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Topic: Drill and Kill

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Subject:   RE: Balancing the drill
Author: markovchaney
Date: Jun 16 2011
Mathematical rigor, like mathematical maturity, is a developing concept in the
growth of a person, not a fixed commodity with an immutable definition that
applies across the board.

There's little, if anything, in the previous poster's definition of "rigor" that
corresponds with what working mathematicians mean by the term, but even in that
lofty company, definitions depend on context.

What, for example, does a working mathematician mean by a "rigorous proof"? I
suspect that if you push a bit, you'll discover that there is rigor, Rigor, and
RIGOR!!! and you very rarely, if ever, see the latter except in the work of
logicians and people look at foundations. You want RIGOR!!! ? Go read Russell
and Whitehead's PRINCIPIA MATHEMATICA. If you get through it and don't blow your
brains out, then you're a heavyweight of rigor. Otherwise, you're more likely
operating at a lower level (of course, my tongue is somewhat in cheek
distinguishing levels of rigor with those three versions of the same word, but
I'm serious about the idea that there are degrees of rigor even for professional

The proofs that appear in journals of mathematics are not examples of the
highest pinnacle of rigor, and as I've suggested, you are a very rare bird if
you want to read a truly rigorous proof.

But if your definition has something to do with being accurate, careful, etc.,
and you're talking about the sort of problems assigned in most K-12
mathematics classes, rigor probably means more like "ball-busting" or
"intellectually demanding" or something like that. It has little to do with
mathematical rigor.

I'm very sure that when people demand rigor in K-12 mathematics, they are more
concerned with how MUCH work is given, how HARD the work seems to be (within the
usually limited understanding most folks have about what mathematics is and what
it means to actually be doing mathematics - computations, no matter how involved
or time-consuming, are not "doing mathematics," but rather a human being doing
the work of a machine. I'm very content to leave that work to machines, as they
are faster and more accurate and incapable of being bored to tears by

These tiresome debates about homework, by the way, generally ignore the wealth
of research out there that suggests that the vast majority of the homework
assignments given in US K-12 classrooms are not promoting meaningful learning.
Indeed, in mathematics classes, if you have a worthwhile problem for students to
do, they'll happily continue to pursue it outside of class and won't see it as
homework. If you assign drudgery, you'll get back dross, if anything at all.

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