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

 Messages: [ Previous | Next ]
 John Clement Posts: 852 Registered: 12/6/04
RE: [math-learn] Transforming formulas
Posted: Jan 29, 2007 11:36 PM
 att1.html (12.3 K)

This particular example shows the problem that students do not have either
proportional or compensation reasoning. The two go hand in hand. Once they
have this type of reasoning, then they will automatically do this
transformation, and even consider the relevant algebraic rules to be
obvious.

So before teaching the algebraic rules they should have activities that
build both proportional and compensation reasoning. Any one who is
interested might investigate "Thinking Math" developed at King's College.

John M. Clement
Houston, TX

>
> With my seventh-grade students, I would do transformations,
> but, depending on context,
> I would not necessarily expect them to be able to do it.
>
> One time, in particular, that I recall using it is with the distance
> formula.
>
> For whatever reason, there were many students who knew that r = D/t,
> and when we started out with problems that required solving for D
> there would immediately be questions, because their recollection of the
> formula
> "didn't solve for" what they needed.
>
> Other students could tell them that D = rt,
> and I would always do the transformation for them,
> to show them that the two formulas are "equivalent"
> before I would show them how to solve the problem both ways.
>
> I always found it fascinating that the students often had no problem
> understanding how to solve the equation (once the values were plugged in),
> but they were totally confused by the transformation, using the variables.
>

Date Subject Author
1/28/07 Antonija Horvatek
1/28/07 John Morse
1/28/07 Zeev Wurman
1/28/07 Ed Wall
1/28/07 Richard Sisley
1/29/07 Rex Boggs
1/29/07 Rex Boggs
1/29/07 John Morse
1/29/07 Chris
1/29/07 John Morse
1/29/07 Antonija Horvatek
1/29/07 John Clement
1/30/07 Paul A. Tanner III
1/30/07 Joshua Zucker
1/31/07 Paul A. Tanner III
1/31/07 Moti
1/31/07 Paul A. Tanner III
1/31/07 timotha@comcast.net
2/1/07 Moti
2/1/07 Antonija Horvatek
2/1/07 John Clement
2/2/07 timotha@comcast.net
2/2/07 John Clement
2/2/07 timotha@comcast.net
2/2/07 Moti
2/2/07 Paul A. Tanner III
2/3/07 Moti
2/3/07 John Clement
2/5/07 Moti
2/5/07 Ed Wall
2/8/07 John Morse
2/4/07 Paul A. Tanner III
2/5/07 Moti Levi
2/4/07 Antonija Horvatek
2/2/07 Ralph A. Raimi
2/3/07 Moti
2/3/07 Ralph A. Raimi
2/4/07 Moti
2/4/07 Ralph A. Raimi
2/5/07 Alva
2/5/07 Moti Levi
2/5/07 John Clement
2/5/07 Ed Wall
2/5/07 John Clement
2/5/07 Ed Wall
2/5/07 Moti
1/30/07 John Clement
1/31/07 Antonija Horvatek
1/31/07 Paul A. Tanner III
2/1/07 Moti
2/1/07 Antonija Horvatek
2/1/07 Antonija Horvatek
1/29/07 Paul A. Tanner III
1/30/07 Jerome Epstein
2/19/07 Jon Wilson
1/30/07 Jerome Epstein