Why Do People Just Hate Mathematics

In my latest post on why mathematics is lonely, I talked about why people just hate mathematics shortly but wanted to write another post, and here I am. In there, I mentioned how our society is kind of divided into two: the ones that are good at mathematics and the ones that are not good at mathematics. I also alluded to how our teaching of mathematics in schools are terrible. In this post, I'm going to expand on what I talked in the other post, giving additional insights.

Teaching, teaching, teaching

In his essay, Paul Lockhart strongly argues that the mathematics education in the US (honestly, it's also the case around the world) is terrible and that it doesn't allow students to learn the art. He likens the current mathematics education in schools to music education in a made up world, where music education (which was created without a single advice from working musicians or composers) is mandatory from primary school to high school. In that world, the "language of music," which are the black dots and the lines in a sheet music, is taught until college. And, the more complex things, such as playing and listening to music, are put off till college or graduate school.

Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way. (A Mathematician's Lament, page 1)

In this world, it is shameful if one third-grader hasn't yet completely memorised their circle of fifths. I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs. In high school, there is more pressure on the students, since they have to prepare for the standardized tests and college admissions. Even if many students don't pursue music later in university, it is nevertheless important that every member of this society be able to recognise a modulation or a fugal passage.

It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school. (A Mathematician's Lament, page 1)

One might think that this imagined world, where such a beautiful and meaningful art is reduced to something so mindless, would never exist and no society would do such a thing to their children, to their future. This might not be the case for music, but it is the case for mathematics. If you replace every music term above with the appropriate mathematics term, you get the current mathematics education. Furthermore, Lockhart describes the current mathematics education as if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

I don't think society actually understands what mathematics is. Most think that it is somehow connected to science (maybe mathematics is the language of science). Nearly everyone would say mathematicians are "rational thinkers" rather than "poetic dreamers." However, mathematics is the purest of all arts. Alright, you might say, why is mathematics the purest? Mathematicians enjoy thinking about simple things, and the simplest possible things are imaginary and pure. They don't care about how a square isn't actually a "square" (since everything is made out of atoms). A square in mathematician's mind is not a physical thing; it is a thing that what the mathematician is thinking; it can be anything, as imaginary as possible.

In mathematics classes, students learn that the area of a triangle is equal to

and they are forced to memorise this "formula," without any of the reasoning behind it, or how we even came to this relation. In reality, it comes from a mathematician wondering—just for the sake of it—what will the area of a triangle be when it's inside a rectangle.

The rectangle and the triangle here are perfect and imaginary and pure. With the help of the orange crossed line, we see that each part of the triangle that the orange line divides is half of the area of the rectangle that the line divides, and in total, the area of the triangle is equal to half of the area of the rectangle. Furthermore, we see that the orange line is the height of the triangle, which also equals to the height of the rectangle. Also, the base of the triangle is equal to the width of the rectangle. Therefore, the area of a triangle is equal to $\frac{1}{2} \times \text{area of the rectangle} = \frac{1}{2} \times \text{base} \times \text{height}$.

This is what the mathematician's art is about: asking simple and pure questions about imaginary things and crafting beautiful explanations. The dotted orange line in the illustration above was the key to solving the problem, but how did we came up with the idea to draw that line? Inspiration, experience, creativity, and trial and error. In my next post (it's a trilogy at this point), I will expand on this, discussing how one can improve their mathematical skills and understand the art. But for now, students are treated to just memorising the "facts" that were set by authorities. And, do you know what is the worst part? These facts are taught with songs. Look at this short by Al. Only the "quadratic formula song" is left in people's minds—in the video, it is said that nobody remembers how to use it, but the song lingers. The reason is that they were never given the chance to discover; they were never able to be creative, be frustrated; they were never told the mankind's relation with numbers; they had no chance to ask questions, because they were answered before they could even ask. And, this is what this amazing and fascinating art is reduced to: a song, a melody at the back of people's minds. Kind of ironic isn't it?

