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Topic: Why?
Replies: 52   Last Post: Oct 30, 2012 9:38 PM

 Messages: [ Previous | Next ]
 Paul A. Tanner III Posts: 5,920 Registered: 12/6/04
Re: Why?
Posted: Oct 24, 2012 11:47 AM

On Wed, Oct 24, 2012 at 5:41 AM, Robert Hansen <bob@rsccore.com> wrote:
...
> I don't consider the teaching and learning of formulas to be algebra at all.
> Just because it has letters in it doesn't make it algebra.
>

I don't care what your definition of algebra is. Call using letters of
the alphabet whatever you want.

This skill of being able to handle formulas or expressions in which
even all the elements of the expression are letters of the alphabet
should not be put off unnecessarily, for what should be obvious
reasons.

> The teaching or learning of methods or techniques like being able to
> solve for x in such as
>
>
> 53/100 = 37/x
>
> in just one step is not algebra foolishness. (Equal fractions with one
> of the denominators being 100 is a standard set-up in percent
>
>

> > You meant to say "pretend to solve for x", right? Or are you pretending to
> us that you just taught them to "solve"? This is my point. When you are
> > walking through the steps to "solve" for x,

Although the phrase "solve for x" can and does have a number of
different uses, one main use is simply through one or more
transformations of equations to obtain an equation such that the
variable in question is on one side of the equation and everything
else is on the other side of the equation.

There is no pretend here. This skill in general is very important and
there is nothing pretend about it, regardless of whether you want to
call it an algebraic skill.

In fact, not being to perform this skill or at least quickly and
easily is one of the main reasons people have problems in mathematics.

The vast majority of people that I have shown some of these quicker
and easier ways with respect to this skill have responded positively
to it. One adult student in particular told me that he would have had
a much easier time of it in chemistry in high school had he discovered
these methods on his own or been shown them. (This, since in chemistry
and other sciences, needing to solve for an unknown - in the sense I
mean above, transforming the formulas, so so present.)

> I am not against formulas for fraction arithmetic, but they must be
> developed arithmetically, not algebraically. In your example above, the
> student must "simply see" when and where to multiply or divide.
>

There is a way of doing things with respect to isolating target
variables that does not going through all that multiplying and/or
dividing both sides of the equation to isolate the target variable. I
shared some of these ideas at math-learn almost ten years ago - see
all my posts in the following thread in 2003:

"Algebra as a spatial motion game of logic, like chess or checkers"
http://mathforum.org/kb/message.jspa?messageID=1364908

I suspect that you will show the same type of hostility to such ideas
as these that make things so much easier and quicker for so many
people, the same hostility I have received from so many in terms of
making it easier and quicker to perform various skills. I wrote about
this also at math-learn in 2005 - see not just this post but all my

"Re: [math-learn] Withholding information in the name of promoting
understanding"
http://mathforum.org/kb/message.jspa?messageID=4012725

Date Subject Author
10/23/12 Robert Hansen
10/23/12 Haim
10/23/12 Clyde Greeno
10/23/12 Dave L. Renfro
10/23/12 Paul A. Tanner III
10/23/12 Robert Hansen
10/23/12 Paul A. Tanner III
10/23/12 Robert Hansen
10/24/12 Paul A. Tanner III
10/24/12 Robert Hansen
10/24/12 Paul A. Tanner III
10/24/12 Robert Hansen
10/24/12 Paul A. Tanner III
10/24/12 Robert Hansen
10/24/12 Paul A. Tanner III
10/24/12 Robert Hansen
10/24/12 Paul A. Tanner III
10/25/12 Robert Hansen
10/25/12 Louis Talman
10/26/12 Wayne Bishop
10/25/12 Paul A. Tanner III
10/27/12 kirby urner
10/27/12 Robert Hansen
10/27/12 kirby urner
10/25/12 Robert Hansen
10/25/12 Paul A. Tanner III
10/23/12 Jonathan J. Crabtree
10/25/12 Robert Hansen
10/24/12 GS Chandy
10/26/12 Wayne Bishop
10/26/12 Robert Hansen
10/27/12 Paul A. Tanner III
10/27/12 Robert Hansen
10/27/12 Paul A. Tanner III
10/27/12 Robert Hansen
10/27/12 kirby urner
10/28/12 Paul A. Tanner III
10/28/12 Robert Hansen
10/28/12 Paul A. Tanner III
10/27/12 Wayne Bishop
10/29/12 Joe Niederberger
10/29/12 Joe Niederberger
10/29/12 Robert Hansen
10/30/12 Louis Talman
10/30/12 Robert Hansen
10/30/12 Paul A. Tanner III
10/30/12 Louis Talman
10/30/12 Robert Hansen
10/30/12 Louis Talman
10/30/12 Robert Hansen
10/30/12 Louis Talman
10/30/12 Clyde Greeno @ MALEI
10/30/12 kirby urner