Tuesday, June 18, 2013

When am I ever going to use this?

If the question is "When are you ever going to use this in real life?" my answer is generally "Who cares?" although sometimes it's "You probably won't ever."

I mean, if you're honest, the great majority of people don't use higher math in their everyday jobs and lives.  But you do use simple concepts like negative numbers - golf is scored with strokes above and below par.  Every time you ask yourself if you have enough money to buy those Skechers, you're using "above and below" estimations.  And the question of here's where I am, and that's where I'm going, so how am I going to get there? is an Algebraic concept that transcends to any field/occupation/basic conundrum. 

However, you really MIGHT use this some day.   If you want to be a nurse, doctor, or pharmacist  .. or an architect, engineer, or any kind of scientist, an accountant (did you know that there is no Nobel prize for Math?  but several mathematicians have won in Economics), you're going to need SOME of it.  And, if you're one of my students, you're too young to rule out any future possibilities.

But my favorite answer is an analogy.  I liken learning math to a learning a foreign language.  There will always be people who only want the minimum - Can I just learn how ask for a burger and the bathroom and call it a day?  To really learn a language takes years of study.  And starting out, it's pretty bad.  You spend two years learning to say "The horse is standing in the road.  The horse was standing in the road.  The horse will stand in the road," and memorizing oodles of nouns and verbs and adjectives with very little context.  But suddenly you get into the third year and you start to learn literature and poetry and a whole other world opens up!  Math is like this.  You spend a long time learning formulas and algorithms and basic rules, and definitions, and trig functions, and then suddenly you get to Calculus and everything blooms! If you're lucky, you like math before then - it clicks for you, or you feel satisfied when you get a right answer - but even if you're not one of those people {dripping condescension}, don't give up hope.  It really might get better.  I've had too many students come back and say how beautiful Calculus was, even though Algebra felt like such slog work.

Lastly, and this is the Real Beauty: even though math is applicable to the real world, it is not bound by the real world.  How exciting is it that mathematicians were discussing Hyperbolic Geometry - its behaviors and definitions - two centuries before Escher drew his Devils and Angels, or biologists saw it in sea slugs, or Margaret Wertheim and her team crocheted innumerable examples?  or that we are seeing now how Hyperbolic Geometry and saddle-points begin to describe the Space-Time Continuum?  It is the abstraction of Algebra - not just how does this number behave, but how would any number behave - that makes these conversations fun.  It's engaging our creativity, our imaginations, to ask "what if..."   but you have to have the basic building blocks - the nouns, verbs, and adjectives - of math to even begin.


And why this diatribe today, you ask?  Because there is a great movement afoot (again?) to teach math to students only a real-world context - that the only way to keep them interested is to pose questions that they might someday have to answer.  

The great question for the Twittersphere this week is: what's the real-world application of "a negative times a negative is positive"?  to which my only answer seems to be "who cares?"  Most (ok, all, but maybe there's one I haven't read yet) seem highly contrived and not any better than those "why would you tell me you're 3 years less than half your dad's age?" questions we're working so hard to eliminate.

Maybe - every now and then - the answer should be "because I told you so."  or "because the whole system falls apart if we don't define it that way."  or  something non-mathy but memorable like "what's the opposite of  the opposite? back where you started!" or something as silly as "because 'ain't got none' means you do have some..."  [and when is a double positive a negative? When you roll your eyes and say, "Yeah, right!"]

Maybe the answer lies somewhere between everything in context and math purely for the beauty of it because success lies - as is true with most aspects of life - in finding the right balance.

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