Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-learn

Topic: [math-learn] Transforming formulas
Replies: 55   Last Post: Feb 19, 2007 11:48 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Jerome Epstein

Posts: 16
Registered: 12/6/04
Re: [math-learn] Transforming formulas
Posted: Jan 30, 2007 2:45 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (13.9 K)

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.
>



Date Subject Author
1/28/07
Read [math-learn] Transforming formulas
Antonija Horvatek
1/28/07
Read Re: [math-learn] 'Simplifying', e.g.,
a 4th root destroys information (?!)
John Morse
1/28/07
Read Re: [math-learn] 'Simplifying', e.g., a 4th root destroys information (?!)
Zeev Wurman
1/28/07
Read Re: [math-learn] 'Simplifying', e.g., a 4th root destroys
information (?!)
Ed Wall
1/28/07
Read Re: [math-learn] 'Simplifying', e.g.,
a 4th root destroys information (?!)
Richard Sisley
1/29/07
Read Re: [math-learn] 'Simplifying', e.g., a 4th root destroysinformation (?!)
Rex Boggs
1/29/07
Read Re: [math-learn] Transforming formulas
Rex Boggs
1/29/07
Read Re: [math-learn] Transforming formulas
John Morse
1/29/07
Read Re: [math-learn] Transforming formulas
Chris
1/29/07
Read Re: [math-learn] 12+0, 11+1, 10+2 all lead to ... graph of a parabola
John Morse
1/29/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
1/29/07
Read RE: [math-learn] Transforming formulas
John Clement
1/30/07
Read RE: [math-learn] Transforming formulas
Paul A. Tanner III
1/30/07
Read Re: [math-learn] Transforming formulas
Joshua Zucker
1/31/07
Read Re: [math-learn] Transforming formulas
Paul A. Tanner III
1/31/07
Read [math-learn] Re: Transforming formulas
Moti
1/31/07
Read Re: [math-learn] Re: Transforming formulas
Paul A. Tanner III
1/31/07
Read Re: [math-learn] Re: Transforming formulas
timotha@comcast.net
2/1/07
Read [math-learn] Re: Transforming formulas
Moti
2/1/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
2/1/07
Read Re: [math-learn] Re: Transforming formulas
John Clement
2/2/07
Read Re: [math-learn] Re: Transforming formulas
timotha@comcast.net
2/2/07
Read RE: [math-learn] Re: Transforming formulas
John Clement
2/2/07
Read Re: [math-learn] Re: Transforming formulas
timotha@comcast.net
2/2/07
Read [math-learn] Re: Transforming formulas
Moti
2/2/07
Read Re: [math-learn] Re: Transforming formulas
Paul A. Tanner III
2/3/07
Read [math-learn] Re: Transforming formulas
Moti
2/3/07
Read [math-learn] Thinking logially [was: Transforming formulas]
John Clement
2/5/07
Read [math-learn] Re: Thinking logially [was: Transforming formulas]
Moti
2/5/07
Read [math-learn] Re: Thinking logially [was: Transforming formulas]
Ed Wall
2/8/07
Read Re: [math-learn] "22 Game": pick 3-digit #,
add up 6 permutations of 2 digits. divide by sum of digits of 3-digit #, = 22
John Morse
2/4/07
Read Re: [math-learn] Re: Transforming formulas
Paul A. Tanner III
2/5/07
Read [math-learn] Re: Transforming formulas
Moti Levi
2/4/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
2/2/07
Read Re: [math-learn] Re: Transforming formulas
Ralph A. Raimi
2/3/07
Read [math-learn] Re: Transforming formulas
Moti
2/3/07
Read Re: [math-learn] Re: Transforming formulas
Ralph A. Raimi
2/4/07
Read [math-learn] Re: Transforming formulas
Moti
2/4/07
Read Re: [math-learn] Re: Transforming formulas
Ralph A. Raimi
2/5/07
Read [math-learn] Terminology (was Transforming formulas)
Alva
2/5/07
Read [math-learn] Re: Terminology (was Transforming formulas)
Moti Levi
2/5/07
Read RE: [math-learn] Re: Transforming formulas
John Clement
2/5/07
Read RE: [math-learn] Re: Transforming formulas
Ed Wall
2/5/07
Read RE: [math-learn] Re: Transforming formulas
John Clement
2/5/07
Read RE: [math-learn] Re: Transforming formulas
Ed Wall
2/5/07
Read [math-learn] Re: Transforming formulas
Moti
1/30/07
Read RE: [math-learn] Transforming formulas
John Clement
1/31/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
1/31/07
Read Re: [math-learn] Re: Transforming formulas
Paul A. Tanner III
2/1/07
Read [math-learn] Re: Transforming formulas
Moti
2/1/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
2/1/07
Read [math-learn] Re: Transforming formulas
Antonija Horvatek
1/29/07
Read Re: [math-learn] Transforming formulas
Paul A. Tanner III
1/30/07
Read Re: [math-learn] Transforming formulas
Jerome Epstein
2/19/07
Read [math-learn] Re: Transforming formulas
Jon Wilson
1/30/07
Read RE: [math-learn] Transforming formulas
Jerome Epstein

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.