Math is Education
Dave Shackelford wrote the following as a part of a larger entry:
While I don't know much about math beyond algebra, I have yet to include that in my own understanding of being "well-taught." I've known enough math to write simple programming algorithms and complete construction projects, which seems to have been just enough.
The further in life I get the more I realize that a part of addressing any matter, simple or complex, is having a vocabulary with which one can express oneself. There are no thoughts that I know of that haven’t been the product of someone else’s imagination and usually such thoughts are a subset of a larger body of knowledge.
Mathematics is a language and I’m convinced it is an essential criterion for being “well taught”. I will stake a claim that is even more extreme: the manner in which one is taught mathematics is often a gauge of how well one has been taught.
Too often we are taught mathematics by people who see it as arithmetic: a tool for budgeting, formulas and Do-It-Yourself projects. The people who teach it write an example or two and then the student is required to copy 100 examples in which a single number has been changed.
If we were instead taught mathematics as a language by people who actually love it we could get a different sense of it. We would learn it as a language of efficiency: why exactly is (3 + 3 + 3 + 3) better expressed as (3 x 4) or is it? We would learn it as a language of beauty: why were even the Egyptians of antiquity approximating pi? Why are fractals so appealing? We would learn it as a language of novelty: why is e so special? Why are numbers like the square root of two so elusive (we can only approximate it) and yet so practical (take a right triangle with two sides having a length of 1, the hypotenuse will be the square root of two, right there under your nose).
Then the high school question emerges: whenever am I going to use this stuff?
Although the practical applications of mathematics are quantification, prediction and modeling I’m convinced that that’s not the heart of it. The heart of it is to teach you how to think. It’s why you know that telling a person “the train arrives at 9:00, the train arrives at 9:15, the train arrives at 9:30, the train arrives at 9:45, the train arrives at 10:00, the train arrives at 10:15…” is tiresome and inefficient and yet to say “the train arrives every quarter hour on the hour” is abstract, efficient and always applicable. It’s why you know there are two ways to engage a concept: an inductive form of brute force memorization, or an abstracted deductive form of learning and loosely applying a principle – I always laughed when kids I met in grade school made fun at how in the American school we stopped doing times-tables at 13. I was always interested in knowing how to solve problems, not to memorize solutions.
Mathematics is fundamental to education and learning it well is learning to think well. But that’s what I think. What do you think?
10:24:26 PM 
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