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Re: Reply to Pragmatic
Posted by Rich/CA/Math on 4/24/08

    On 4/24/08, Howard Rosenbaum wrote:
    > On 4/21/08, Pragmatic wrote:
    >
    >> You got a MASTER'S in math and never had this stuff?
    >
    > 1. When I studied Linear Algebra, I took what seemed like a very theoretical
    > course. There were no pictures in the textbook, and no application to geometry.
    > Perhaps this is the kind of course Lawrence also took.
    >
    > 2. I for one am not qualified to state unequivocally what every Linear Algebra
    > course contains. Perhaps Pragmatic feels he is so qualified.
    >
    >> Was it a masters in education with a math specialization that didn't require
    > you to know any advanced math?
    >
    > 3. Here it seems Pragmatic is making an assumption about Lawrence's educational
    > credentials. Based on Lawrence's reply, it is an incorrect assumption. This
    > reminds me of students who assume from the diagram that a particular angle is a
    > right angle, without having adequate proof of this.
    >
    > I think this is a valuable lesson. One of the things we teach in math is the
    > need to clearly state one's assumptions, and to recognize that an argument
    > becomes invalid when it rests on an invalid assumption. Thank you, Pragmatic,
    > for reminding us this.

    Another assumption we need to question is that someone is what they represent
    themselves to be on an anonymous discussion board.

    One of the technology standards in CA is teaching students how to assess
    credibility of information found online. Key factors are who says something and
    how is it supported.

    Lawrence_NJ and Howard Rosenbaum seem to be new to the board, having no other
    presence going back to February, while Pragmatic is a regular (and valuable, IMO)
    contributor. Maybe Lawrence and Howard are just what they say they are. But the
    fact is that we don't know and, as I'll show, their substantive claims are suspct.

    And let's bear in mind that this is an anonymous message board and anyone can
    claim anything they want. Maybe Lawrence and Howard are just what they say they
    are. But the fact is that we don't know and, as I'll show, their substantive
    claims are suspect. Personally I find it very hard to believe that a person with
    a Masters in Math could possibly encounter anything new to them on a Middle School
    Praxis test.

    I have found it very hard to find any description of Linear Algebra that does not
    include the concept of linear transformations. Anyone can do a google search for
    themselves on linear algebra and see for themself. And linear transformations are
    not some peripheral aspect of linear algebra they are central to the whole notion
    of linear algebra, again as anyone can see by doing a simple search.

    The Wofram site, one of the most respected and authoritative sites on the web
    defines linear algebra as "the study of linear sets of equations and their
    transformation properties."

    But even more telling is that linear transformations are on the curriculum of most
    algebra 2 and pre-calculus HS courses. Not to mention Pre-Algebra. For reference
    I point to pages 428-431 of the McDougall Littel book called Mathematics: Concepts
    and Skills, Course 2, which is based on the CA 7th grade standards. This is the
    material that we are to believe that a Masters in Math has never seen before.
    (The index of the book has no entry for Black-Scholes.)

    One need not have been a math major, let alone have a Masters, to have encountered
    the notion of linear transformations.

    So I think the essential point that Pragmatic was making, that it is not credible
    to claim that there is material on the Middle School exam that a person with a
    Masters in Math would never have seen, is correct. Or at least that linear
    transformations is not a credible example of such material.


 
 
 
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