reasoning abilities, and grit. Children who are confident in their mathematical abilities and have a deep conceptual understanding of math grow up to be adults who are confident and capable in money management, time management, and future planning. A child does not need to be failing to benefit from working with one of our tutors.
Because these aren’t just math lessons, they’re life lessons too.