🚀 go-pugleaf

In article <92Oct14.033708.24102@acs.ucalgary.ca> quigley@acs.ucalgary.ca (Martyn Thomas Quigley) writes:
>bh@anarres.CS.Berkeley.EDU (Brian Harvey) writes:
>
>>                                                The original problem is to
>>compute n! and instead of getting CLOSER to the solution by computing (n-1)!
>>you get FARTHER AWAY by computing x*n! instead.  This turns out to be helpful
>>but it's a total rabbit-from-hat.
>
>I've never been comfortable with this, but for a different reason.  Children
>invariably start from 1 and work up, they simply do not start from n and
>work down.  Ask them.
>
>Martyn

Not true. Our daughter Sierra originated the following dialog at about age 3,
roughly one month after learning to spell her name:

Mother:	"What's your name?"
Daughter: "Sierra."
Mother: "Oh, Sarah!"
Daughter: "No, SIERRA!!!"
Mother: "How do you spell that?"
Daughter: "S-I-E-R-R-A. Sierra. When I ask you if you think I can spell that
	backwards, you say no. Do you think I can spell that backwards?"
Mother: "No."
Daughter: "A-R-R-E-I-S"

I remember this dialog so well because we repeated it dozens of times
before she got tired of it. She came up with the idea itself. Also the idea
of counting 10-9-8-7-6-5-4-3-2-1-0, followed by liftoff or explosions or
some other loud and usually catastrophic event, seems to resonate with the
kids. Counting backwards subtrahend steps from a minuend to a difference
also seems to be working fine for learning subtraction. Her first crack
at subtraction was counting off the number of screws left to put in her
brother's foot braces at bedtime (thank God that's over). I'll agree that
spelling the name forward and counting forward came first, but of course
that's how they were presented.  If the kids have a good physical model for
a computational process, they'll use the process.

Dale Parson, Bell Labs, dale@mhcnet.att.com

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|    "These words are too solid, they don't move fast enough           |
|     to catch the blur in the brain that flies by, and is gone..."    |
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|     Suzanne Vega                                                     |
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