Posts tagged with boring

It’s not universally agreed that mathematics is the worst subject everyone has to study in school, but I would say the agreement is close to universal. Why is it so boring?

Aesthetically, I prefer non-miraculous explanations that don’t invoke unique, incomparable properties of the thing considered. So for example I wouldn’t like the explanation that $AAPL is a $10^8 company because of “the magic of Apple”. I would prefer an explanation that involves definite choices they made that others didn’t—like that the Walkman was quite old when the iPod came out and they correctly assessed what the average consumer wanted and spent the right amount on an ad budget, and so on.

Even if it’s about company culture, there are probably some mundane, tangible, doable actions or corporate structures that cause culture—Greg Wilson pointed out, for example, that code is less tangled when multiple programmers are less separated in the organisational chart.


So here’s a theory of that aesthetic kind, about why mathematics is different from other subjects and ends up being taught worse.

  • The model of one teacher with a chalk and a blackboard, is more insufficient to explain mathematics than it’s insufficient in other subjects.
Here are some differences between mathematics and other subjects—not incomparable differences like “Well mathematics has group theory" or "Mathematics is for logical minds"—but comparable differences.
  1. One doesn’t become conversant in mathematics—like knowing the basic grammar and syntax—until after 3 years of upper-level courses. Typically linear algebra, analysis, modern algebra, measure theory, and a couple applied topics are required before one could be said to “speak the language”—not to be like Salman Rushdie with English, but to be like an 8th grader with English. So whereas an English teacher who went to university was working on honing skills and developing to a level of excellence, a maths teacher who went to university was becoming functionally literate.
  2. Visuals are necessary to teach mathematics. An ideal lecture in geometry would have heaps of images, videos, and interactive virtual worlds. Virtual worlds and videos take a long, long, long time to create compared to for example a lecture in history. History can be told in a story, whereas talking about for example hyperbolic geometry is not really showing hyperbolic geometry. Sure, a history lecture is nicer with some photos of faces or paintings of historical scenes—but I can get the point just by listening to the story. See my notes on a lecture by Bill Thurston to see how ineffective words are at describing the geometries he’s talking about.

So it takes longer to program a virtual world or a video than it does to write a story, and it takes longer to become functionally literate in mathematics than it does to become functionally literate in history.

Suddenly we’re not telling a story about mathematics being a special subject area with unique problems that can never be overcome. We’re not talking about heroes or villains or “Mathematics just is boring”. (Which is a ridiculous thing to say. That’s saying the way things currently are, is the only way things could ever be. “Mathematics by some intrinsic, unique, incomparable property is more boring than, say, history.” In reality, either can be taught in a boring way and yet both topics have interested people for thousands of years.) Now we’re telling a story about a subject in which it takes a lot of resources to produce a talk, compared to a subject in which it takes fewer resources to produce a talk.

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “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.”

“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.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one.

“To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.”

Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, 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.

Everyone knows that something is wrong.

The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.