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[Phys-L] Re: student mathematical capability



OK - I'll bite.

WHY is 2 + 2 = 4?

I always thought it just IS! If I place two apples next to two
other apples, I have 4 apples. Where is the WHY?

I learned math by memorizing times tables. Seemed to work OK.

Bob at PC

-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-
L@list1.ucc.nau.edu] On Behalf Of Hugh Haskell
Sent: Wednesday, September 14, 2005 2:56 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: student mathematical capability

At 12:24 -0600 9/14/05, SSHS KPHOX wrote:

However, as I have watched students get pushed to achieve more
and sooner
( and there are many that can) I find the early teaching in
the younger
grades focusing on an algorithmic approach and foregoing the
development
of real understanding. I am not convinced that all students
are really
ready to master algebra in grade 8 at age 13 or 14. Many can
but not
all
by any means. I should not be surprised.

I suspect that this is mostly due to the fact that teachers of
mathematics at the middle-school level are themselves mostly
stuck in
an algorithmic mode. If students were taught from the very
beginning
to understand why 2+2=4, etc., rather than merely being
required to
memorize that fact, or more importantly, why 2*2=4 and 4/2=2,
they
wouldn't have nearly some much trouble transitioning to the
type of
math that requires this sort of thinking. But to do that
requires a
complete restructuring of how we teach early math, and after
the "new
math" debacle in the 60s, it is unlikely that will happen any
time
soon. However, if we did do some restructuring and the students
saw
why multiplication works, as a form of repeated addition, I
rather
think it would become much easier for them to then memorize the
multiplication tables that we all decry their lack of knowledge
of.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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