Is Subtraction Separation or Taking Away?
Date: 01/24/2002 at 00:51:43 From: Geeta Mahashabde Subject: Subtraction Dear Dr. Math, Do we introduce subtraction as 1) separation of a group into two parts and we know one part and are trying to find the other, or 2) taking away ? We feel that there is a thin line between separation and taking away. Please help us. Thanks, Geeta
Date: 01/24/2002 at 09:14:40 From: Doctor Ian Subject: Re: Subtraction Hi Geeta, In the following diagram, /\ /__\ +-----+ | | | | +-----+ is the triangle above the square? Or is the square below the triangle? They are really just two ways of expressing the same idea. Similarly for 'separation' and 'taking away'. The only difference between the two concepts is that in separation, you still know where the subtracted items are, while in 'taking away', you might not. In general, the more ways you understand something, the deeper your understanding of the thing. So I would say that there is no reason to prefer one conception to the other; and it would be better for the students to be exposed to both. My own preference is to unify subtraction with addition, by showing that addition and subtraction are just two ways of looking at the same fact. That is, if a + b = c this is exactly the same thing as saying that c - a = b and c - b = a I think this is a simpler idea than thinking of addition and subtraction as being different things. (Of the two approaches you mentioned, this corresponds more closely to the idea of separation.) This approach works for multiplication and division, as well. That is, if a * b = c this is exactly the same thing as saying that c/a = b and c/b = a Is the cat on the mat? Or is the mat under the cat? Why make a distinction? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 01/29/2002 at 07:30:25 From: Geeta Mahashabde Subject: Subtraction Dear Dr. Ian, Thanks a lot for the reply. Yes, really the cat is on the mat and the mat is under the cat. Geeta
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