Re: [MATHEDCC] If factoring is not important

Bret Taylor (bret@IAG.NET)
Thu, 1 Apr 1999 12:55:35 -0500 (EST)

At 07:41 AM 4/1/99 -0500, Edward Laughbaum wrote:
>At 07:26 PM 3/31/99 -0500, Bret Taylor wrote:
>>At 11:18 AM 3/31/99 -0800, Sandy Wagner wrote:
>>>Bret, first I'm only talking about polynomial factoring, not numerical or
>>>common factor factoring. I see value in both of them for different reasons.
>>>For polynomial factoring I think we should distinguish between the *process*
>>>of finding factors and the theorems themselves. So few (essentially 0%) of
>>>polynomials are factorable by pencil and paper that I think we waste a lot
>>>of our time and our students' time with the processes when there are so many
>>>more interesting and valuable things we could be doing. And remember, the
>>>*only* places that trinomials are factored are in the math classroom and
>>>(decreasingly so) on SAT's etc.. Ask any engineer.
>>>-Sandy
>>
>>I understand what you are saying, and I agree your points are valid.
>>However, I still think understanding the concept of factoring polynomials is
>>important. Especially using graphing calculator technology, students tend
>>to just memorize and regurgitate rather than understand the relationship
>>between x-intercepts, factors, and zeroes.
>___________________________________
>Bret,
>
>I am courious about how you know that "...using graphing calculator
>technology...students...memorize and regurgitate...". Do you think this is
>so because most teachers do not know how to teach with the graphing
>calculator? Or because all algebra textbooks don't integrate the use of
>graphing calculators appropriately? Or is this something you think to be
>true based on experience? Or have you seen research on the issue?
>
>Ed

Great question. Anecdotal evidence only. Based on my very limited personal
experience, I think the primary cause is your first suggestion. when the
TI-85 and 82 first came out, I went to several local high schools and taught
students there how to use them. (15 hour, 1 semester credit course) I also
taught about 7 high school teachers a one week seminar on how to use GC's.

Unfortunately I see a considerable number of students who use the
calculators as a magic black box which supplants their brains. They draw
rational functions exactly like zoom standard shows them (demonstrating no
understanidng of a vertical asymptote). they say, "But that is what my
calculator said." they thin "exact answer" means write down all digits
shown on the calculator. (The exact value of 2/3 is .666666666667)

I love teaching with graphing calculators. but, I've also seen them grossly
misused.

Graphing calculators do not kill mathematical understanding; but they are
the weapon of choice of some teachers. :-)
>_______________________________________
>
>
>

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