Robert Hansen (RH) posted Jun 15, 2014 6:09 AM (http://mathforum.org/kb/message.jspa?messageID=9486842) > > On Jun 14, 2014, at 12:26 AM, GS Chandy > <email@example.com> wrote: > > > (GSC): I don't believe ANY subject or discipline > > under the > > sun has ever developed "coherently". While a subject > > or discipline is in its 'formative stages', the > > discipline itself as well as the methods of imparting > > knowledge about it are necessarily 'incoherent'. > > (RH): Well, that goes against the observations of actual > children learning arithmetic. The ones that excel > *get* the coherence quite early. > If on occasion, RH, you'd do yourself the favour of reading AND understanding what you have read, I believe our conversations might even become somewhat fruitful, notwithstanding the very different ideological stances you and I are 'coming from'.
In this particular instance, please observe that nowhere in the paragraph you have quoted, which you've totally misunderstood, have I said anything about "children learning arithmetic" (as a coherent discipline), or about 'children that excel *getting* the coherence', etc, etc.
DO PLEASE kindly note that, in both the fairly simple sentences in that paragraph you've totally misunderstood, it is entirely clear that I was talking about 'a subject in its formative years' not being 'coherent'. I reiterate that.
Arithmetic is, as you well know, NOT in its 'formative years' at all.
Do please note that elsewhere in that misunderstood post I had clearly accepted that arithmetic as a discipline is, in my opinion, definitely coherent - and (I believe implicitly) that it might well serve as the 'core' that Liping Ma had written about.
I had claimed that Liping Ma had made her case very incoherently. Also that Mark Saul had not demonstrated any way to proceed on the one sound suggestion he had made - I had suggested that there are practical means to discuss such issues clearly and coherently.
I repeat: +++++ - -- 'Arithmetic' as a discipline IS definitely most coherent (IMHO, and in the opinion of practically everyone around). [I am not sure about Mark Saul's views on the 'coherence of arithmetic', but I gather that he questions its value as a 'core subject' which is what Liping Ma seems to be suggesting (most incoherently, as suggested by me earlier);
- -- There are (I claim) serious doubts about the coherence of the entirely different discipline of 'imparting knowledge about math' (and about arithmetic, for that matter, in particular).
I had stated elsewhere that much of the difficulty appears to be rooted in the insistence of the 'system' to treat 'teaching' as, more or less, a 'thing-in-itself' and not as a member of the dyad of 'learning + teaching'. In order to handle the 'system issues' that develop when one wishes to discuss dyads and suchlike, we require a minor extension of our conventional prose, which I call 'prose + structural graphics' (p+sg) [which you prefer to call 'ps&g'].
Mark Saul in his rejoinder to Liping Ma, had one useful suggestion, namely to 'synthesize' positive aspects of the Chinese system of elementary education and those of the US system. He did not, alas, suggest any practical means whereby such 'synthesis' could be achieved. (&&See NOTES below) +++++ && NOTES: 1. In another post, I had suggested that the US system may have a couple of good things going for it, namely that US society has structured itself over centuries to permit more or less free expression of 'stakeholder concerns'. This could be very useful indeed, if US citizens knew just HOW to take such stakeholder ideas into *effective*, *working* consideration in what they do. That knowledge is, unfortunately, not widely available.
2. Chinese society has for long operated more on a 'command-and-perform' mode, which is not the best option in any democracy. I'm of course not suggesting that China is about to shift to a 'democratic system' (not even to a 'nominally democratic' system such as the US enjoys today).
To revert to 'coherence':
Indeed, I claim there are serious doubts about the coherence in the educational system as a whole about how knowledge is imparted to learners about ANY subject or discipline.
The incoherence I had written about was relating to the way that knowledge about math is imparted to learners.
I do not deny your suggestion that "(the children) that excel *get* the coherence quite early".
Unfortunately, the children that excel in math are the exception; most students graduating from school ACTUALLY 'fear and loathe' math. This is the case in the India, I know; I believe this is the case in the USA as well.
The seeds for this fear and loathing are in fact planted very early in the learner's mind.
I have glanced through the rest of your post. It is clear that it is entirely based on your misunderstanding of what I had written. It's a response to some ideas of your very own, arising from a complete misundderstanding of the case I was making.
I observe you have stated: "Suppose you are selling OPMS like crazy, yet the results people are getting are no better than before. Worse even". As those are some ideas of yours arising from your initial non-understanding of what I had written, they make no sense at all. So I refrain from commenting further. If you have something to say on which you want me to comment, I'd suggest you try writing something coherent, for a change.
You might well consider taking some of your own advice to look at some (American) English and (English) English poetry to help improve matters.
