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.