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Topic: Drill and Kill

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Subject:   RE: Balancing the drill - return to rigor
Author: LFS
Date: Jun 16 2011
Today's quote of the day for the New York Times was:

"How many times do you have to add seven plus two? I have no problem with doing
homework, but that put us both over the edge. I got to the point that this is
enough."  DONNA CUSHLANIS, of Galloway, N.J., on the amount of homework assigned
to her son, a second grader.

Here is the article:

There is a very good line in there: "I think people confuse homework with
rigor." I am a fanatic for mathematical rigor. But I am very tired of people
thinking drill=rigor or difficulty=rigor or tricky questions=rigor.

And a major problem with kill and drill worksheets is that rigor is actually the
first thing to go. You get tired, you get sloppy and you stop writing everything
down. (e.g. Problem: Find area of rectangle with sides 10mm and 9cm. Answer:

In my opinion the following do not constitute rigorous math:
1. Is this equation (x^2-4)/(x+2)= x-2 correct?  Yes/No (This is just
2. In the following, give a reason for your answer that does not depend upon
solving the equation:  
a. Does the equation: (t+2)/(3+t)=1 have a solution?   or
b. How many rational/real/complex solutions does 16-(x-3)^2=9 have?
(Common core standards "equations" examples.)
3. How is the square root of a number the key to the Sieve of Eratosthenes and
finding prime numbers (problem given to my niece in 4th grade.)
4. Prove sqrt(x+sqrt(2x-1))+sqrt(x-sqrt(2x-1))=sqrt(2) on [0.5,1] (1 of 10
"easy-review" homework problems given to my daughter 1st year engineering.
Notice the word "prove", i.e. a formal proof.

To me, some key principles in rigor are:
1. Using the word "solve" for equations and "simplify" for expressions.
2. Making sure variables are well defined. Let x=water is NOT well defined (but
better than nothing). Let x=#gal water is well defined.
3. Making sure equations are equations. 3x=24=x=8 is NOT good. 3x=24 => x=8 is
4. Keeping track of units (and that the units match on both sides of an
... just dismayed because again "bad math" made the quote in a major newspaper.

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