Q&A #7370

Use of commas in math

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Nov 27, 2001 at 08:01:26
Subject: Re: Use of commas in math

Hello Jean,

First let me state that I would never presume to tell someone else HOW to 
grade, or what to grade.  But I think I can offer guidelines for how I have 
overcome some (but never all) of my concerns about how to grade and what to 

Commas make numbers easier to read because, I believe, they move the student 
from the aspect of memorizing numbers to a system of generating numbers. This 
happens much earlier in countries that have a more generous relation between 
their language and base ten numbers.  Japanese, for instance, allows one to 
start reusing old knowledge as early as 11 when they say (literally) ten + 1. 
At twenty they say "ni juu" (literally, two tens) and for the next number, 
they add one to get "ni juu ichi".  Unfortunately this still requires a new 
number ever power of ten, and so after a thousand (which actually came from 
"great hundred") it becomes sensible to group numbers into periods of three to 
more easily express them...(although the Japanese actually use a denominate 
unit for 10,000. {See how easy that is to read accurately with the comma?} )

  So if you are at that point where you want to insure that students see and 
can understand the grouping of periods, then yes, it may be reasonable to 
count off if a student does not use commas to seperate the periods. But you 
might prefer to test this more directly, such as to ask "in the number 
4567891, what are the numbers in the thousands period (or millions, etc). 
At the advanced high school level I encourage it because it makes it easier 
to see obvious mistakes.  2357 * 4012 = 945684 is harder to notice as wrong 
than is 2,357 * 4,012 = 945,684. In the latter case the existance of an error 
sort of leaps out, allowing me to glance again at my calculator and realize 
the answer should have been 9,456,284... much more reasonable.

  I think if we demonstrate good practice, and point out the advantages, most 
students will choose that path because it really is easier to do. It is not 
like asking them to eat vegatables on the promise of some future gain, this is 
a right now kind of change.

Hope my confused response is of some use to you.
good luck

 -Pat Ballew, for the T2T service

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