Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!zaphod.mps.ohio-state.edu!sunybcs!uhura.cc.rochester.edu!rochester!koomen
From: koomen@cs.rochester.edu (Hans Koomen)
Newsgroups: comp.cog-eng
Subject: Re: Elementary math without 4 basic algorithms
Message-ID: <1989Dec11.181422.10477@cs.rochester.edu>
Date: 11 Dec 89 18:14:22 GMT
References: <1989Dec6.224935.1817@agate.berkeley.edu>
Reply-To: koomen@cs.rochester.edu (Hans Koomen)
Organization: University of Rochester Computer Science Department
Lines: 38

Anthony Finkelstein <acwf@doc.ic.ac.uk> writes in article
<1989Dec6.224935.1817@agate.berkeley.edu>:
>Copied [without permission] from letters section of
>_NEW_SCIENTIST_, 25 November, 1989
>| ...
>| The project [Calculator Aware Number, CAN], was set up with the
>| objective of trying to develop a number curriculum for
>| primary mathematics which would take account of the new technology.
...
>| The children learn to recognise patterns created by number
>| sequences of all kinds because because are able to generate
>| them so much more quickly with a calculator; they also
>| make attempts to generalise the patterns in "rules"
>| for continuing them, a good prelude to later algebra.
...
>|	Janet Duffin, Numeracy Tutor, School of Mathematics, U. of Hull
...
>	-Brad Sherman (bks@alfa.berkeley.edu)

It's just one data point, but a pretty illustrative corroboration nonetheless:

Our seven year old son (bright but no genius) received a small calculator as a
St. Nicholas present last week.  Within minutes he inquired what the "/" was
for.  After a verbal explanation (but no demonstration) he went off to
experiment some more.  Half an hour later he came back to me and said, "Dad,
did you know that when you take a number made up of a bunch of the same digits
and divide that number by that digit, you get the same size number made up of
1's?  See, take 8888888 and divide by 8, you get 1111111!"
Shortly thereafter he figured out the inverse rule, using multiplication.

In the space of 30 minutes (counting time spent on other presents :-) he went
from trial and error to deliberate experimentation to rule formation,
verification, application and demonstration.  The calculator clearly helped
him in both random probing, experimentation and verification in ways that
would have been hard if not impossible with paper and pencil.
-- 

- - -	/-/ a n s