Added: The rest of your LONG message, responding to what you had utterly misunderstood, follows:
GSC > > I am pretty sure > that Joe is using the term *coherence* to mean a > logical consistency in the subject. I remember a girl > in my son?s kindergarten class that got the > coherence, the method to the madness, in addition > quite early. She was adding 2 digit numbers like a > 3rd grader. Unfortunately, nothing came of this gift > (she is still in my son?s classes) because the > curriculum isn?t coherent, which I will explain > shortly. > > You can easily tell when a text book is working from > a pedagogy of coherence. For example, the really old > text books, 100 years or so old, go - One plus one is > two, one plus two is three, and so on. They rely > almost entirely on coherence and progress steadily > through it. The newer-older textbooks, 30 to 50 years > ago, retain that thread of coherence but also added > more visceral relevance. Here are two apples, and > here is another apple, now we have three apples. I > think these offer a better balance than the much > older books, but we can suppose that teachers 100 > years ago added visceral relevance to their lesson > plans when they desired. And I am using extreme > examples to make a point, there are examples of > visceral relevance in text books 100 years ago, > though certainly, as printing technology advanced, > the examples in textbooks became much better in later > years. Another later development was spiraling. > > The newest textbooks however have broken the subject > into a collection of distinct topics which are no > longer coherent. One week you are doing fractions and > the next week you are doing integer subtraction. > There is no continuity and without continuity it is > impossible to have coherence. It is what I was > harping about in third and fourth grade, and that Joe > captured in the word *coherence*. I stopped harping > because I gave up on the school?s version awhile back > and have shifted to more at home work to give back > the coherence the subject deserves. > > The way this came about is complex and I can?t > describe all that I have uncovered in the last 10 > years in one post, but as more students attended > school and took more classes in these subjects, more > of them were not getting it, and the drift starts > there. Education became very political and > pedagogical theories that explained away differences > became more popular than those that took them into > account. A theory that promises that all students are > good at math is acceptable and one that promises that > only some are good at math is not. Even if some means > a bright little girl in kindergarten. Talk about > getting shafted twice. 50 years ago when some were > allowed to be good at math, the little girl was not. > Now she is not again because no one is allowed. And > then there is the issue of money. Suppose you are > selling OPMS like crazy, yet the results people are > getting are no better than before. Worse even. Would > that stop you from selling OPMS? Of course not. The > only thing that sto! > ps anyone from selling anything is when people stop > buying it. That is what an economy is. People selling > things and people buying things. Colleges, schools, > teachers and politicians will not stop doing any of > this as long as it is economically viable, to > themselves I mean, not to the parents or the students > or the nation for that matter. Sure, bottled water is > stupid, but as long as there is a market, why stop > selling bottled water? The first rule of business, > give the customer what they want, period. > > But back to the topic of textbooks and pedagogy. Due > to political pressures of equality and > accountability, education was transformed from an > exercise in coherence to an exercise in remediation. > In the past, pedagogy and testing were quite > separate. How you taught the subject was based on how > the subject naturally flowed (coherence) and tests > were only used to gauge how well the student did. > Students not doing well could try harder or could try > something else. Something else that they were > possibly good at. For political reasons, this all > changed. It was politically unacceptable that some > kids were good at math and some not, especially when > the issue of color or sex was involved. The new edict > was that all kids are good at math and it is up to > the schools to make that so and if they couldn?t make > it so then it was the schools' and the teachers? > fault. The schools in response had to refactor the > curriculums and the tests. Even if they thought this > was all hogwash, the custome! > r is always right, period. > > The refactoring started in earnest in the 1980?s. > Gone right away was coherence. How can you continue > to teach a subject as it naturally flows if only the > students with innate abilities get it that way and > your edict is that everyone gets it? How do you > identify and remediate student failure in that model? > Coherence had to be replaced with something tangible > and it was replaced with conceptual pedagogy. Since > all students weren?t getting the topic naturally, as > it flows, and since the notion of *naturally* itself > was no longer even allowed politically, the > educationalists changed the subject from a flowing > and coherent exercise into a non-flowing and > explainable exercise. Focusing on concepts is > different from the visceral relevance I mentioned > earlier. Visceral relevance offers tangible examples > of the coherence while conceptual pedagogy offers > tangible examples in place of coherence. For example, > a coherent student refers to the example of two > apples and one apple as a tan! > gible example of what they already know and feel > inside, that 2 + 1 is 3. A conceptual student on the > other hand looks to the example of two apples and one > apple to to know anything at all. It isn?t a visceral > example of something they already know, it is in fact > all they know. It is a substitute for coherence. > > Also, another factor that I won?t belabor has to do > with weaknesses with tests and very low cutoff > scores. > > I don?t rely on our system of education anymore and > it seems that is true for most affluent parents. I > will say that I was one of the longer holdouts > though. I am proud of that, but the last few years of > the realities of the global economy, our economy and > the realization that I, a citizen, am often a > minority at work, has made me realize the reality of > the situation. Fortunately, I am able to fix it, > easily, at home. And I know that other don?t have the > same opportunity as me. I do get my hopes up though, > when I see a new vocational school open, only to have > them dashed again when the next paragraph reads ?To > increase the number of girls" or ?To increase the > number of students of color" or ?To increase the > number of X?. How exactly and why exactly do you make > a school do both? I mean, teach the subject well and > increase the number of X? It seems that all you can > do is create a school that teaches the subject well > and encourage X to give it a shot. Just make more > schools for! > all the paths and make them relevant to the economy > y and labor market and the students will choose. And > more of them will be successful. > > Bob Hansen > > > ------- End of Forwarded Message