
Re: [mathlearn] Transforming formulas
Posted:
Jan 30, 2007 2:45 PM



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. >

