lajones posted Oct 20, 2012 7:36 AM (GSC's remarks follow): > Beautiful... and exactly on point! > > "We should demand to hear the pros and cons of every > argument when it comes to our children's math > curriculum. The distracting buzz of irrelevancies > like "pickaninnies" points to a failure in logic that > has no place in a discussion about math, of all > things." > > I believe that the general public would demand the > same now (10 YEARS LATER!) if they were aware of the > problems with mathed "research" cited repeatedly in > support of K-12 math programs. > (I presume you are writing about the .pdf document linked by MPG. I'm afraid that it is loading very, VERY slowly at my end, so I may not be able to see it for quite some time - finally, I've not yet managed to see that document, even though I finished this message quite some time ago).
Anyhow: It's entirely true, Mr Jones, that the general public should get to understand, in adequate detail, the pros and the cons of every argument to decide on math issues (or, for that matter, on any other issues [in any democracy]).
The underlying problem is that, using the conventional form of debate on any complex issue, this is almost impossible. It rarely ever happens in real life that we actually get to understand these pros and cons: it doesn't matter whether the issue is a school curriculum to nuclear disarmament. In almost every case, the decisions are made by some 'empowered people', with those who empowered them following because those empowered people saying it's so. It turns out, most of the time, that the empowered people themselves don't properly understand the basis of the decisions they take, the actions they get others to perform!
Citizens of ostensible democracies (like the USA, or India, or wherever...) like to believe that decisions are taken by the 'empowered people' with full consent and knowledge of issues involved - but this is not so at all. Witness the number of wrong, and indeed even foolish, decisions taken and actions performed that, on later examination, turned out to be entirely contrary to common sense. In the US, you have your Vietnam (and probably many other 'happenings'), some of them current; we in India have a whole lot of such matters - some of them are current. But it's not ONLY Vietnam on which wrong decisions were made; it's there in practically every walk of life, right down to the school curriculum!
It's NOT the fault of our leaders: the underlying profound fact of life - not realized by most of us - is that, using the conventional 'prose mode' of debate (and thinking), it's almost impossible to arrive at a reasonably commonsense view of events and situations: in most areas of life we have whole tangles of horrendous messes - and most of them we don't even begin to realize! A great deal of what goes on in society (from international relations to national economics to school curricula - defy commonsense (though we like to believe everything is tickety-boo and hunky-dory). This is not true at all, as an informed glance at the headlines any day will tell you.
The late John N. Warfield (JNW) devised a way of looking at the world that enables us quite clearly to see how actions performed day to day may "CONTRIBUTE TO" each other and to things that happen in the course of events. This he did by developing (systems modeling) tools that enable people to see clearly, by way of simple graphical models showing relationships, the contributions of ideas and actions on each other via graphical models. More information about Warfield's developments is available at http://www.jnwarfield.com and from the "John N. Warfield Collection" held at the library of George Mason University, Fairfax, VA (where Warfield was Emeritus Professor). (For information about the JNW Collection see http://ead.lib.virginia.edu/vivaxtf/view?docId=gmu/vifgm00008.xml;query=;). Warfield developed a scientific process that led to practical means to allow us to see and understand 'systems' as they never have been understood before.
I've developed an integrative aid to problem solving and decision making based on Warfield's seminal contributions to systems science; this tool is called the 'One Page Management System' (OPMS). In brief, the OPMS enables anyone, at any level, to apply the sophisticated concepts of systems science to any issues of interest. The OPMS can help teachers and parents (and others involved (INCLUDING students who've reached a degree of maturity) to understand clearly 'the pros and the cons' of issues (including issues related to math teaching AND learning) from models they develop themselves. More information about the OPMS is available at the attahment to my initial message at the thread "On realistic and practical tools for the US education system..." (http://mathforum.org/kb/thread.jspa?threadID=2405705).
I have in other posts described how a freshman college student, extremely poor at math right through his school career, very successfully worked on the ambitious Mission "To understand thoroughly all topics of my math syllabus and THEREBY to improve, very significantly, my results in my math exams, tests, quizzes". The remarkable thing about this Mission is that I gave him no math tuition at all - he got whatever he needed from his teachers and his peers in college who were good at math.
I know nothing about the new (or old) K-12 math ed programs; nor do I know a great deal about the 'Math Wars' (except that they were in fact entirely unnecessary [I suspect]: on examination, it turns out that those wars were (and still are, as they are still ongoing) somewhat like the Lilliputians going to war to decide from which end an egg should be broken: the only issue in math is "to enable the student to learn it to a level that he/she will need in life".
Apparently the 'new math' ways are not working. Well, neither are/were the conventional math training methods: via the 'traditionalist way of teaching math', most students come out of high school (in India as much as in the USA) fearing/loathing math. In the US, as it is in India, it's apparently the accepted thing to say, "I'm terrible at math!" Most such issues can be quite easily resolved using practical means to show us just how the things students are taught from day to day MAY CONTRIBUTE to the goal of learning the math (and other things). The only important issue is to develop children and young people so that they would become responsible and hopefully productive citizens. Of course, the definition of what exactly constitutes 'productivity in society' (and even the issue of why should we be 'productive') is very much up in the air today