I think that the current mathematics education boils down to just pattern recognition. Students just memorise formulas and facts and apply them only with different numbers. No thinking is done in this process; even an AI can do those exercises at this point. When the "why" and the creative process is removed from mathematics, only the "what" and the result of that process remains, and those remains are this soul-crushing class that is left for students to "learn." The art of mathematics is the argumant and the explanation itself. If you don't allow students to engage in this art—to pose their problems, solutions, conjectures; to be wrong, creative; to have an inspiration—only the result and the technical details would be concentrated, not the big picture or the intuition, and you would deny them the mathematics itself. With that said, I didn't experienced these in high school, because I had an, honestly, amazing teacher. Everyone knew that we had to memorize these "facts" to succeed in the exams and be placed in a good university, but our teacher went over her way for us to learn. I even taught Maclaurin Series in class, our teacher never directly followed the curriculum or the book (any book), and I am really grateful for it.

Mathematics education in college or graduate school is also problematic, since most professors care more about research than teaching. This problem is also exacerbated by many universities and schools not caring enough about passionate educators without good research outputs and disregarding them. Also, the whole academia is actually another entire problem in and of itself, which I might talk about in the future—look out.

Tests

Learning suffers when a test is looming over students, because they learn just to pass. You can't be angry at the students that their goal is to achieve the highest grade either, since the system requires this. The "problems" that are asked in those tests aren't even problems either—they are much, much worse—because problems, problem solving, problem solvers mean very different things in "mathematics" and "mathematics education." These "problems" that are asked in tests are not problems, because fundamentally, the answer to them are known. But, what makes something a problem is that you don't know the answer or solution to it. That's what makes it a good problem: the need for frustration, the need for being lost. When students learn just to achieve the highest grade and don't learn what mathematics actually is, they will not like this class. You can't blame them for hating this class too, because this class is not mathematics.

The fact that mathematics is in standardized tests (such as SAT and ACT) is also a problem. Because you now guarantee that the education establishment will suck the life out of it. No school board, no educator, no textbook author, no maths teacher know what mathematics really is. Also, putting easy (you can't say that it's not trivial) mathematics in standardized tests discourages students that "cannot" do maths, while resulting in no distinction between students that can somewhat do mathematics. These exams only tests whether a student can memorize all of this stuff and can do the same thing in the test that they did hundreds of times before just to understand the question—not the mathematics. And the students that couldn't do well in these exams will hate mathematics for the rest of their lives, just because mathematics is taught like shit.

"Mathematics" in and of itself

Most of the things that I will talk about here will mostly be the result of the teaching of mathematics and the things that are left of mathematics that are taught in schools.

Mathematics can be unforgiving for some. For most of their time in school, students mostly see questions for mathematics that only have one correct answer and the distinction between correct and wrong is like black and white. Mathematics is not like English or history. If you just write a sentence, you would get a 6/10 in those classes, but if you wrote $3 \times 3 = 6$ in a mathematics test, you won't get anything other than a 0/10, because it's fundamentally wrong. Students just don't have enough flexibility with mathematics. But, another problem is that English and similar subjects are just too subjective. Some students like myself that are good with mathematics sometimes fail at other subjects that are subjective, because there is uncertainty. I want to emphasize that mathematics having strict answers melts after high school with proofs and such. Even before that, like IB mathematics, examiners allow different solutions to questions, but the thing is that, the answer is always the same—a number. Continuing on, when students fall behind in mathematics, they can never just back up for a second and relearn the fundamentals, because we have to move on, the tests are coming, we can't linger any longer.

Sometimes people are just not interested in mathematics, just like I'm not interested in history or literature. I don't think there's anything surprising about that. A lot of people aren't interested in history, literature, or the arts either. I am interested to know, however, why maths is not an acceptable topic for conversations at parties whereas all of the above are. Like, what's the difference? You can always write on a napkin or something, you can always do mental mathematics (I'm not talking about doing calculations in your head).

I don't want to end the post like that. I do believe that, while it may seem really hard for the entire mathematics education and the mentality towards it to change, it's our—mathematicians, mathematics enthusiasts, to-be-computer scientists—duty to try and share this beauty with outsiders. And with that, I will take the first step and write the third post in the series about mathematics as an art. Stay tuned.

Made and written by Mehmet Kutay Bozkurt. All rights reserved.