Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Defining Decimals
Posted:
Feb 13, 2009 11:44 PM
|
|
Come on, Bill. The only reason you keep arguing
for defining decimals too early is to support
calculator use in the early grades, possibly even
kindergarten forward, fuzzy math biblical
precepts to avoid learning arithmetic properly.
As I suspect you actually understand, 0.123
means what you want it to mean only by looking at
that portion of the number line that is the sum
of some segments obtained by repeatedly
subdividing the identified identified segment
into tenths. Nobody chops up the entire interval
[0, 1] (or [0, 1) to agree with Lou's
sophisticated reference) into 1000 subintervals
as you indicate; just try it once if you don't
believe me. To start, [0, 1) is divided into 10
equally spaced points corresponding to 0-9. The
point in question is between the points
corresponding to 1 and 2 so we start with a
segment of length 1/10 and subdivide the next
interval that corresponds to [1/10, 2/10). Next,
refine [1/10, 2/10) into tenths, again
corresponding to 0-9, to get hundredths. Here we
see that the point in question is in the interval
between the points corresponding to 2 and 3 so
now we have a new segment, this one of length
2/100, to add to the existing segment of length
1/10. Moving on, we subdivide the next segment as
before recognizing, but probably not explicitly
writing, that these are thousandths. Seeing that
3 is "dead on", we have a third segment, this
time 3/1000, to add to the earlier segments and
we terminate. We don't continue ad infinitum as Lou's example has us always do.
Apparently, you really are into this fuzzy stuff;
your post to "Where's the Math" seems to imply
that you believe the IMP self-promotion:
<http://mathunderground.blogspot.com/2009/02/10-year-old-imp-lies-are-still-alive.html>http://mathunderground.blogspot.com/2009/02/10-year-old-imp-lies-are-still-alive.html
----------------------------------------------------------
Dan tells us: "I went to examine Beaverton Oregon's proposed math adoption.
Here is what I found. A link to Interactive Math
Program, which seems like a blatantly dishonest IMP sales pitch!!!"
He then mentions http://www.mathimp.org/research/exemplary_award.html
Going there, we find
http://www.mathimp.org/downloads/IMP_research4DB3.pdf,
in which there is a reference to: White, P., A.
Gamoran, and J. Smithson, 1995. Math innovations
and student achievement in seven high schools in California and
New York, Madison: Consortium for Policy
Research in Education and the Wisconsin Center
for Education Research, University of Wisconsin.
<snip>
---------------------------------------------------------
I recently posted (2/11/09) some facts about the
WCER "study" and the Jo Boaler borders on
outright fraudulent misrepresentation of the
schools, especially her "exemplary" Railside High
School. Once identified, the school was, based on
data she had at the time, arguably the worst
performing regular high school in the state of
California. The "Exemplary" rating by the US
Department of Ed was made by a panel that
included exactly one mathematician, "Manuel
Berriozábal", who refused to sign off on any of
the curricula under consideration for lack of
supporting data when the rating was supposed to
be based primarily on supporting data. In fact,
it consisted primarily of laudatory articles in
newspapers, the WCER study, and the like, not
real evidence. It was somewhat ironic that the
"Exemplary" rating occurred after IMP was well on
its way to going belly-up across California.
So sell it in Washington State and elsewhere
across the nation. It's really quite amazing.
Wayne
At 06:34 PM 2/12/2009, Bill Marsh wrote:
>[I submitted this almost a week ago. I don't
>know what happened to it. By chance, it deals
>with several things in Wayne's most recent note.]
>
>Wayne's [earlier] comments have been helpful to
>me. He has said: "I think you are making way
>too big of a deal over an issue that is not
>worth the effort." He asks: "And more
>importantly, why try to assign meaning to it
>[i.e., .123] without the ability to add
>fractions?" and he doubts that Wu "objects to
>talking to a three-year-old about, say, "half an
>apple" or "a quarter of a cookie" before the
>child has ever seen a formal number line."
>
>I, too, am sure about the cookie. I believe
>that Wu wants a clean definition of fraction so
>computation can be taught well. I want to use
>number lines prior to this computation so kids
>can see how decimals and fractions fit in with
>counting numbers and with each other.
>
>I am surprised that he asked: "What does 0.123
>mean without the concept of addition; specifically, 1/10 + 2/100 + 3/1000?"
>
>I guess I don't explain things well. I have
>tried to say that a decimal can be read as
>specifying a way to (start to) "zero in" on a
>point on a given number line, a step at a
>time. "0." can specify the closed interval [0,
>1]. Then "0.1" specifies the closed interval
>[.1, .2]. "0.12" specifies the closed interval
>[.12, .13]. And then "0.123" specifies the closed interval [.123, .124]. Etc.
>
>Finally, Wayne asks: "And more importantly, why
>try to assign meaning to it without the ability to add fractions?"
>
>So we and the kids won't have to wait. I
>believe kids are interested in measuring, or can
>be interested in it, in ways that can help us
>teach them about numbers. Or to help them
>discover things about numbers and about counting number arithmetic.
>
>As I have mentioned, perhaps too often, I think
>that the "naming trick" I came up with can give
>second graders a powerful tool to measure with
>that can serve as a scaffold for learning how to
>use decimals for measuring in grades three and
>four, earlier than we teach fraction addition.
>
>I have something else I'd like to see tried and
>worked with, what I would call "picture
>numbers." The idea is to draw a picture of the
>unit interval a measurement is in, something
>like 3 |-*-------| for pi. I'd enjoy hearing from anyone who is interested.
>
>Bill
>
>------- End of Forwarded Message
>
>
>__________ Information from ESET NOD32
>Antivirus, version of virus signature database 3852 (20090213) __________
>
>The message was checked by ESET NOD32 Antivirus.
>
>http://www.eset.com
------- End of Forwarded Message
|
|
|
|
