It's not a secret that I get good grades at school. I don't particularly make a secret of how I get them either. I just don't tend to think about it, much. I'm trying to do that now, and it's led me to some interesting realizations about myself.
The theme of this week's post is going to be something that I realized about myself and how I tend to work on things.
The revelation came in the form of two sentences. They're from John Flanagan's Ranger's Apprentice series, the 8th book in the series.
An ordinary archer practices until he gets it right. A ranger practices until he never gets it wrong.
On the surface, it seems to be more of the legendary ranger mystique that he's so big on in the books. (I think it's fun for a few books, and then they get repetitive and "Oh, look at how cool the Rangers are.") But I've found it to be a much more fundamental life lesson. Let me re-phrase it how I see it apply to life in general:
You can be proficient, even good at something, if you work at it until you can do it. If you want to be great, and truly know what you're doing, you have to work until you don't make any more mistakes. You have to work until you are at that level.
In gaming speak, my language, it says that, while there are diminishing returns on doing more work, there are still returns for quite a while. If you want to master something, you have to take advantage of those returns.
That's all nice and good, but what does this actually mean for me?
I took two tests two weeks ago in the testing center. I complained about them on here; I was in there taking them for about 6 hours over the course of two days. I've since gotten my grades: 95 and 97. Keep in mind, these are for Differential Equations and Calculus IV. I've also talked to some of my classmates; they took longer than I did, in general. The class averages were below 70, and there were plenty of scores in the 20s.
So, what did I do? I studied, but so did many other people. You don't get into these classes without being able to study. Everyone here is almost definitely in some type of engineering or mathematics degree plan. They want to do this kind of stuff.
What I did was, among other things, extra homework. When the teacher assigns problems, like 1-25 odd, I do 1-26 all. And if at that point, I don't feel supremely confident in my ability to solve more problems like the ones assigned in the homework, every time, then I find more problems. I don't stop working when I can solve a problem. I stop when I know I can solve the problem every time - including on a test, after I've been in the testing center for three hours straight and my brain is fried.
I also, to make absolutely sure that I'm doing things right, and that I know it, check every answer I can with the back of the book. If I don't get their answer, I will work the problem again. If I still don't agree, I'll try to confirm the answer with a computer if possible. If the computer agrees with the book, I keep trying. If I get really frustrated with trying, or the computer doesn't agree or won't work for this problem, I go in and bug my teacher about it. I do not give up on any homework problems; I work until I understand, and can confidently work all of them, every time. (So far this semester, I've found around 10 wrong answers in the back of the book.)
I guess another way to say it is to be a perfectionist. Don't be satisfied with enough. Go until you get everything. Then, you'll have it all, and tests will be easy.
Final word: Some people still insist at this point that I'm naturally gifted at math. It drives me nuts. They say this because, even though they know how much work I'm doing, I seem to pick up on things in class more quickly than they do, answer more questions, etc. This is because I have a better foundation in all of my math, because I've been working this hard for years. The better you know what you know, the easier it is to add on to it. I am not gifted. And, as my Calculus II teacher said, "Math is ruthlessly cumulative."