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View Diary: A Blue-Collar Girl in a White-Collar World (105 comments)

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  •  As a big math person myself, I agree... (2+ / 0-)
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    FloridaSNMOM, Alden

    The best math classes I had were the ones where I spent all my time at the chalk board explaining my problem solutions and proofs.  I liked the algorithmic and logical sequences of math proofs, it really resonated with me.

    My degree was in computer science, but could easily have gone the direction of electrical engineering.  But with the EE degree in Los Angeles in the 1980s I would have ended up working in Aerospace probably building weapon systems.  So I went the computer science route and the more high paying jobs were in business systems, which appealed to my interest in systems theory.

    So I was a math geek, but my own kids clearly are not.  They should be able to pursue their own different passions.

    Cooper Zale Los Angeles http://www.leftyparent.com

    by leftyparent on Sat Aug 25, 2012 at 09:13:58 PM PDT

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    •  However... (2+ / 0-)
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      reconnected, angelajean

      In 35 years of applied computer science, most of it spent at an advanced level creating tools used by other programmers, I can recall only a single occasion when I called on any non-trivial math of the type required so extensively in my CS curriculum.  

      That was when I needed to transform the output of a random number generator from its uniform distribution into a normal distribution.  Alas such a transformation was not among any of the map theory or calculus or even statistics that had been rammed down our throats.  Instead I looked it up in a handbook of engineering formulae.  Granted, I might have had some difficulty finding and understanding it without at least some of my college-era math studies.

      Additionally the math/science-track math courses (not the simplified ones for liberal arts majors) focused so intently on computational and derivational details that they largely obscured the grand concepts and their beauty, which began to emerge for me only later in life in a more recreational context.  

      I've sometimes wondered if the difference in American and European student performance in math, and the absence in many European countries of the boy/girl divide in outcomes we see in America, might be a result of the way we jump straight into heavy computation and manipulation of formulae with insufficient focus on the abstract concepts and their intuitive applications in the real world.

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      Ideology is when you know the answers before you know the questions.
      It is what grows into empty spaces where intelligence has died.

      by Alden on Sun Aug 26, 2012 at 09:27:25 AM PDT

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      •  Difference skills (3+ / 0-)
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        reconnected, angelajean, melo

        In fact, in teaching programming courses to people from various backgrounds over the years, I've come to the conclusion that math and the kind of sequential logic and visualization used by programmers must be not only separate skills, but perhaps different ways of looking at the world or different types of intelligence.

        I found that many (not all) mathematicians in my classes had trouble with the sequentiality of programming.  They expected a certain relationship to simply BE true, it seemed at times -- something they could assert by knowing it is so --  without going through intermediate steps to make it beCOME true.

        That's not easy to reconcile with the notion of a mathematical proof, which is indeed sequential, and yet I saw this sort of difficulty recur over and over again in students coming from a primarily mathematical background.

        One of the most promising backgrounds seemed to be music.  I have only an intuitive notion of why that might be so, and it has to do with music as an unfolding process, a cyclic, iterative process, in which certain "things" (events, alterations, whatever) are stored (or occur) at certain "locations" along the way.

        Math and music both require visualizing and remembering complex, abstract structures, but there must be a difference in the way they are processed in the brain.

        There is also a certain arbitrariness to music or a computer algorithm.  Unlike how it is in math, there is no single inherent truth to uncover and represent.  Rather there is an arbitrary path to create in order to achieive a certain desired impression, effect, our outcome.  There are few points of reference along the way that an tell you if you are 'right' or 'wrong'.  You're right if the outcome in the end is what you were looking for.

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        Ideology is when you know the answers before you know the questions.
        It is what grows into empty spaces where intelligence has died.

        by Alden on Sun Aug 26, 2012 at 09:46:04 AM PDT

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        •  Abstract math is such a conundrum... (2+ / 0-)
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          Alden, angelajean

          when it comes to education and requiring all kids in high school to take several years of it.  That abstract math requirement (rather than an option) is what seems to make school problematic and unpalatable for a lot of kids, including both my son and daughter.  It really struck me when I saw it in them, since I had always been a "math geek" myself.

