Q&A #17179


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From: Ralph (for Teacher2Teacher Service)
Date: May 24, 2006 at 15:16:33
Subject: Re: Rigor

Dear Fred,

Your last sentence really strikes at the heart of the dilemma surrounding
"rigor"--it has become a popular "buzzword" among those who argue that in our
efforts to improve the teaching and learning of mathematics in schools, math
programs are becoming less "rigorous", and supposedly this is a bad thing! :)   

However, to show how much the "rigor" discussion depends on perspective, 
consider this observation about the development of mathematics,

"Rigor is fundamentally a matter of mathematical proof...The level of rigor 
expected in mathematics has varied over time; the Greeks expected detailed 
arguments, but by the time of Isaac Newton the methods employed were less 
rigorous." So even Newton was seen as a "softie" by some standards! :)

From a personal point of view, I think in general discussions surrounding
"rigor" are a red herring.  I think what is desired is the very best
mathematics program for preparing our students for life in the 21st Century,
which will almost certainly see yet another shift in what is regarded as
"IMPORTANT" in mathematics (I prefer a discussion of mathematical importance
over mathematical rigor. A couple of quick examples: 

I spent a lot of time in school mathematics in learning (and becoming very
good at!!) the paper and pencil square root algorithm--I can vouch for its
"rigor" (I can calculate a square root to 20 places for you if you'd like),
but can no longer support its mathematical importance. I was also a whiz at
interpolating from log tables by hand--again certainly "rigorous" enough--but
important today??  

In closing (and with tongue firmly planted in cheek :) ), to those who
continue to insist on rigor as the ultimate mathematical goal, I offer the
following dictionary definitions of rigor:

1. Strictness or severity, as in temperament, action, or judgment.
2. A harsh or trying circumstance; hardship. 
3. A harsh or cruel act.
4. in Medicine. Shivering or trembling, as caused by a chill.
5. in Physiology. A state of rigidity in living tissues or organs that 
prevents response to stimuli.

I'm sure I haven't cleared anything up for you, but perhaps I've provided 
some fuel for your discussion as your school undergoes its "redesign".

 -Ralph, for the T2T service

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