Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!ames!hao!husc6!purdue!tlh
From: tlh@cs.purdue.EDU (Thomas L. Hausmann)
Newsgroups: comp.edu
Subject: Re: Mental arithmetic, was: Calculators in exams, was: Becoming CAI literate
Message-ID: <3362@arthur.cs.purdue.edu>
Date: 1 Mar 88 17:13:02 GMT
References: <2032@ukecc.engr.uky.edu> <3900008@nucsrl.UUCP> <24954@cca.CCA.COM> <1988Feb28.224421.6922@jarvis.csri.toronto.edu>
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Organization: Department of Computer Science, Purdue University
Lines: 31
Summary: Clarification needed

In article <1988Feb28.224421.6922@jarvis.csri.toronto.edu>, tjhorton@ai.toronto.edu ("Timothy J. Horton") writes:
> 
> I don't think mental arithmetic is very important for strong mathematical
> facility.  

  What do *you* mean by strong mathematical facility, I am not agreeing or
disagreeing with what you say here, I am just asking.  Because (as I stated
earlier in a discussion with elg@killer) doing mental calculations quickly
lets me concentrate more on my eventual computational goal.

>         'Amusing oneself and startling others' may be important for TV
> game shows, but how much else?  If the 5 functions on your basic calculator
> were the core of mathematical prowess, every student in the world capable
> of pressing buttons would surpass the accomplishments of Einstein, given
> enough 9 volt batteries.  Understanding arithmetic is important, but I
> question the value of the hours that would be needed to teach QUICK, MENTAL
> arithmetic in schools, when some much else of value is 'out there' in math
> to be learned.

Here I agree with you, heuristics that work for one person may not work for the
next. We all have our own mental tricks for doing quick computations and hence
we have preferences as to which to apply in a given instance.  Although, there
are some heuristics that can be taught (e.g. grouping additions of single digits
into pairs of treys s.t. intermediate sums are multiples of ten) others are
more obscure (15% of x [for tips] is .10*x + .5*(.10*x) because moving decimals
and halving are easy mental operations.)

-Tom
-------------------------------------------------------------------------------
Tom Hausmann       Dept. of Computer Sciences     Purdue University
tlh@mordred.cs.purdue.edu    | My ideas?  There has never been an original
...!purdue!tlh               | thought since Plato.