Robert Hansen posted Mar 25, 2012 11:09 AM (GSC's responses interspersed): > > On Mar 24, 2012, at 11:24 PM, GS Chandy wrote: > > > Robert Hansen posted Mar 24, 2012 9:08 PM (regret > delay in responding; was off Internet for a day or > so): > >> This (web site) is a very poor representation of > >> critical th inking. Critical thinking is first and > >> foremost about thinking and being correct in that > >> thinking. > >> > > "..being correct in that thinking" > > Could you clarify as to just how one becomes > "correct" in one's thinking"? I agree that being > correct in whatever thinking we do is important, but > just how does one ensure that one is "correct in that > thinking"? > > One succeeds in what they set out to accomplish. > IS THAT RIGHT?!!!
Go back to the Inquisition, for instance. Certainly many of the Inquisitors succeeded in what they set out to accomplish - at least in all the specific cases where through terror of torture and worse their victims confessed to whatever those Inquisitors wanted them to do. Even Galileo recanted, if I recall my Western history right. (Does that mean the Catholic Church succeeded in whatever it was that it set out to accomplish?)
We have much more recent examples: Adolf Hitler and his loathsome 3rd Reich certainly succeeded, for quite a while, in doing what he set out to accomplish. (It took many years for people to understand that the 'accomplishment' was entirely phony).
GW Bush 'flew a jet plane' onto the USS Abraham Lincoln and proudly announced: "MISSION ACCOMPLISHED!" (Again, it took quite a while - and the squandering of several TTTTTTTrillions of $$$$$ for people to realize that the 'accomplishment' was entirely phony).
Gandhi at least partially succeeded in moving his followers to push the British out of India - but his thinking was a meld of a good bit that was correct and even prophetic in many ways (from many points of view) and much that was ludicrously incorrect (from other points of view). Some of these points of view, both for and against Gandhi's ideas, have been developing lately - and the debate is still very much on).
I am trying to attach herewith a PowerPoint presentation that argues something quite different from what you claim. (If I do not succeed in doing this now, that does not mean that I have failed [or even that my thinking is incorrect] - only that my Internet connection was poor. I shall find myself an adequate Internet connection in due course and attach that file - but that will not mean that my thinking then is any better than it is now -- sorry to be facetious - I just wanted to make clear that your definition of what is "correct thinking" is utterly ludicrous). The 'argument' there is NOT based on your very superficial measure of "(success) in what they set out to accomplish".
The very argument that you have put up above smacks of very poor "critical thinking". > > > -- one can very easily (and quickly) infer > incorrectly. It happens all the time. I've seen it > happen all too often right here at Math-teach - often > enough by you. > > Give me some examples. > The best example I have is based on your and Haim's ludicrous argument that "OPMS is just list-making and nothing else!"
Could there be anything to illustrate a total failure of "critical thinking"? I believe not. > > > -- "attention to detail" when carried to needless > extremes can often lead to the phenomenon of "missing > the forest for the trees" - this too happens, all too > often, and it happens right here, at Math-teach. > > That is called obsessing over details, which is > something else. > True enough. I accept. > >Attention to detail has to do with > the ability to recognize the significant details. > Yes. But all too often, right here at Math-Teach, I find a whole number of people - both from your side and from the side of your opponents in your various arguments - obsessing over details which do not really carry the argument forward. (This largely happens because both sides are using 'pure prose' for their arguments - which is a very poor of enabling people to understand each other's arguments. To get over this utterly foolish 'running aroundthe mulberry bush', I strongly recommend 'prose + structural graphics' (p+sg). There is some information about p+sg in the presentation I want to upload. > > > I would tend to agree with you if you were to claim > that the traits listed (Intellectual Humility; > Intellectual Courage; Intellectual Empathy; > Intellectual Integrity; Intellectual Perseverance; > Faith In Reason; Fairmindedness) are by no means > "sufficient" to ensure "correctness in thinking", but > I must most strongly disagree with your claim that > they are "counterproductive to thinking". Just how > have you been able to infer that? On what grounds? > Please specify. (I have drawn the attention to the > e people at the "Critical Thinking" website to this > opinion of mine). > > > What then is it about? (I personally don't see it > as being anywhere near what I would feel is even > 'satisfactory' [view ensuring effective "critical > thinking"] - and I have drawn the attention of the > website to this opinion of mine). But just what is > the site about other than "critical thinking"??!! I > believe you are grossly wrong here. > > The web site is exactly how people lacking critical > thinking skills view critical thinking. They think it > is a formula. > That is a ludicrous statement from you, I'm afraid, demonstrating very poor "critical thinking".
The website does NOT - to my best understanding - view "critical thinking as a formula" as you seem to be claiming above. I agree that they have not adequately put together their case - but your definition of "correct thinking" (attention to detail; ability to quickly infer; robust memory) and also as you are here arguing it, is rather weaker than theirs. That you are unable to recognize this is more evidence of a failure in critical thinking on your part. > >I was in a meeting at NASA awhile back > and we were discussing a problem and I having had > much experience with the problem threw out a > solution. One of the (seriously not too bright) > managers in the meeting said "Let's slow down, we are > all smart people here, let's discuss the > alternatives." There were no alternatives. He no > longer works there. This site reminds me of him. > Things people say when they lack the required > ability. > So - what ability have you been showing in your argument that "OPMS is list-making and nothing else"???
