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Re: Is this an exceptionally hard set of questions to answer?
Posted:
Nov 2, 2002 10:01 AM
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On Sat, 02 Nov 2002 09:55:50 -0500, Alberto Moreira
<junkmail@moreira.mv.com> wrote:
>Kevin Foltinek <foltinek@math.utexas.edu> said:
>>There's also the problem that students have with expanding
>>(a+b)*(c+d). Many students have memorized the pneumonic "FOIL" for
>>"First, Outer, Inner, Last", meaning to group things as (a,c), (a,d),
>>(b,c), (b,d), and then multiply and add.
snip
>>For these students, this is the kind of "magic" to which I was
>>referring, because they do not see any reason why one would do this;
>>it seems arbitrary. They see neither that this is simply three
>>applications of distribution of multiplication over addition,
>>(a+b)*(c+d) = a*(c+d)+b*(c+d) = a*c+a*d+b*c+b*d, nor that they are
>>doing (nearly) the same thing as they did when they were multiplying
>>multi-digit numbers.
snip
>....... The problem is, students confuse the
>notation and many will believe that when you write (a+b)(c+d) what
>you're asking for is a+bc+d. The issue here is not the application of
>the distributive property, the issue here is one of notation.
No, the issue here is expanding the expression by use of the
distributive property and there is no intuition involved.
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