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

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Paul A. Tanner III

Posts: 5,920
Registered: 12/6/04
Re: [math-learn] Re: Transforming formulas
Posted: Feb 4, 2007 1:09 AM
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--- elkashish <forums@learningbyyourself.com> wrote:

>
> I very much agree that the tension between language, thought, and
> mathematics is a key issue [see my word problems book excerpt to what
> I view as a way to overcome it].
>
> I would (counterfactually? ;-)] be careful about using
> counterfactuals
> with students. The reason is exactly because of the problem I believe
> many have with it (illustrated in the example below). The reason is
> that counterfactuals require more mental processes than factual
> language. One has to hold both states in his mind when one is using
> counterfactuals. It's more accurate mathematically (logic wise) but
> more complex thinking wise.
>
> Thus, I prefer them to simplify the language and then translate to
> mathematics.
>


But is it? All I'm saying is that after seeing students (including when
I was a student) struggle and struggle with trying to make sense of the
conditional, and teachers trying and trying to explain it, I kept
asking myself, "Why doesn't the teacher just change the tense of the
verb?" Is is really less simple language to use a tense other than the
present tense? We have children pretend things all the time, using the
counterfactual tense. Example: As a creative writing exercise, we could
have them fill in the blank in "If I were a bird, then _____." I don't
see that it's necessarily more simple and more appropriate language to
use the present tense, and ask, "If I am a bird, then _____."

Another example, in the math realm: Which question would more likely
cause less of a problem for students, the first one using the
counterfactual tense, or the second one using the present tense? (1) If
Earth's radius were the same as Jupiter's, then what would be Earth's
circumference? (1) If Earth's radius is the same as Jupiter's, then
what is Earth's circumference?

Paul




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

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