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Topic: creative opening question for a lesson

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Subject:   RE: creative opening question for a lesson
Author: Craig
Date: Jun 29 2006
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.

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