          How do we design an education system that identifies the students with an aptitude for abstract math and get enough of them to pursue it as a career to staff the needed job slots requiring this skill set? An how do we do that while not inflicting all this abstract math on the rest of the kids who just do not think that way and are debilitated by being forced to embrace these abstract methodologies.

          Certainly concrete arithmetic is important for most everybody - budgeting, accounting, etc.  But requiring that all kids have three years of abstract math to graduate high school is an awful imposition on minds that don't readily think that way.

          I think right there in abstract being a big part of the teach-to-the-tests high-stakes standards we are destroying the public school system as a viable institution to actually help all kids with their development.

          Cooper Zale Los Angeles http://www.leftyparent.com

          by leftyparent on Sun Aug 26, 2012 at 11:11:32 AM PDT

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          •  Abstract is a misnomer (2+ / 0-)
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            angelajean, Alden

            for, at least, secondary math education.  Arithmetic, basic algebra, basic geometry, basic trigonometry ... what concepts could be more concrete?  These are the basic tools that move our everyday technology from the realm of dark mysticism to the realm of bright possibility.

            Put another way, mathematics is one of humanity's greatest achievements, and it is all the greater because it developed across boundaries of culture, gender, race and history.  Why do we take for granted that children are enriched through exposure to the subtleties of Shakespeare but not the beautiful infinities of calculus?

            The only rule of freedom is not to destroy freedom.

            by fuzzywolf on Sun Aug 26, 2012 at 02:54:42 PM PDT

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            •  IMO good drama resonates more broadly... (1+ / 0-)
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              Alden

              Because it is about the range of human interactions, and most everybody is invested in that and can get some inspiration for leading their own lives.  I think a significant percentage of people just don't resonate with the numbers that lie under the biology and physics of our lives.  It's hard to give them context.

              Neither of my kids were at all interested in algebra, geometry and trig.  Many other young people I interact with are not either.  Others are.

              IMO it is a way of abstracting the real world that resonates with some but not with others.

              Cooper Zale Los Angeles http://www.leftyparent.com

              by leftyparent on Sun Aug 26, 2012 at 05:46:08 PM PDT

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              •  I don't resonate with numbers, but... (1+ / 0-)
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                leftyparent
                a significant percentage of people just don't resonate with the numbers
                I don't resonate with numbers but I resonate all the more with abstract concepts and sometimes with the curves that represent them.

                Internalizing the symbolism that represents these concepts has always been difficult for me, just as the sounds of Ancient Greek never leapt off the page at me the way the sounds of something in a Latin alphabet do.

                The swoops and swings and tapers of nature are particularly interesting and I find them in the rhythm and dynamics of music as well.  But I would be in baby steps at telling you how to codify and parameterize them mathematically.

                I did acquire (recreationally) some new physics/mathematics terminology two weeks ago, relating to the higher-order derivatives of position:  In addition to velocity and the change in velocity called acceleration, there are changes to the changes (higher order derivatives) known as jerk and then jounce and thereafter, in the words of some wags, snap, crackle, and pop.

                Whether there is anything in all of this to inform the mathematical education of future generations, I do not know.  But math seems to be taught with a bottom-up approach.  Maybe some kind of top-down approach that starts with the concepts would work better for some of us.

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                Ideology is when you know the answers before you know the questions.
                It is what grows into empty spaces where intelligence has died.

                by Alden on Sun Aug 26, 2012 at 09:54:46 PM PDT

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                •  I think more context for math instruction... (1+ / 0-)
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                  Alden

                  would be very helpful.  That said I still think abstract math should not be a high-stakes requirement for all our youth.

                  Cooper Zale Los Angeles http://www.leftyparent.com

                  by leftyparent on Mon Aug 27, 2012 at 08:24:32 AM PDT

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                  •  abstract math includes . . . (1+ / 0-)
                    Recommended by:
                    Alden

                    abstract algebra, number theory, complex analysis, topology and a dozen other fields that 96% of people have never heard of.

                    What students learn in high school is more properly called concrete math.

                    The only rule of freedom is not to destroy freedom.

                    by fuzzywolf on Mon Aug 27, 2012 at 09:14:04 AM PDT

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