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Teachers' Lounge Discussion: Geometer's Sketchpad

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From: Loyd Epperly <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2002080912:06:10
Subject: Re: Re: Re: Exponents and grouping symbols

Re the problem 2^3^3.

Using Microsoft EXCEL, the formula =2^3^3 results in 512.  Same for
the Texas Instruments TI-83 graphing Calculator.  Parenthesis are
required if you want the 3 to be cubed first.  Thus, 2^(3^3) yields
134217728. which equals 2^27 

Students often do not use grouping symbols such as braces {}, brackets
[] and parenthesis ().  Failure to use them can result in errors.  For
example,

If a student wanted to write in three line form:

  3        1           4
----  +  ---    =    ---
 4+1      2+3          5

But because he/she was using a typewriter, and therefore used the one
line form such as:

3/4+1 + 1/2+3 , the result would be 5 1/4 because of the failure to
use grouping symbols.

The student should write, 3/(4+1) + 1/(2+3) and that equals 4/5.  

The grouping symbols make the difference.  I was out of college with a
BA in math when I first wrote programs in FORTRAN programming
language.  It was that programming experience that made me keenly
aware of the importance of proper use of grouping symbols. We wrote
programs for a mainframe that was remotely located.  Cards had to be
punched.  Two or three days later the program would come back for
debug because the dumb computer had to be told precisely what you
wanted to do.  Math is that way too. 

I now often tutor, and most of the kids I tutor, fail to use grouping
symbols.  Maybe the teachers don't enforce that or were like me, and
didn't use them properly at first.  

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