GS Chandy
Posts:
7,218
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: Enrichment
Posted:
Aug 17, 2012 2:53 AM



Responding to Haim's post of Aug 17, 2012 7:54 AM (which is pasted for ready reference below my signature):
(Minor modification  transposition of desired results  has been made in 1st para): Remarkably enough (and highly improbable though it may appear at first glance), I do agree with much of the critiques by Robert Hansen and Haim of Peter Duveen's thoughts about "enrichment" of his student's math skills by taking him through some parts of calculus  while I still do maintain very strongly that a great deal can (and certainly should) be done to enhance that student's knowledge of math and THEREBY to enrich his "life in math".
There is no contradiction at all in this position of mine, as may be clear from the case recounted below:
(The underlying problem, I suspect, is that Duveen's concept of "enrichment" is profoundly flawed  impoverished, as a matter of fact. The suggestions below may help to "enrich"  but that will require some thought and serious work).
QUOTE Example of math learning using OPMS  Student Mission: "To understand thoroughly all aspects of my math syllabus  and THEREBY to improve, very significantly, my results in my math exams, tests and quizzes"
My Mission (as OPMS facilitator): "To help the student by demonstrating what to 'OPMSmodel' and how to do that" +++++ The subject for the OPMS application was a student who had never through his school career got above 45% in math, and now in college his results were far worse.
I worked with him for about 1 hour a day for a little over 30 days to help show him how to construct his needed models related to his Mission; how to interpret the models he was constructing; what to do next  at which point I had to leave Bangalore on a longterm assignment to Mumbai.
I left him with plenty of 'homework', in particular, with suggestions on how to interpret models he constructed and would be constructing; "what to do next" at each stage of development of his OPMS.
(The correct interpretation of models can be quite tricky; we also have to train ourselves quite intensively to systematically continue the ideageneration and modeling work  see section "Difficulties" in presentation attached).
The Internet wasn't available those days, so we more or less lost touch, till, about 8 months later, he wrote to me saying that he had systematically continued development of his OPMS for his Mission  and Lo! and Behold! he was now consistently getting over 75% in his math exams, tests and quizzes.
Two things should be emphasized:
i) I gave him NO MATH TUITION at all  there were 'elements' in his models that suggested he should seek help from his professors, peers and textbooks, etc, and he did just that;
ii) those days the OPMS software had not been developed, so he had the added burden  besides learning his mathdoing problems, etc  of having to develop his models as he went along. Without the OPMS s/w, this is quite a burdensome and extremely tiresome task  but he was able to do it.
(Actually, there is no "Lo! and Behold!" at all about his success with respect to his Mission. It is the simplest common sense: it simply has to happen (if there is a minimum amount of perseverance by the user)  or, the user (the student in this case) would have esily recognized that his Mission was inappropriate for him and he would have modified it).
UNQUOTE
(Here I must apologize in advance to Robert Hansen for the "boxes" that he despises, which are contained in a couple of the attached documents  sorry about that, I cannot help it at all, I'm afraid).
GSC (As always: "Still Shoveling Away!") Haim's post dated Aug 17, 2012 7:54 AM: > Peter Duveen Posted: Aug 16, 2012 6:23 PM > > >Bob, Chandry, this is what I am getting at. > > > >It seems to me that calculus is placed on a pedestal > as > >something unachievable by the masses. But looking at > it, > >I see a lot of material in the calculus that could > be > >approached by students on a sixth or seventh grade > >level. If they can graph a straight line and a > parabola, > >they are game for calculus, at least some calculus. > > No they are not. Teaching calculus to 6th and 7th > 7th graders would be like teaching a dog to dance, > http://youtu.be/Nc9xqTVyHI > > So, in this video the dog appears to enjoy the music > and to know how to dance. Michael Coren thinks this > is almost certainly impossible > http://www.amazon.com/HowDogsThinkWorldLooks/dp/07 > 43222334/ref=sr_1_1?ie=UTF8&qid=1345168269&sr=81&keyw > ords=how+dogs+think > > In other words, you can get the kids to go through > the motions (to some extent), but what you have > actually accomplished remains in considerable doubt. > > Why do I feel this way? Because that is what > hat actually goes on a lot of the time (maybe most of > the time) in college. That is the reason for the > Calculus Reform Movement. So, your hypothesis, > Peter, must be that you can more easily accomplish > with middle school kids than with college students. > This seems unlikely. > > The problem you are having, Peter, is what I have > ave called "Mathematician's Disease", > > http://mathforum.org/kb/message.jspa?messageID=7656422 > > Haim > Shovel ready? What shovel ready?
Haim posted Aug 17, 2012 7:54 AM: > Peter Duveen Posted: Aug 16, 2012 6:23 PM > > >Bob, Chandry, this is what I am getting at. > > > >It seems to me that calculus is placed on a pedestal > as > >something unachievable by the masses. But looking at > it, > >I see a lot of material in the calculus that could > be > >approached by students on a sixth or seventh grade > >level. If they can graph a straight line and a > parabola, > >they are game for calculus, at least some calculus. > > No they are not. Teaching calculus to 6th and 7th > 7th graders would be like teaching a dog to dance, > http://youtu.be/Nc9xqTVyHI > > So, in this video the dog appears to enjoy the music > and to know how to dance. Michael Coren thinks this > is almost certainly impossible > http://www.amazon.com/HowDogsThinkWorldLooks/dp/07 > 43222334/ref=sr_1_1?ie=UTF8&qid=1345168269&sr=81&keyw > ords=how+dogs+think > > In other words, you can get the kids to go through > the motions (to some extent), but what you have > actually accomplished remains in considerable doubt. > > Why do I feel this way? Because that is what > hat actually goes on a lot of the time (maybe most of > the time) in college. That is the reason for the > Calculus Reform Movement. So, your hypothesis, > Peter, must be that you can more easily accomplish > with middle school kids than with college students. > This seems unlikely. > > The problem you are having, Peter, is what I have > ave called "Mathematician's Disease", > > http://mathforum.org/kb/message.jspa?messageID=7656422 > > Haim > Shovel ready? What shovel ready?
Message was edited by: GS Chandy

