Plain English.

I spent about 30 minutes the other day practicing my math skills. Specifically, I checked out an Algebra textbook from the library about a month or so ago, and am slowly working my way through it. I'm learning a lot about both mathematics, and myself. About math, I've learned the difference between the associative property and commutative property of addition, and about vulgar fractions, which isn't as interesting as I'd hoped it would be...

About myself, I have learned something interesting. I have a mental block when it comes to translating between what I understand in my head, and how to explain it on paper. Take the following word problem for an example:

A 36 pound bag of fertilizer will cover 5,000 square feet. How many pounds of fertilizer would be needed to cover a 22,000 square foot lawn?

Now, in my head I know that what I want to find out is a ratio. There's a couple different ways to look at it. This was what I came up with first:

5,000/36 = 22,000/X

This, to me, didn't look right, although I could justify it this way: 5,000 sq.ft/ 36 lbs should tell me how many square feet can be fertilized by a single pound. I'm getting square feet per pound on one side, and square feet per pound on the other side. The ratio should be the same. Next, I came up with this:

22,000/5,000 = X/36

Now this makes more sense to me. Whatever the association is between the square footage, it should be the same between the poundage. Bearing in mind, I got the right answer anyway (158.4 lbs.), since I did most of the math in my head, but I began to wonder if the reason I didn't do well in math in school ("Show your work, Mr. Maxwell!"), is because of that mental block between my mental understanding of mathematics, and my ability to translate that into mathematical language.

I did poorly in math in school. The reason I checked out the math book from the library is because I wondered if the problem was that I was bad at math, or just bad at school. Having taken school out of the equation, I think I may have found why math was so difficult for me. What I so far understand intuitively, I have difficulty translating into the proper language to explain it to a mathematician. So now, the focus shifts from learning the mechanics, to learning the language. If I had understood the language better, would I have done better with math in school?

My apologies to Mr. Altiere, my freshman year algebra teacher, both for my attitude and my aptitude. ;-) If I gave any math teacher a hard time, it was him. An example: Just after I took the final for his class, which was a multiple-guess, fill in the bubble type, he asked me to stay after class for a few minutes. I agreed and once we were alone, he told me, "Your current grade in this class works out to exactly 60%. Your score on the final determines whether or not you pass or fail. I'm heading over to the Scantron machine now. Want to come with me?" I nodded, and we went to the scoring machine. He put mine in first.

"86%. Good luck in Geometry next year, Mr. Maxwell."

I got an A in geometry. I have no idea why.