Tag Archives: math

What do Grades Really Measure?

Everyone knows that getting high grades is getting good grades. A high grade is supposed to show that you really understand the material in an academic course. It’s supposed to reflect your intelligence, or your talent, or both.

These are not what grades really measure. Talent and intelligence and understanding all help in getting good grades, to be sure—but they’re not fully necessary.

Academic grades measure dedication. Without dedication—the will to go to class, stay on top of assignments, and struggle through the challenges—Einstein would fail at physics.

I’m finishing a tough course right now. Calculus II, and we’re doing infinite series, which are perplexing to me. I have little talent nor mathematical intelligence (I only imitate math, I don’t create), and I often feel like a Chinese Room when it comes to math problems. I would be doomed if grades didn’t reflect dedication.

I am dedicated. Up until recently, I wondered whether willpower could make up for lack of talent and interest. It can—to an extent. And I wondered whether I could succeed by willpower alone in a subject that doesn’t come naturally to me, or whether I’m bound by fate and genetics to do what I’m good at and interested in.

This weekend, I accidentally convinced myself that there’s no substitute for passion. I had two things on my mind: Tuesday’s math test, and a video for film history that was due a week later. What did I do? I spent 17 hours editing video, and 3 hours struggling with math.

The difference between these two activities was passion. When you’re passionate about something and actually want to do it, you end up giving it more of yourself—even your spare time. And putting in all those hours is what it takes to become a master. So I don’t think I could ever be that successful in a subject I’m not passionate about or talented in. The fire just isn’t there.

A lot of college and growing up seems to be about finding the place you fit in the world—that little niche where you’re talented, passionate, and better than most other people at doing what you do. A grade can help you find out what you’re good at. We’re all naturally dedicated to something or other, and when you find what you’re interested in, you tend to notice a change of focus—away from trying to motivate yourself just to do the homework, and more towards building a beautiful final product, be it a movie, a program, or a thoughtful new idea.


5 Reasons Why Artists Should be Trained in Math

By most people’s standards, my professional work is artistry. I’m not a scientist or technologist, nor an accomplished scholar. Why then should I be interested in mathematics, the language of the Universe?

These are my reasons.

          1. Pattern recognition

When you practice many problems in many different forms, you see patterns emerging. Not only do you notice these patterns, you learn to recognize them and react appropriately.

This skill translates to every aspect of life. Especially useful is recognizing patterns of human behavior, so you can understand the human forces acting around you and be a better judge of character. This understanding enables you to make wiser choices about your own actions.

          2. Succinct Representation

Mathematics is an elegant language, efficient and full of meaning. For example, the single character π is customarily used to represent an infinite string of numbers. Mathematicians always strive for concise representation of ideas.

Simplicity, elegance, and efficiency are valuable to everyone. As a communicator, I deeply admire the language of mathematics and try to imitate it in my artistic works: I organize my words in a hopefully clear way, and delete unneeded material. Elegance follows from these.

          3. Diligence

Mathematics has taught me diligence like nothing else has. I’ve done enough problems now to know that there is always a solution to be found. (Teachers tend to avoid giving unsolvable problems, though it took me many years to finally believe that.) I want that solution, and if one technique doesn’t work, I’ll jolly well try another! And another. And another. And finally, I will get that solution.

          4. Confidence

From diligence and the repeated satisfaction of finally solving a hard problem all by yourself comes a confidence that can only be won through struggle. I know that I have the ability to solve hard problems, because I’ve seen my skills tested, and seen that I’m competent by an objective measure. Confidence translates into other areas of life.

          5. Beauty

Mathematics can be unspeakably beautiful—or horrendously ugly. Suffice it to say that math need not be sterile, boring, or grey. The patterns that live beneath the figures speak volumes to those that listen, and artists should take notice of this natural beauty.



The Best Kind of Memorization

This morning, I had an animated discussion in math class with our professor about whether memorizing certain integrals (natural log in particular) is a good idea. The professor stated that it’s important to know the general steps of the process through which you can find a particular integral, and I agree. She also said something that really seemed counterintuitive to me.

“Why memorize when you can compute?”

From my point of view, the class had recently made sure to memorize (as instructed) an assortment of trig integrals and derivatives. We’ve begun to memorize calculus-style formulas for area. We memorize these because no one wants to reinvent the wheel.

From her point of view (as I understand it), it’s good to know how these derivatives, integrals, and formulas are derived—know where they come from. And it’s silly to try to memorize the solution to every specific multiplication problem (58×27 for example) when you can simply learn the general solution to all multiplication problems and thus understand the process.

But we still memorize the multiplication table. We’ve done those numbers so many times that we don’t have to think about them—most of them anyway. I suppose the reason the Professor and I had a little scuffle this morning is because she thought my integral was a 58×27, and I thought it was a 2×10.

In any event, I never meant to memorize the integral of natural log. It happened while I was looking the other way, engrossed in a puzzle of equations. That’s the best kind of memorization, the kind that lasts and that you don’t notice happening. It’s experiential, quite painless, and results in intuitive understanding.

There’s also one other “best” way to memorize, quite opposite to this approach, but that’s for another day.

The Right Way to Waste Time

Don’t you hate wasting time? Everybody does.

I worry about wasting time less than I used to, for two reasons. First, I hate wasting time, and ironically, one of the best ways to waste time is to worry about wasting it. Second, my first year of college taught me that sometimes, wasting time is necessary—some things are just more worth wasting your time on than others.

My brother, still in high school, is a programmer. He generally astounds me with his tenacity when it comes to bugs in his program—he’ll work on a single problem for hours on end (seemingly getting nowhere from my perspective), and feel that it’s all worth it when he finally gets the bug fixed.

I’m not a programmer, and I don’t like fixing bugs. Or so I thought.

Do you like math? Not many writers do. But I enjoy it in a classroom environment, and took a calculus class last spring. By the time finals rolled around, I had a good handle on most of our concepts, and I finished my once-over of the exam in about half an hour. In the next half hour, I figured out most of the remaining problems. And then I had just one problem left and an hour remaining.

Getting that last problem perfect didn’t matter statistically. My grade would be good regardless. Yet I spent the hour doing that one simple problem over and over and over again . . . it was almost right, almost! Over and over and over . . .

And suddenly, my brother’s obsession with getting a problem solved didn’t seem so inexplicable after all.

I couldn’t figure it out, and handed in my exam with the page backs covered in pencil marks. So, it was wasted time, I guess. But math still helped me learn where diligence can get you—the great satisfaction of a problem finally solved. And even if the problem never is solved, there’s real satisfaction in devoted work.

I didn’t think I had it in me. Wasting time for a cause! And that, if I may say so, is not wasted time at all—it’s diligence.

So, it seems the key to using time well is this—forget about it. The time will pass anyway, expire just like a gift card. Find the right things to waste time on. That’s living in style.

Don't let the Fear small

P.S. Want to know what got me on that final problem? It was a fraction. A simple little unassuming fraction. Derivatives and integrals I can handle, but addition—that’s something else.