Cap’n Refsmmat’s Blog of Doom

You can tell there’s something wrong with our system of keeping GPAs based on class average — i.e. out of 100 instead of out of the 4-point scale — when I get annoyed that I have a 96 in a class.

Stupid system.

Today I was looking through my introductory calculus textbook* for no particular reason. Well, I say introductory, but I think that’s a particularly bad choice of word.

You see, it was clearly intended to be an introductory text, but it failed at that rather miserably. I’ll give an example. Here’s how the textbook introduces the basic technique used to find derivatives (derivatives can give you the slope of a graphed function at any point on the curve):

To find the tangent to a curve at a point we use the same dynamic procedure. We calculate the slope of the secant line through and a point . We then investigate the limit of the slope as . If the limit exists, it is the slope of the curve at and we define the tangent at to be the line through having this slope.

Whew. To figure out what that means, even to someone good at math, takes several moments of thinking to understand what the hell all the symbols and points and stuff are referring to, and how that gives the slope of a line. Compare the method used by the textbook to how Dave explained derivatives in his calculus tutorial (later edited and reposted by me). Sure, it’s longer Dave’s way, but you’re left actually knowing what is going on.

The textbook gets worse from there. It’d be more useful to someone who already understands the concepts and just wants to check some obscure property of logarithms or something. Understanding is buried beneath mounds of mathematical rigor.

If we want people to understand math, or at least not hate learning it, we’re going to have to make our textbooks less painful for a start. Take a look at the way Randall Munroe explains some basic physics in his blog: cartoon diagrams and jokes about death rays. Isn’t it so much more fun that way?

If I had more time on my hands, and if I could draw, I’d be writing a complete introduction to calculus. With stick figures, lasers, and actually understandable text.

Maybe I should try.

* Calculus: Graphical, Numerical, Algebraic, by Finney, Demana, Waits, and Kennedy.

I’ve often blogged (click the words to see my previous posts) about education in the past. As I am a high school student, it’s a topic that’s rather close to my heart.

I recently came across a like-minded blog post that spurred me into action. I’m a student: I can easily talk to dozens of teachers and students to get their opinions on the state of our education system. At the same time, I’m a website administrator: I can easily set up a website to spread my message.

These two facts collided shortly after I read the aforementioned blog entry. The Web is an amazing place to spread ideas and coordinate a grass-roots movement, so, why not? Assuming nobody’s done it before (tough assumption on the Internet), I think I have a new website to start.

What’ll it do? A variety of things, really. I think the key point will be to collect all of these ideas espoused in blog posts and personal websites into one neat and concise resource for students and teachers to read, then start spreading this around to teachers. If you’d like to help, or you know a blog post that has some helpful ideas, post a comment.

I hear people say they aren’t good at taking tests all the time. “I understand the material, but when I take the test, I fail!”

I can understand this problem for people who get excessively nervous and can’t think when they take the test. But for people who take the test with a sound mind?

I think this is a problem of understanding. I don’t think “not being good at taking tests” is a fair excuse; the problem is far deeper.

Refer to my earlier post for details.

PowerPoint seems to be a popular teaching aid. After all, it saves lots of messy writing on the board or the use of boring overhead projectors. And who doesn’t enjoy bulleted lists swooshing on screen complete with sound effects and little clipart stick figures?

I don’t.
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I spend quite a bit of my time helping high school students understand physics and mathematics concepts, so I’ve also spent some time wondering how I can better help them understand things. It’s a tough challenge, because I’ve never been like other people in terms of understanding — I’ve always been such a voracious reader that I can use my prior knowledge to make sense out of things.

I do not, however, see many other people doing the same.
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