
[mathlearn] Re: Transforming formulas
Posted:
Feb 19, 2007 11:48 PM



Use a table instead of FOIL.
For example let's use x, 2 and 4: (x^2 is x squared)
x 2
x _x^2_______2x
4 _4x________8
Now, combine x^2, 2x, 4x and 8 into:
x^2 + 2x + 4x + 8 = x^2 + 6x + 8
I know this table above is rather crude in this editor, but my students have been able to address binomials, trinomials and quadratics in a forward and reverse direction. FOIL has advantages too, but I'd wait until they master this and are comfortable working in both directions.
Use product, sum or difference and leave "F" (first) "O" (outer) "I" (inner) "L" (last) until later. The FOIL method can also be modeled using the aforementioned tabular method.
Hope this helps.
Jon
 In mathlearn@yahoogroups.com, "jepstein" <jepstein@...> wrote: > > 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@... 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. > > >
[Nontext portions of this message have been removed]

