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Re: math and arithmetic



Juanita,

I'm not disagreeing with you at, but I want to tug at something you said. I
think students in 4th grade can do "advanced" mathematical thinking. By
this I mean that 4th graders can work with concepts like tessellations, for
example, and create some pretty advanced mathematical theories through that
experience. Or they can work with angles and speculate how a knowledge of
angles and their degrees can relate to some common tools and constructions
in their world. The same kinds of things can happen in language arts where
students can describe language in action and draw up some theories or
hypotheses about language structures. These are advanced theories that they
are working with, but played out in ways that are appropriate for their
developmental levels.

I read something somewhere that said arithmatic was not really mathematics
but a trick people could learn. "Doing" arithmetic was not the same as
thinking mathematically, The whole idea behind mathematics is to help
students approach logic from that direction. We need to understand, of
course, that there are other pathways to logical thinking than mathematics.
I think many people assume there is a connection for students between
arithmetic and mathematics, that by teaching arithmetic, students are
thinking mathematically. This is an assumption we shouldn't make. Just as
we should not make the assumption that the ability computate in your head
necessarily means you are a good math thinker.

Nancy

At 12:58 PM 2/23/02 EST, you wrote:
>In a message dated 2/23/02 6:19:48 AM Pacific Standard Time,
>gbracey@EROLS.COM writes:
>
>
>> Here's the question: Given FITW's overall stellar performance, do the above
>> data not indicate that mastery of "the basics" is not necessary for the
>> acquisition of advanced mathematical skills?
>>
>> In the college town where I grew up, it was a cliche that mathematicians
>> couldn't cope with arithmetic. Are arithmetic and math independent of each
>> other? My guess is yes.
>>
>>
>
>Aha! I think you've got something here, Jerry. And I think it's sort of
>like spelling and communications skills. Some of the worst spellers are the
>best communicators. However, to assume that all can master advanced math at
>4th, 7th, and 10th grade, which is what we are doing here in WA, is illitist.
>And skipping the basics denies people of what the majority need to function
>in the world.
>
>Juanita
><HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF"
FACE="Arial" LANG="0">In a message dated 2/23/02 6:19:48 AM Pacific Standard
Time, gbracey@EROLS.COM writes:<BR>
><BR>
><BR>
><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT:
5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Here's the question:&nbsp; Given
FITW's overall stellar performance, do the above data not indicate that
mastery of "the basics" is not necessary for the acquisition of advanced
mathematical skills?</FONT><FONT COLOR="#000000" style="BACKGROUND-COLOR:
#ffffff" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"><BR>
> <BR>
></FONT><FONT COLOR="#000000" style="BACKGROUND-COLOR: #ffffff" SIZE=2
FAMILY="SANSSERIF" FACE="Arial" LANG="0">In the college town where I grew
up, it was a cliche that mathematicians couldn't cope with arithmetic.&nbsp;
Are arithmetic and math independent of each other?&nbsp; My guess is
yes.</FONT><FONT COLOR="#000000" style="BACKGROUND-COLOR: #ffffff" SIZE=3
FAMILY="SANSSERIF" FACE="Arial" LANG="0"><BR>
> <BR>
></BLOCKQUOTE><BR>
></FONT><FONT COLOR="#000000" style="BACKGROUND-COLOR: #ffffff" SIZE=2
FAMILY="SANSSERIF" FACE="Arial" LANG="0"><BR>
>Aha!&nbsp; I think you've got something here, Jerry.&nbsp; And I think it's
sort of like spelling and communications skills.&nbsp; Some of the worst
spellers are the best communicators.&nbsp; However, to assume that all can
master advanced math at 4th, 7th, and 10th grade, which is what we are doing
here in WA, is illitist. And skipping the basics denies people of what the
majority need to function in the world.<BR>
><BR>
>Juanita</FONT></HTML>
>
Nancy G. Patterson, PhD

"To educate as the practice of freedom is a way of teaching that anyone can
learn."

--bell hooks

patter@voyager.net
<http://www.msu.edu/user/patter90/opening.htm>
<http://www.npatterson.net>
<http://www.npatterson.net/standardizedtesting.html>

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