10.29.2012

Day 525

Hi everyone.

Today was Monday.  That is a fact.

It was pretty standard: homework/get stuff done in the morning, class, come home.  I talked on the phone with mom later in the evening.  She caught me up to date on the latest going-ons of Primrose and other Findlay events.

So here's the thing.  I've been thinking about the current state of math education for a week or so.  Actually, it's been a few years but my views have been resurfacing recently.  Since this is my soapbox, I get to talk about whatever I want.  Those are the rules.

I severely dislike and disapprove of how mathematics is taught to the main populace.  To those who do not seek to involve mathematics into their education or career, math is nothing more than that class you have to take because someone deems it necessary.  And when you're in those classes, math is nothing more than memorizing stuff and putting numbers into equations.  Think of it like freshman biology (or from what my Biology friends told me, most of a Biology degree): it's all memorizing stuff.  But math is so much more than formulas.  In fact, math is really not at all about numbers and formulas.

Words are limited.  It's difficult to completely describe things using standard words and grammar.  Sure, we can express colors and shapes and actions.  We can express those things to a degree, anyhow.  But there comes a point when words fail and subjectivity arises.  Is it "red" or is "scarlet"?  Do you really "feel my pain," or do you just empathize with me?  Is that a true sphere, or just a round object?  There comes a point when you want ultimate accuracy and precision.  YOU might not want that.... most of us just want the ability to effectively communicate with others.  But at the core of knowledge is precision.  There is a difference between royal blue and navy blue.  But do we all agree on the definitions of royal blue and navy blue?  We could go the route of scientific classifications (kingdom, phylum, class, order, family genus, species), but there are plenty of instances where biological entities were improperly classified because they appeared to be related some other being... but after further observation (post-classification) the two were deemed unrelated.

So we could try to use words to dissect life and describe everything, sure.  I guess we could do that.  Or we could not.

What if we had a language that perfectly described the world in which we live?  One that is not limited by anything?  Flawless, precise, descriptions.  Any good poet will tell you that no language is good enough to grasp the beauty of thought.  But there is a language, a not-strictly verbal language that is flawless.  And it's flawless because it was designed to be so.

Examine mathematics.  It is a way of thought, exploration, and description that is built with the building blocks of the most pure substance known to man (logic).  Symbols and numbers are just used as shorthand.  We use equations like y = 3*x - 50 because it's more convenient than saying "our company income will be thrice the number of items sold, minus a flat overhead charge of $50."  In math class, we often start an idea with something like "Let x be the number of claims in a year."  Symbols are just shorthand.  Numbers... numbers are beautiful.  They are the masterpiece language of mathematics.

Tell me.  Is the earth big?  I'd say so.  How about the sun?  I would also say that the sun is big.  Is it bigger than the earth?  Certainly.  But... the earth is still "big"?  How large does something have to be before we call it "big"?  What if we compare the sun to the size of the known universe?  What is "big"?

Tell me.  What is "red"?  Describe "red" to me, please.  I can't describe "red." But I do know that if we assign it a value of #FF0000, then #FF0001 will be really really close to "red"... but it will not be "red."  To the naked eye, #FF0000 and #FF0001 are identical.  But they are not truly equal.

My students hate math.  Most of them, anyhow.  And I can't blame them.  The text book teaches (for most of the chapters I am required to teach, anyhow) arithmetic, not mathematics.  Now, arithmetic is cool.  By arithmetic we make our numerical language do stuff.  In words, we can clumsily describe the velocity, acceleration, and arc of a cannonball... but it's a nightmareish task to explain how everything changes every nano-second.  All of that is easy with math and each nano-second change is discovered with arithmetic.  But humans of the twenty-first century need not waste undo time on arithmetic.  We have powerful computers, calculators, and cell phones to do that.  Humans, with their logic, reasoning, and ideas, should be spending their precious thinking power on those things.

Math is beautiful.  Arithmetic is a tool to achieve mathematical means.  But arithmetic is not the end result.  We use arithmetic to do things with our numerical language.

I could go on... but I'm tired and have already written a nice 3-page paper.

Have a good night, everyone.

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