This is difficult to do in 'prose mode', so I am attaching some documents showing a couple of illustrative structural graphics, which should be read alongside my prose remarks below. These may help clarify, to some extent. In the absence of facilities that would enable us actually to discuss these issues *interactively* using 'prose+structural graphics' (p+sg), this is about all that's possible.
1. The 'systems' within which we live and work (and think and play) are extremely complex. In the conventional 'prose mode', it is impossible to capture the complexity of the relationships our minds perceive when we discuss or work on any issue.
As an instance, take a look at the 'mechanical model' of actions involved in the task "To write a letter", illustrated at page 7 of the attachment "How to Accomplish a Mission". These mechanics are something we all over the years have learned to do almost without thinking about it. However, a few aspects of the complexity of the task "Writing a letter" do come through in the model illustrated. I note that the model "How to write a letter" represents only some 'elements' that I, GSC, thought about - you will doubtless wish to add other elements of your own: this is easily done if you use "Interpretive Structural Modeling" (ISM).
(I emphasise that the model looks only at the 'mechanical aspects' of actions involved in writing a letter - not at the much more complex aspects of the 'thought processes' involved in writing the letter).
2. If that model on "writing a letter" adequately brings home at least some minor aspects of the sheer complexity of the things we think about and do in our daily lives (almost 'without thinking about them'), then it may be appropriate to look at the more complex issue of "How to accomplish a Mission". Check out the whole of the attachment with the underlying idea that the whole of what we do is enormously complex indeed - and that some 'assistance' to aid us 'capture at least some parts of that complexity' may be useful.
3. If the above argument at '1' and '2' above is even partially convincing, then it may be useful to glance at the other attachment herewith, "Deep Logic". It'll take a while to read and adequately understand. It'll take a while to read and understand adequately. Some understanding of the properties of "Interpretive Structural Models" (ISM) and how they are developed (and how they are to be 'interpreted' is needed for adequate understanding of issues discussed here.
By the way, please do NOT believe you've understood ISM if you have created PERT Charts (even 30-foot PERT Charts, as Robert Hansen has often recounted with great pride). There's a whole world of difference between PERT and ISM. ISM ('Interpretive Structural Models') can enable us to understand the 'deep structure' of systems, in particular our thought systems. As for PERT Charts, they are are only trivial representations of how Events/Milestones in a complex system may "PRECEDE" each other: unfortunately, the "PRECEDENCE" of Events/Milestones in complex systems can in fact NOT be understood effectively (by modeling) until we already have some understanding of that system. It is my claim, in fact, that the management 'scientists' (by focusing over the past several decades on PERT Charts as though that was exploring complex systems) have in fact severely HINDERED the *effective* understanding of systems by the stakeholders in them. (These are in any case issues that will be debated in detail with management 'scientists' in due course). Back to "Deep Logic":
The structure illustrated at "Deep Logic" may be useful to help us understand the profound complexities that come into play whenever we think on any issue.
Suggestion: develop this little structure a bit, using your own ideas about how 'elements' in the postulated 'system' "MAY CONTRIBUTE TO" the understanding of 'problem solving'.
4. Warfield developed powerful modeling tools, in particular "Interpretive Structural Modeling" (ISM) llustrated for example in the attachments herewith] and briefly commonted on in 2 and 3 above.
What's important about ISM is that it enables us to develop graphical structures to represent, visually, our mental models on issues of interest - and that ISM can help us *integrate* YOUR mental models with mine (or with anyone else's). ISM - when we learn to use it effectively - can help us 'dig beneath the surface of things in a way that's impossible with PERT Charts (even if you were to create PERT Charts that are 50 or 100 feet long and put them up at Madison Square Gardens).
However, in order to be fully convinced of my arguments above, you would have to do some of this modeling yourself, on issues of specific concern/interest to you..
My post heading the thread "'Complex Systems' and important relationships within them" briefly discusses some of the important 'system relationships' that could lead to an enhanced understanding of systems amongst stakeholders in those systems.
5. Should the above arguments have convinced you that it should be worthwhile to learn how to dig beneath the surface, the attachments to my post heading the thread "Democracy: how to achieve it?" would be useful - see http://mathforum.org/kb/thread.jspa?threadID=2419536.
Those attachments explain a bit about the OPMS and how 'prose+structural graphics' (p+sg)enables us to go somewhat deeper on any issue than 'pure prose', by enabling us to see the graphical representations of the 'structural relationships' that are implicit in any description in 'pure prose' - the 'structural graphics' explicating to a fair extent the interpreslationships between factors that generally remain ambiguous or entirely hidden in pure prose. I emphasise, however, that real understanding will come about ONLY if you actually construct, develop and interpret models on issues of interest to you.
The OPMS goes a bit further than Warfield, in that it enables any individuals or groups (high-school upwards) to apply the sophisticated concepts of systems science to issues of interest to them (as individuals or as groups) - with no special infrastructure or background knowledge of systems, mathematical modeling, or mathematics being needed at all to help 'analyse' + 'synthesise' complex structures of interest.
We have already considered an extremely simple instance, consider the 'structural model' for "How to write a letter" (page 7 of the attachment "How to Accomplish a Mission"). We go a little further into the matter here:
Doubtless this particular structural model can be quite easily written down in prose - but it would be difficult (and boring!) to read. The claim is that the model DOES explain to a considerable extent the mechanics involved in "writing a letter", and this model may help explain some aspects of the utility of constructing such models, especially when complex or tricky issues heednt9 be clarified.
