### The Pencil Rant

Maybe you can do math in ink. I’ve seen it done. But most of us need to use the eraser quite a bit to get anything done at all. Why make things any harder on yourself than they need to be?

OK, now that’s out of the way. What I’m really here to talk about is the simple fact that until you’re moving your pencil (the eraser counts), you’re probably doing something other than seriously studying mathematics. This is presumably what everybody means by that wellworn saying “mathematics is not a spectator sport” (more here).

Students find this very hard to believe. Or think they’ll be the exception to the rule. Or something. It’s actually kind of amazing … and I say it even though I can remember some of my own efforts at avoiding exercises pretty well. In my first Abstract Algebra course, for example … I’d just keep reading the same passages over and over (from Herstein’s Topics in Algebra) and wondering why nothing would sink in …

Now, every academic subject is about learning to read certain documents and write certain others. But I want to suggest here that the “writing” end of things has even more importance in the context of learning math than it does in, anyway, most of the others (I’m willing to accept that, for instance, composition classes might give us a run for the money). Part of the message for beginners is that one must learn to trust the code: don’t wait for some mystic vision to descend and make everything clear all at once; get down in the dirt and calculate. You ought to be able to trust me on this …

1. I have been advocating the use of calculators a lot lately. But I’m mostly doing it on behalf of others. While I will grab a keypad to crank out mindless arithmetic of large numbers, when it comes to what I consider real math, I grab for an old-fashioned number two. There’s just something about putting pencil to paper that translates those abstract connections into reality.

On the other hand, I like pens as well. The strike-through is every bit as satisfying as the rub out, and it has the added bonus of saving apparent mistakes that later turn out to be a step down an intriguing path.

2. I’m with you here on the main idea. But I still prefer a pen over a pencil, and I tell my students to use pen as well. The reason is basically what Tony above said — in math, even the screwups can be useful. You might make what looks like a mistake but actually contains the kernel of a really good idea. And if you erase it, it’s gone forever! But if you scribble it out, you can at least decode the original message.

3. well, i’m not about to try to persuade you guys.
but. sure, strike-outs are great; i’d never erase
a big block of calculation just because i’d found
that i didn’t want to look at it anymore … just
draw that big ol’ line right through and move on.
(all with reference to paper & pencil; blackboards
of course call for different behaviors.)

blotted-out plus signs that should’ve been “minus”?
“less than” for “greater than”? stuff like that?
a whole nother story. it’s tempting to believe
that those ugly blots won’t distract us from
whatever we’re really trying to think about.
but when we’re working somewhere near
the limit of our current understanding
(which should be most of the time!), it matters.

i don’t typically make a point of pen v. pencil
in classes, by the way … i just occasionally
mention more or less in passing when i work
with a inkophile one-on-one that i think
they’re making their own work harder.

i’m so addicted to pencil in my *own* work
that i actually mark papers in (colored) pencil
and’ll never go back to ink without compulsion.

4. I’m with you on this. But I cross out, too. And I ban white out (why, oh why do teenagers carry white out into math class?)

5. i’m becoming quite the white-out user
now that i’m involving myself again in
*production* of *graphical* material.

i haven’t had the wit yet to use blue pencil
to put the inks over and so i’m also
using *erasers* quite a bit…

6. i’ve found out why white-out is so popular
and lived to be chidden more than once for
*over* using it.

meanwhile, one hears of those who do
crosswords in ink. like this is something
to boast of. wha. are they proud of doing
crosswords that are way too easy for them
or of putting blots all over the page.

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)