[In case I am not successful in uploading the document I want to put up here, check out any of the documentation about the OPMS that have been attached to a whole number of postings of mine here at this very Forum to understand just how ludicrous that argument of yours is - and you carried it on over a couple of years! (And, for all I know, you are still carrying it on - when it is clear to any high-school student that OPMS is very much more than "vacuous list-making"!)]. > > >> > >> For example, when someone excels at critical > thinking > >> they dispel other's opinions quickly when they are > >> wrong, not because they are not open minded but > >> because they are simply that fast and that > >> experienced in critical thinking. This is the > indeed > >> the goal of critical thinking, to become good at > it, > >> and this site doesn't even recognize that. > >> > > > Please see and adequately understand the model > attached and then do consider rethinking the above. > > I am quite successful with what I wrote above. > Nothing you have offered here indicates that a > rethinking is necessary. Your model is a formula and > a formula can't model what isn't a formula. > My model is NOT a formula. (You may ask anyone who knows what a "formula" is and what a "model" is. Kindly do become aware of what that model means. )The fact that you can claim that model is a "formula" is an excellent illustration of a failure of "critical thinking" on your part). > > >> > >> To put it simply, the goal of critical thinking is > to > >> be right. The goal of critical thinking is not to > >> mimic critical thinking as this site and its goofy > >> elements pretend to do. The same can be said for > many > >> fraudulent curriculums. > >> > > > See above. (Though I do agree with your thoughts > about the many fraudulent curricula we see around). > > Here is my thinking on this GS... > > Math, music, critical thinking, and many other > abilities are artful processes that require talent. > Things that require talent are not rote, are not > procedural and are not formulaic. > Things that are not rote, procedural or formulaic > cannot be reduced to a list. > Q.E.D. > There you are! Back again to your "reduced to a list"!!!
See any of the OPMS documents and check out if there is ANYTHING in ANY of them that says the reality can be "reduced to a list". (It does claim that some aspects of reality can be "represented by a model" - which is a horse of a different color though you seem to be color blind to the different color that the horse is). > Note... > > This proof does not require us to determine who has > talent or not, only agreement that those things > listed (i,e, Math, Music and Thinking) require it. > > This proof does not depend on whatever process you > claim to be using, only that the result is a list (a > graph counts). > > Any site that claims to be teaching math, music or > thinking by modeling is a FRAUD. You can't teach > artful things that way. I don't think you can teach > artful things at all, you can only coach them. But > cheer up, education does not seem to have a > definition for fraud. If you had a leaky roof and > paid me to fix it and it continued to leak, that > would be fraud. Either I return the money you paid me > or we end up in small claims court. Go to college and > fail to get a degree or get a degree of such poor > quality that you cannot find gainful employment and > that is not fraud. The biggest problem I see in > education today is fraud. It is rampant. > Kindly do carefully note (and DO NOT DISTORT!): I am NOT claiming that one will "learn math through modeling". (That is YOUR misstatement and no one else's!)
One learns math through doing needed problems on specific topics, theorems, lemmas and so on (as you have rightly noted elsewhere). The models could help identify what the things to do that could "contribute to" progress at various stages of the journey. (Some of those things do include things like "Doing enough problems till I am sure I can apply the principle with confidence" and so on).
The ONLY math student I ever had (using OPMS) took up the Mission "To understand thoroughly all topics of my math syllabus and THEREBY to do well in my exams, tests and quizzes".
The first trigger question I asked him was: "What, in your opinion, are the THINGS TO DO to accomplish your Mission?" He wrote his ideas down and then modeled them to discover how they may have "contributed to" each other and to the Mission.
Over a period of 7-8 months he continued developed his models of his current ideas on various math issues and problems he was facing - and, over time, he succeeded rather brilliantly: from never EVER having gotten above 45% in any math exam or test right through his school career, he went to getting regularly above 75% in all his math exams in college!
In particular, I was extremely punctilious about giving him NO MATH TUITION at all [though I could have done that more easily than the route I chose - which was more difficult for both him and for me, but which turned out to be truly effective]. When he asked me for such help, I helped him identify just what the thing was that he needed to do to get that specific help he needed.
There developed elements in his models telling him things like the following: "To get needed help from my math professors/lecturers..."; "To get needed help from my peers who are good at math..."; and so on. (Yes, initially I did have to stimulate him to write such things down and model them - it was quite painful to begin with, both for him and for me).
The thing was, he had to work out for himself just what it was that he needed to do at each stage of his journey - and then work out just what he had to do to get to each point that he wanted to reach next.
Yes, there did develop elements like: "To understand Maclaurin's Theorem"; "To understand the use of Maclaurin's Theorem" - which he resolved by working on elements like "To do plenty of problems on Taylor's Series, Maclaurin's Theorem" (and the like). I recall that, on occasion, he went into fair detail into such elements also - specifically to help him identify exactly what were his weaknesses topicwise, where his understanding was poor, and so on.
I understand from one of my contacts that there are a couple of college students who wish to improve their skills in math (through use of OPMS) - I shall probably be meeting them by mid-April. Let's see what develops then. Now, of course, things are very different from when I took that student of mine: those days there was no Internet; no OPMS software to help with the modeling, and so on. These new students will have it all very much easier. That student had to spend about 1 hour each day doing his OPMS modeling - these students will need to spend no more than 10 minutes or so.
Whatever: if it's OK by them (and by the Moderator here), I may put up some of the elements and the models that they create for themselves.
(Sorry - my Internet connection is far too slow to upload the file I wanted to put up: that will have to wait till I get to faster connection). GSC