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Re: Saxon ad
Posted:
Feb 26, 1995 10:18 PM
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Andrei, thanks for the responses--Hope my were taken in the spirit in which
they were intended...
On sunday, Feb 26, Andrei Toom wrote:
>On Sun, 26 Feb 1995, Tim Hendrix wrote:
>
>> The written document expressing the Standards that NCTM endorses certainly
>> does include some problems and examples of each standard.
>
>I suggest that these problems and examples are poorly chosen.
>And that this is extremely important. After all, ideas evaporate,
>examples condence.
--->I agree that some of the problems and examples are poorly chosen. Not
everyone is an expert on everything. For example, I believe that the
Standard at the 9-12 level of Reasoning <Power> is not explained well nor
well-demonstrated. The hint that formal proof is not desirable...I still
think that it is a viable goal and is needed. However, the standards do
not adequately express what *IS* desirable in meeting this goal of
reasoning power.
I am not sure that the Addenda series has quite met this daunting challenge
or if they could in such a document. However, I still support the standard
and am capable of developing the parameters myself...
>
>> At each grade
>> level, after the statement of each standard, the writers attempt to
>> "unpack" the idea behind that standard and demonstrate one example of how
>> that standard can be employed in a classroom at that grade level.
>>
>> It is absurd to think that the authors are going to give an example
>> of every single type of problem application of any one standard.
>
>It would be useful.
--->No...it is an infinite task and could not be done...I don't want to
limit the creativity and ingenuity of my own brain by having everything
addressed for me...
>
>> That is left for mathematicians and mathematics educators
>> to do on their own.
>
>Do you think that an average teacher has time and competence to do it ?
---> Time? Who does? Those who are serious about their profession will
find time...Competence? I don't know--because I don't every high school
teacher...but I know that students who enter & leave my classroom are able
mathematically to explore many of these areas...It's high time that we
dropped the old adage about the lack of mathematical ability of math
teachers...It's like a bad student...if we ignore them, maybe they will
leave the field of play...Instead, let's concentrate on modelling teachers
who are competent--both matheamtically and educationally.
>
>> I agree, however, that there are topics not covered as
>> thoroughly in the document as could have been covered.
>
>Could or should ?
>Are there topics that are covered adequately ?
--->Adequately enough that most teachers can decipher the intent and the
content of such a standard.
>
>> For example, the standard PMG used from K-4 of calculators and computers.
>
>You mean that PMG chose a wrong example. Which is the right one ?
--->No...I meant that which follows...the Standards higlight technology at
the K-4 level, but they don't adequtely address how it is to be
incorporated at the other levels. We need impetus to show us how to use
technology not only for making life easier...but also to expose the
mathematics more clearly...Why are graphing calculators more useful in
introducing parabolas than a no-technology approach? Is faster better or
more intuitive? Rather than speed, the reason that I use them is that
students seem to understand better the amplitude, magnification, and the
phase shift hidden in the standard form of the parabola more clearly.
>
>> Unfortunately, at the other levels, 5-8, and 9-12, the use of
>> technology as a means of exposing the mathematics is not addressed
>> very concretely. Yet, the document was 5 years ago, and now we
>> know of many examples that were not fully developed then.
>
>Was there the stone age 5 years ago ?
>Do you mean that the document is obsolete ?
--->It is not obsolete...it is still quite reflective of our goals, but if
the document endeavored to present every application of the standards to
practice, with an example of every type, it would have been obsolete before
it would have been completed!!! For example, the technology of graphics
calculators, software (such as Geometric Supposer and Sketchpad), etc. have
been around this long...but there have been so many new interpretations of
how to employ technology...e.g., Texas Instruments'
Calculator(Computer)-Based Laboratory attachments, the growing use of the
Internet and the many mathematics projects found on the internet, etc.
Hope that I have addressed many of your concerns or questions...If not,
please feel free to respond.
Tim Hendrix
*****************************************************
Tim Hendrix (hendrix@uxa.cso.uiuc.edu) *
Division of Mathematics Education *
Department of Curriculum & Instruction *
University of Illinois *
*****************************************************
382 Education Building *
1310 South 6th Street *
Champaign, Il 61820 *
*****************************************************
(217) 333-3643 *
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