Wayne Bishop posted Jun 28, 2013 10:33 PM: > You already said it The answer to both questions > is the not very profound "YES". Nearly always > emphasis on one rather than the other - almost > exclusion of one in deference to the other - is > implicitly obvious from the context so the real > question is: Why waste anymore time on it? > > Wayne > There is a little more to it than that 'not very profound "YES"', as you would have realised if you had troubled yourself to look a little deeper into the comment you're responding to - or, failing that, at some of ideas of others who have looked somewhat deeply into various aspects of the issue (a few references were provided there). In fact, there is, IMHO, a whole lot more to it. And yes, my subject-title should have been better articulated. I'm sorry about that.
I have always felt (and still do feel) that we do need to explore this matter quite a bit more - in particular if we wish to arrive at a somewhat deeper understanding than we have today of logic AND of math; and in particular if we wish to arrive at a better understanding of how to bring home an appreciation of the power, practical utility - and sheer beauty - of math (*real math*) to students. [*By 'real math', I do NOT necessarily mean 'advanced math'].
We in general do know (and readily accept) that a sizable majority of students leave school loathing and/or fearing math. Why is this so? We do not know now - and I've seen few signs that we're approaching the issue in a way that would actually help to resolve it.
President Obama had, I believe, said (in regard to attitudes regarding math in the USA) something to the effect that that he had been less than adequately competent at it in school - and he seem to accept this as an an 'OK' state of affairs for the USA! (I believe that such is the case more or less in math education worldwide; I know it is the case in India). How to change that attitude? -- WE DO NOT KNOW!!
It is entirely clear (from all your contributions here at Math-teach) that you do not have the faintest inkling of how to go about changing such a societal attitude.
[Insofar as I have understood your approach to changing such damaging societal attitudes, it consists of quoting the wisdom of experts called Reid Lyon (reading research expert) and then Assistant Secretary of Education under Secretary of Education Roderick Paige as follows: "You know, if there was any piece of legislation that I could pass, it would be to blow up the colleges of education" (see http://mathforum.org/kb/message.jspa?messageID=9146253].
I believe the basis of a practical way forward on changing that 'leaving school attitude to math' must look elsewhere than Reid Lyon et al - and I've outlined the basis of my belief at several postings here at Math-teach. I do accept that more development is required of this 'practical way forward' that I propose.
The 'inclusion' relationship ("is a part of") is useful and important - but it is not all of the story, as you seem to have assumed (from your examination of the title of the thread). Some other relationships were noted in the comment.
There are several other relationships that can help us arrive at a 'working understanding of systems' (which could then help us arrive at an effective means to tackle the societal issue of why most students loathe and/or hate math).
I believe that exploration of the transitive relationship "CONTRIBUTES TO" (in the specific context of the issue of how to change student attitudes to math) could help significantly to change those attitudes. [Check out the attachments to my post heading the thread "Democracy: how to achieve it?" (http://mathforum.org/kb/thread.jspa?threadID=2419536) for information about practical tools that can help us better explore systems, including 'thought systems'].
That, in brief, is why it would be useful to spend time on the issue: it will not be, as you have claimed, a "waste of time".
The conventional management approach to 'systems' (practically built into us over the past couple of centuries) implicitly and explicitly uses "PRECEDENCE" as the only structuring relationship in a system. Despite being very widespread, this has not been a very useful development in our 'management' of human affairs - see most of our human affairs for evidence. In brief, the approach does not enable understanding of the issue of why most students loathe/fear math. It does not enable understanding of any issue.
Alas, most of our existing societal understanding on practically every issue that confronts us appears to be based on the assumption that "PRECEDENCE" is the only system relationship of importance.
[All of the argument I have tried to make here in pure prose demands what I call 'prose + structural graphics' to enable adequate understanding all round].
GSC > > At 09:13 PM 6/27/2013, GS Chandy wrote: > >The questions in the subject-line have long <snip>