The clarification is not likely to occur by writing down the 'prose translations' of the "CONTRIBUTION" relationships perceived. There are a large number of reasons why this will not work. Here are just a few of them that come readily to mind:
i) Such masses of prose are likely to be extremly boring to read with attention - and will therefore go unread and not understood. Graphical models presented of just those relationships are easy to read, and give us a memorable 'shorthand' approach to understanding the system relationships.
ii) Other stakeholders to the issue(s) under consideration are likely to raise different points to consider. It is relatively easy to add such new items to models, and the new models are easily understood all round where examination of the detailed prose relationships is likely to be extremely difficult if not impossible.
iii) In complex issues, it is not merely the "CONTRIBUTIONS" of various actions that need to be taken into consideration - but also we do need to understand how certain actions may impede desired outcomes, i.e., we need to find out how weaknesses, difficulties and barriers may "HINDER" or even "PREVENT" accomplishment of the 'Mission' as well as of the various things to be done to accomplish the Mission.
iv) It can be demonstrated, via 'analysis' + 'synthesis' of any issue, that such models - when developed and discussed by the stakeholders to the issue - would lead to enhanced understanding of the issues by all stakeholders. Thereby, they would be enabled to move towards actually resolving the issues under consideration, instead of simply 'running around mulberry bush', which we've seen happen all too often right here at Math-teach.
I claim that, were stakeholders in complex issues were to take the small trouble to learn a little about 'systems' - and how we may cope with them - we'd progress swiftly towards resolution of the whole number of complex inter-twined issues that lead us to keep 'running around mulberry bush' endlessly 'sloganeering', for instance:
-- (A): "PUT THE EDUCATION MAFIA IN JAIL!" (Haim, who is alas no longer with us);
-- (B): "BLOW UP THE SCHOOLS OF EDUCATION!" (Wayne Bishop, who has made it his life's work to promote this slogan first thought up by Reid Lyon [Reading Research Expert].
-- (C): "Children must be PUSHED (or GOADED) to learn math (and doubtless everything else) [Robert Hansen]
When I draw attention to 'A' and 'B' I am by no means claiming that stakeholders in education should tolerate the incompetence and unhealthy attitudes to education that doubtless do find expression in various parts of the education system, e.g. in Teacher Unions or in the schools of education. I am merely pointing out that neither of the slogans 'A' or 'B' is likely to help cure or lessen the illnesses that doubtless do exist in the 'system'. These slogans will certainly not help cure the problems of (/in/by) the Teacher Unions, nor will they help improve the schools of education (which doubtless do need to function far more effectively than they are doing today).
When I claim that 'C' is utterly ridiculous as an 'educational philosophy', I am claiming that the slogan reveals clearly that the persons who promote it understand very little indeed about systems and how learning may be promoted in the educational system.
In order to develop effective educational systems (whether it be for math or for any other discipline), we do need to go 'beyond such empty sloganeering as we have seen. It's high time, indeed.
GSC Kirby Urner posted Apr 3, 2014 11:05 AM (http://mathforum.org/kb/message.jspa?messageID=9427562): > On Wed, Apr 2, 2014 at 2:49 PM, GS Chandy > <email@example.com> wrote: > > > > > Well, I don't know whether "milk is bad for you" - > but certainly the > > widespread belief that "milk is good for you" > appears to have huge > > commercial interests pushing it. > > > > > USA-based high school aged students in many cases > have Netflix or some > other video on demand service, and so it is easier > for them then in > previous generations to bypass "established wisdom" > as disseminated through > a very few network television channels, later > multiplied with cable, and > watch documentaries which contravene such > "established wisdom". > > This technological transformation, the provision of > "video on demand" or > "dial up video" to many households, is a new headache > for teachers as > students raised on video are more likely to research > using that medium. > Youtube provides a complementary repository. > > So whereas the common wisdom is a bovine blood > byproduct aka "milk" helps > build strong bones and makes your teeth stronger, the > real problem being > solved is the North American farmer's ability to > extract huge amounts of > milk from a vast cattle herd, many times bigger than > any in world history. > > Finding a ready market willing to engage in high > volume milk consumption > was not going to pan out unless managed pro-actively. > Creating a ready > market of high volume milk consumers, through the > power of advertising, is > what industry undertook, and mostly succeeded. The > grain industry colluded > with its Breakfast of Champions requiring lots of > milk mixed with sugar. > > So, using OPMS language, I would say "high bovine > milk product consumption" > (aka the Cult of Milk, zealous and powerful) > CONTRIBUTES TO high methane > production and global warming, and to the obesity and > morbidity of our > adult and young adult population. > > Coca Cola likewise a cultic faith (i.e. a sincere > stakeholder community of > many widows and orphans), CONTRIBUTES TO the general > unhealth of our > school-aged and older (and younger) population. > > What's interesting about math class is that story > problems are often > tightly focused to those of the individual consumer, > trying to make change, > shopping for the best interest rate on a car or house > and so on. > > However, the minute you try to "run the numbers" or > "crunch data" more > globally, studying the "what if" effects of various > changes to national or > global averages ala 'Diet for a Small Planet' (famous > book), right at that > point you are accused of "politicizing" the children, > and your math is > suddenly called "rainforest math", a blanket > anti-STEM term of ridicule > for global modeling in general. > > Our induced and artificial milk cravings are helping > turn the Amazon jungle > into cattle farms, so lets remember that "rainforest > math" remains an apt > term for global modeling software (Sims, SimCity, > SimEarth...). > > Acting locally to buy a home based on a few story > problems is OK, but > "thinking globally" is more like communist (more > Russian?) and should be > discouraged by milk-pushing, fast-food-loving public > school teachers. > That's a prevalent attitude in math classes today I'd > say. Don't use math > to question the posters on the wall around you, > sharing the "established > wisdom" about milk. > > Kirby