"Slogging throught the arithmetic" might be a way of getting them to think about what they are doing, regardless of how exhausting it might be.
 
Three stories:
 
1) In graduate school the group under my mentors had to "slog through" the most tedious procedures for doing 4-way ANOVAs with repeated measures on one factor, analysis of simple effects, multiple comparisons, etc.  Students in other areas could use the new-fangled procedures (involving large stacks of IBM cards and BMDP) to avoid the tedium.  On several occasions , they visited those of us in the "backwards" part of the department, printouts in hand saying, "I've just completed the analyses for my dissertation, can you tell me what all of this means?"
 
2) My oldest boy was a math-whiz at a very early age.  One afternoon, he came home from school with some homework.  One question was "15 - 7 = ?",  when he got to this point, he reached for a calculator.  I asked him why he was doing that, since I was sure that he knew the answer.  He said, "Yeah, it's 8, but the teacher wants us to use a calculator."  (Later, I was on a committee to hire a director for a new charter school.  The "winner" was a person who said, rather spontaneously, "Some people might think of it as rote learning, but children do need to learn multiplication tables."  The school has been remarkably successful.)
 
3) Earlier this semester, I gave an undergraduate statistics test with problems that I thought were simple enough to not require a calculator.  One was to obtain the mean of 4 numbers, which happened to add to 26.  Probably about 1/3 of the class gave answers like, "6 R2," "6.2," or simply "I don't know how to do this without a calculator."
 
Calculators and statistical packages can be a high-tech way of "dumbing down."
 
—----------------
From: Marc Carter [mailto:[EMAIL PROTECTED]
Sent: Wed 11/9/2005 11:49 AM
To: Teaching in the Psychological Sciences
 (For most students, just slogging through the
arithmetic interferes with thinking about why they're doing it in the
first damned place.  By the time they get a result, they're too
exhausted to think about what it means.)

 
Michael T. Scoles, Ph.D.
Associate Professor of Psychology & Counseling
University of Central Arkansas
Conway, AR 72035
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