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Q&A #7370 |
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 grade... 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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