[Phys-L] Re: Calculators a Distraction?

[rlamont <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

It has been so long since I looked at elementary school math
topics that I have to rely solely on anecdotal observations from
when my daughter started school 15 years ago. I noticed a
pronounced de-emphasis on rote memorization of multiplication
tables. Could this be the source of students difficulty with
fractions and manipulation of exponents in algebra? I can see a
value to being drilled, drilled, and drilled again on simple
multiplication, division, and fractions. But I see little reason
to learn longhand techniques to do multiplication and division of
complicated numbers. Once the fundamentals are ingrained to the
point that they are reflexive, the use of calculators frees up
time to learn other things - possibly estimation techniques -
where the material learned by rote can be applied and actually
reinforced..

When I give exam questions and assign homework, I do require
students to show me how a calculation was done. I want to see the
numbers written down each step of the way so I can trace their
reasoning. I would not be impressed in any way if a student
showed me the longhand calculations of each multiplication and
division required to get to the answer.




> -----Original Message-----
> From: Forum for Physics Educators [mailto:PHYS-
> L@list1.ucc.nau.edu] On Behalf Of Wes Davis
> Sent: Sunday, February 06, 2005 2:06 PM
> To: PHYS-L@LISTS.NAU.EDU
> Subject: Re: Calculators a Distraction?
>
> I can't say that any "real-world" scenarios come to mind to
> justify the need for division, but I certainly see the effects
in
> my Calculus classes.  Because math teachers have opted to
> teach calculator skills, few of my calculus students can do
> any algebra that involves fractions - complex or otherwise.
>
> Isn't knowledge of fractions, multiplication and long division
> necessary for doing algebra (and therefore calculus)?  I find
> that I have to teach long division and complex fractions in my
> Calc classes so that students can learn to do such operations
> as integrating certain functions and finding oblique
asymptotes,
>  among others.
>
> I agree that these are not, for most people, necessary.
Nonetheless,
> I don't think that students should come into advanced classes
without
> a firm foundation in these skills.
>
> Perhaps (likely) I've misunderstood the point being made by
Bob.
> John Denker writes:
> > I've been racking my brain, trying to think of a real-world
> > scenario where somebody would need to do division, without
> > having easy access to a calculator.  I haven't come up with
> > any.  The only times I've done long division recently is
> > when I was teaching the subject!