imprecision

Friday afternoons seem like a good time for blogging.  It's 3:19 p.m. and I am disinclined to start something new this close to the weekend.  Plus, I haven't posted anything in over a week, so... I've been thinking a lot lately about entitlement.  No, not the government handout kind (although there is probably a blog post there somewhere), but the personality disorder afflicting so many of my fellow Americans.  I was helping my son with his math homework earlier this week; here was the assignment:  Estimate by rounding.  526,391 - 184,767

Those aren't the real numbers (and it doesn't matter for my purposes here).  As a mathematician, I immediately recoil in horror at this problem.  The directions are entirely too vague.  How am I to round off?  To which place?  I see at least six correct answers to this question:  341,624; 341,620; 341,600; 341,000; 350,000; 300,000.  Which one is it?  Do you know?

I don't know, either.  I'm pretty sure it's not the first answer since that's the exact difference and I was supposed to round first.  It's also probably not the last one since that seems much too brutal a truncation.  But there are clear arguments in favor of any of the others.  In the end we settled on 350,000 (well, my son did and I didn't contest it).

Imprecision is the bane of the mathematician's existence.  I suppose our tendency (some would say compulsion) to frame problems exactly drives others nuts in their interactions with us.  This also leads to some of us having superiority complexes (but again, that's yet another post for another day).  We use the word "trivial" a lot and have a unique talent for making people feel dumb.  Not me, of course; I'd never do such a thing (intentionally at least).

Anyway, the more I pondered this seemingly innocuous homework assignment the more irritated I got, and it got me thinking about the way we teach kids today and the resulting consequences when they get to college.  I'm not going to go on some tirade bashing K-12 teachers, because I (a) believe it's one of the most difficult and underappreciated jobs in the world, and (b) I don't have any better solutions.  But I will say this:  I think this homework problem is at the root of many of our educational problems today.  The imprecision of its statement allows for at least six correct answers.  The chances are pretty good that even a kid who doesn't know exactly what's going on will find one of them.  Hooray!  Everyone's right!  No one feels sad or inadequate.

Except they're not right.  I claim there is no correct answer to this question since it hasn't been framed properly.  Maybe I'm just being too rigid, but I don't think it's unreasonable to state things clearly and expect a certain answer.  And I don't think there's any shame in getting it wrong.  But if you're never wrong, then you're always right (right?).  This way of thinking can get embedded in a kid's psyche.  "I'm always right.  I'm awesome!"  And it's true that my kid is awesome, but he's also nothing special.  None of us are.  We are all just trying to get through traffic and the line at the bank and the checkout at the grocery store and pick up our dry cleaning and get to the restaurant and wait for a table and...

I don't count more than you; you don't count more than I do.  But if we're never wrong, we start to see things differently.  "Well, I know I'm not wrong, so you must be."  Pretty soon, you have a society of people who think they're entitled to everything they want, when they want it.  There's no hard work, because every answer we provide is correct.  And when there's no hard work, we get soft.

And softness leads to entitlement.  So here we are.