On Sat, 02 Nov 2002 09:55:50 -0500, Alberto Moreira <firstname.lastname@example.org> wrote:
>Kevin Foltinek <email@example.com> 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.
>>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.
>....... 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.