29 November 2007

A puzzle, and some brief thoughts on education

A puzzle, from arpatubes.net.

There's no trick here. Still, only twenty percent of the people answering it have gotten it right, because it's the sort of thing you have to read very carefully.

The comments at fark.com (where I found this puzzle) are interesting. One common theme seems to be "this isn't really a math problem, this is a reading comprehension problem" or "this is a logic problem". But reading comprehension and logic are, of course, large parts of mathematics. I have a sense I'm preaching to the choir here.

On a similar but less frivolous note: from Pencils Down, A Letter to a Young Mathematician is a (fictional?) answer to what seems to be a student asking "what good are proofs?" (From vlorbik.) I'm reminded of the recent book Letters to a Young Mathematician, by Ian Stewart (who also wrote Does God Play Dice?; the resemblance of titles is almost certainly intentional. I suspect that students would, for the most part, feel differently about proofs and other things that aren't just rote calculation if they were introduced from the very beginning of their mathematical training, before they get the idea that all mathematics is arithmetic. But this might not be possible, because abstract reasoning is something that young children just aren't capable of, yet we need to start getting arithmetic into them at a young age. Their brains haven't matured enough yet for abstract reasoning.

As it is, students seem to resent being asked to prove something. A large part of this seems to be that proofs often require writing words, and mathematics, they feel, does not properly involve words. I actually spend a fair bit of time trying to counteract this in my teaching, but I can only do so much insisting that calculus students should know how to write complete sentences and be able to clearly explain their logic before they start to rebel.

And there is of course the problem that many students probably learn their first mathematics from an elementary school teacher that never much liked math when ey was in school.


Anonymous said...

i got it in one ... but am much
more impressed with whoever it was
that took 11 tries.
is it math?--well, on several occasions
i've mentioned a line i'd *like*
to say to certain students but dare not:
"math is thinking straight.
when you say, 'i don't like math',
i hear 'i don't like thinking straight'".

getting students to try to write well
is one hell of a project.
i'd've given up long ago
if i weren't convinced that
despair is sinful (never give up!).
and probably i'm being too kind
to myself--most of the time
i don't really fight the tide
(a lifetime'se experience of
math teachers having settled
for anything resembling an "answer");
i let a lot of stuff slide
that ought to be corrected and just
spout off a little in class about
how in a well-regulated universe,
clarity of presentation would
carry a lot more weight than it does.
it's cathartic for me but doesn't
actually cause anyone to change
their bad habits ...

"ey", eh? -- i like it!

Anonymous said...

that was me, vlorbik
(rewriting a comment; probably
i hit "preview" and forgot to
actually post the doggone thing).

thanks for the nod.

Aaron said...

A large part of this seems to be that proofs often require writing words, and mathematics, they feel, does not properly involve words.

Plus, words are long. I dream of the day when I can write all of my homework in first-order logic notation. ;)

Scott Carter said...

Children *can* think abstractly! It is adults who have trouble with this process.

Tony said...

While, the title of my post was certainly inspired by Ian Stewart's book, the letter was an exact copy of an email that I recently sent my little sister, who is currently embroiled in high school geometry.