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Re: [math-learn] Transforming formulas
Posted:
Jan 30, 2007 2:45 PM
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Yes, you are making good sense.
Memorizing FOIL gives the student no clue as to how to
multuiple a binomial by a trinomial, and countless other
examples could be cited.
Jerry Epstein
>
> I agree with much of the below, but I still have my fears.
>
> Yes, people like you and me who become fluent with algebra
> eventually start moving around the game pieces instead of
> thinking about the reasons at each step. But we have
> enough experience with the reasons that we could justify
> our steps if we had to.
>
> At the introductory level, what I fear is that if we teach
> the "rules of the game" manipulation methods, then
> students will end up making the common algebra mistakes
> they all make, but instead of being able to think for
> themselves about why it does or doesn't work, they will be
> memorizing what is to them an arbitrary set of "rules of
> the game".
>
> To me, the purpose of teaching them the less efficient
> "theorem application" style instead of the more efficient
> "game piece" style is that with the theorems they have
> more tools for explaining why a rule works or doesn't work
> in a given situation. That's why students in my classroom
> aren't allowed to say "FOIL" but must say "distribute",
> and aren't allowed to say "cancel" but must say "divide
> out" or "subtract out" or "are inverses" instead.
>
> Am I making any sense?
> --Joshua Zucker
>
>
>
> On 1/29/07, Paul A. Tanner III <uprho@yahoo.com> wrote:
> > I do not
> > think along the lines of how we usually see algebra
> > taught, which is to actually apply the proofs of these
> > theorems, this proof being the two steps of adding or
> > multiplying on both sides and then applying the inverse
> property. I'm essentially just eliminating variables, or
> > just moving variables around, changing them into their
> > inverses, sort of like moving chess or checkers pieces
> > on a game board according to some rules of the game.
> >
> > I believe that many of those who "get good at algebra"
> > also do this more efficient way of thinking, consciously
> > or not. That is, we apply the theorems in question in
> > one step, rather than apply the proof of these theorems,
> this application requiring more than one step. >
> > I also believe that not teaching students this more
> > efficient way of thinking of applying the theorems, not
> > becoming fluent in their direct application, could be a
> > reason why so many fail Algebra I the first time they
> > try. I never cease to be amazed at how many students
> don't learn to think this way on their own, and that when
> > I show them this more efficient way, how transforming
> > equations (isolating variables) becomes easy - no longer
> a problem.
>
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