schoolyard subversion

2000-09-24 [< * >]

I like to think that I'm the type of student who comes to school with an open mind, ready to learn. Unfortunately, when I open my mind, I feel as if the only thing I'm getting poured in is dirt. The endless babble from the teachers slows my thinking as my brain begins to shut down to protect itself. The only way I can survive is by making myself push through the mush and figure out why it's wrong.

Yes, wrong. Not only am I taught boring, uninteresting facts, but I'm also taught wrong, boring, uninteresting facts. I have this strange problem: when I'm taught something, I can't just take it as fact. Instead, I need to see the whole picture. Often, doing this forces me to take a critical look at what I'm being taught, and sometimes I find that what I'm being taught is wrong.

Hotel Incorrect: Infinite Vacancy

Knowing what I do about the Hotel Infinity, I was surprised when I heard the following from my math teacher. He mentioned, somewhat casually, that there were an infinite number of points on a line, but a larger infinity of points not on the line.

Warning! Warning! This sent off large warning bells in my mind. Wait a second, he's saying that the infinity of one-space is smaller than the infinity of two-space. I don't think so.

So I went home and checked my facts. Sure enough, I was right. But this was just the beginning.

How slow can you grow?

Later, in Biology, the teacher explained why cells never got very big. He said that the cell's volume increased cubically, while its surface area only increased quadratically. Thus, as the cell got too big it didn't have enough surface area to feed its growing volume.

He even showed us a neat little chart he had taken out of the Biology textbook. It explained that as a cell got larger the ratio shrunk, it started out 6:1, but got closer and closer to 1:1.

Something smelled fishy here. I wondered what would happen if you renamed the units. You'd have 1 quang, by 1 quang squared, by 1 quang cubed -- the ratio went back to 6:1.

Hmm, I asked the teacher, but he dodged the question. That's OK, it's not his fault -- he's a biology teacher, not a math one. I tried to discuss it with my friends, but they all thought I was insane. Soon enough, however, I discovered what the problem was.

The ratio didn't make any sense! It was like trying to measure how many inches fit in a gallon, or how many pints in a second! You can't compare square units with cubed ones -- it just doesn't make any sense.

Note: [Added 2000-9-26] Several people have responded to this section of the article. I have clarified the issue, with contributions from readers.

Illogical Logic

In Geometry, we began to learn basic logic. But the whole thing seemed illogical. We started out with postulates that were really theorems, and continued with laws that didn't make much sense. The whole thing made my head spin and spin.

I tried to ask the teacher to clarify, but instead he just got angry with me and told me to stop asking questions and do the work. My guess is that this is because he didn't understand either.

How Sad

How can teachers teach students that which they themselves do not understand entirely? Apparently they can, and do, with significant regularity.

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