Re: [MATHEDCC] Calculators and Fractions

Al Roy (aroy@BRISTOL.MASS.EDU)
Sat, 04 Oct 1997 11:22:42 -0400 (EDT)

Hi all,
I was encouraged by this entry of Bret's. He is raising the question of
whether or not Math should be taught for understanding. I'm encouraged
because the
cycle may be turning back to what was called the "Modren Math" of the
early sixties. Questions like : Does 2/3 =0.666? Why or why not? Were the
norm in the days when Math was supposed to be taught for
understanding.Another typical question was:"Why does 1/2 + 1/3 = 5/6?
Explain using a step by step process giving a reason for each step."These
questions are difficult to answer using a calculator.
Keep the faith,
Al Roy
On Fri, 3 Oct 1997, Bret Taylor wrote:

> Not to beat a dead horse, but I'd like to share a letter that I received
> (from another listserv I am on). Names have been omitted to protect the
> anonimity (and the innocent?). A student wrote:
>
> Hello,
>
> I have a questiion with regards to (a graphing calculator). When solving
> f(x) = 6-2x. When f(x) is 2/3 I get the answer of 4.6667. I know by
> looking in the back of the book that the answer is 4 2/3. How can I get the
> calculator to show me that .6667 is 2/3? I knew it had to be 4 and a
> fraction and I guess I could have solved it by hand but 2/3 = .6666666667
> according to my calculator. With all this technology there must be an
> easier way. To find the answer I did set my table to independent ask and
> the answer is 4.6667. If worked on the home screen I get 4.6666666667.
> Then I can convert it to 14/3 = 4 2/3. Is there an easier way? I hope so.
>
> End of letter.
>
> My impression based on this letter is that this student is a bright,
> industrious, inquisitive, and serious student. He wants to figure out what
> is happening. he knows something is wrong and is working diligently to try
> and find out what. I have nothing but commendations to give him.
>
> My concern is this: Is he being trained on how to use a calculator to get
> right answers (the answer he got is different from the back of the book)?
> Is he being trained to never do anything by hand that the calculator can do?
> Is he being educated to understand concepts?
>
> BTW, I assume it was just a typo and when he said "When f(x) = 2/3" that he
> meant to say "When x = 2/3".
>
> Does he understand the relationship between decimals and fractions? Does he
> understand the concept of repeating decimals? Does he think that 2/3 really
> does equal .6666666667? Does it really matter?
>
> Please don't misunderstand. I use technology in the classroom. I love it.
> I think it can enhance teaching. But every year, it seems, I get more
> students who are experts on punching buttons on a calculator, but extremely
> weak on understanding algebraic concepts.
>
> Have we decided that training is better than educating? Do students need
> to understand concepts and relationships? Am I over-reacting? I keep
> hearing the words of Jaime Escalante, "Do you want to be the guy who repairs
> the car, or designs it?"
>
> Off my soap box and out of my ivory tower,
>
> Bret
>
>
>
> Bret Taylor Lake-Sumter Community College Leesburg FL
>
> "It matters not the subject taught, nor all the books on all the shelves.
> What matters more, yes most of all, is what the teachers are themselves."
> John Wooden
>
> John 3: 3^3 + 3
>
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