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 Subject: RE: creative opening question for a lesson Author: Susan Date: Jun 29 2006
On Jun 29 2006, Craig wrote:
> I recently heard a talk about the purpose for mathematics after
> arithmetic (elementary school).  The speak claimed that "you need it
> for the next math course" is usually true, but doesn't spark much
> student interest.  "People use this in lots of careers" is probably
> not true, especially with some topics like factoring polynomials.
> His answer, while probably not one that students relate to any more
> than preparation for the next math course, is that in the study of
> mathematics students learn reasoning, logic, and problem solving in
> ways they don't see in other parts of the secondary curriculum, and
> it is precisely these skills that make mathematics so valuable in
> the workplace and in academics.  Most people don't use the fact that
> a water molecule consists of two hydrogen atoms and one oxygen atom
> (but most probably know it).  Factoring is a form of molecular
> decomposition--it breaks down a polynomial into smaller, somewhat
> more manageable, pieces.  This process (breaking down into smaller,
> more manageable pieces) is a crucial component in problem solving,
> whether in math, science, engineering, social science, even in the
> fine arts.  Therefore, it is a skill worthy of attention in the
> curriculum.

That said, students usually don't care about the long
> term "big picture."  The response about the crazy math teacher, or
> the jailer who only releases prisoners who can factor, at least
> elicits groans from the student and allows the teacher to plow
> ahead.  Factoring polynomials is the same as "eating your
> vegetables."  You do it either because YOU realize it's good for
> you, or you do it because someone else who realizes it's good for
> you required you to.

Craig
We must be on the same wavelength.  I was sitting here thinking about the big
picture to, and breaking down big things into smaller pieces.  I like your
examples.  My idea is to have the students look at a movie trailer (can be found
online).  Most see a movie trailer as one big thing.  But if you have the
students count the number of shots in a trailer, they will see that it is
composed of many parts.  You could then have them look at some tv commercials at
home with the same idea in mind. This will drive home the fact that a whole is
made up of many components.  Then when you show them a polynomial, you can show
that it too can be broken down into components.  I don't know if this is the
best idea...i was just trying to think of somthing "real" that could be broken
down.