Here, just to indicate the kind of issues that could beneficially be taken up using the OPMS (and also, perhaps, to support some of my arguments in my earlier response), I have just extracted some possible 'Missions' from Kirby's thoughts and ideas expressed - these are listed below. Just a few potential Missions are listed (those that came to mind as I read through Kirby's post). There are a great many others, which I've not listed.
The 'One Page Management System' (OPMS) process could help very significantly to develop *effective* Action Planning for each of the 'Missions' listed. The attachments to my post at http://mathforum.org/kb/message.jspa?messageID=7934528 provide some information about the OPMS, which is strongly recommended for use in complex systems.
SOME MISSIONS OF INTEREST: ======================== 1) To ensure that our discussions always reach a conclusion and appropriate Action Planning for the issues discussed.
2) To understand clearly what is meant by "stakeholders" to an issue. (List some of the stakeholders you perceive for the various issues you discuss).
2a) To list, as fully as possible, the stakeholders of the 'public school education system'
3) To arrive at a clear and workable understanding of our 'citizen responsibilities' in a democracy
4) To understand clearly that our 'citizen responsibilities' in a democracy comprise much than merely voting at elections
5) To work effectively towards implementing a true democracy in this nation
6) To remove some of the common misconceptions about 'democracy'
7) To understand clearly what is involved in 'learning'
8) To understand clearly just how we learn
9) To understand clearly how a child learns
10) To understand clearly how an adult learns
11) To understand clearly the differences that may exist between the way a child learns and the way an adult learns
12) To enable students to provide feedback on their educational experience
13) To enable parents to provide feedback to the schools that their children are attending
14) To ensure that the school system is designed so as to take in and use the feedback received (from children; from parents; from teachers; from others)
15) To ensure that the students in the schools get over the bad thinking habits of the adults they come in contact with
16) To understand clearly that the 'aggregate' of a school is not just the students, their parents or their teachers
17) To understand clearly just how to 'characterize' the aggregate of a school
18) To understand clearly just how to 'characterize' the aggregate of the whole nation
19) Etc, etc, etc. (A very sizable list of elements could be created. I have just listed a very few).
GSC > > On Tue, Jan 29, 2013 at 9:24 AM, GS Chandy > <email@example.com> wrote: > > > > > > What, no Euclid's Algorithm? Doesn't matter. Of > course they're not "high > > > bar" standards. What, no ASCII and Unicode > covered? In my book, you're > > > wasting their time, trust, everything, but that's > par for the course. > > > > > > > > > What, in your opinion, was the opinion I might have > expressed by which I > > was "wasting their time"! > > > > I had merely suggested that the stakeholders > (including students) should > > properly put their minds to what they (the > students) should learn (and want > > to learn - in math and in everything else). [That > was, and remains, my > > opinion]. > > > > > > Yes, that's the kind of thing we do on this > discussion list, with or > without the assistance of the governors. It's a > social discussion that > must always continue and not "arrive" at some > terminus. > > Teachers should engage in it, but so should students, > parents, everyone. > As I was mentioning to Paul Tanner, one's > responsibilities in a democracy > are oh so much more than merely voting. If one > thinks voting is the extent > of one's responsibilities, one has no real feel for > democracy. > > That one would have such a misconception (that it's > all about voting) would > be understandable if one went to a USA school, where > civics is not taught > (usually) and democracy is not relayed (a more > authoritarian ethic tends to > insinuate itself though the schools, anti-USA in many > ways). > > The first thing students should learn is there's lots > of disagreement about > what's being taught, which isn't an excuse to stop > learning or not learn > (people have a natural hunger to learn in my model). > And there's some > agreement as well. Their job is to listen to the > adult babble for awhile, > and then to join in. > > Students should think critically about their own > educational experience and > start offering feedback as to how it might be > improved. Schools that don't > have built in mechanisms for student feedback are > less likely to grow and > adapt, same as if they close off faculty feedback > channels and just go with > some top-down approach. > > In my view, mathematics as taught too often lacks any > historical > perspective and that's much to its detriment. One way > to address this is to > open the classroom to more of the debates we're > having here. > > Students should tune in a sense of intellectual > history and see their own > educations in historical perspective. That's part of > my own minimum > standards as to whether mathematics is taught in a > useful way. No > history? What a waste!  > > I'm not the first pedagogue to suggest something like > this. Ralph Abraham, > a prof at UCSC at the time, worked on a curriculum > that would take kids > through several civilizational stages during their > elementary school > career. My approach is less radical in that I'm not > committed to > preserving any particular temporal order. My drivers > are the topics, not > chronology. But I do want to see history expounded > through math. Subjects > should piggy-back on each other, not be strictly > segregated (part of that > sorry Anglo heritage I was talking about, is that > compartmentalization > reflex and the mental retardation it engenders). > > > Currently it does appear that this is not being > done effectively at all in > > the USA. > > > > > > In many contexts it makes very little sense to speak > of "the USA" in > aggregate, "India" too. I know people like to think > in these nationalistic > terms, and it is convenient at times, especially when > telling stories about > history. But in fact we have many many schools, and > they're quite > different, not carbon copies. > > "The USA" in aggregate is too clumsy a concept to be > of much use in many a > debate, and people who use it in these types of > conversations are for the > most part just being lazy in my view. Not that I'm > against being lazy > . I'm not a Protestant and I don't cultivate the > stupid "work ethic" > that leads Protestants to be so unethical and cruel > towards people they > regard as "not working". > > Of course I'm poking fun at myself here, as the word > "Protestant" is about > as clumsy and meaningless as "the USA". > > > > > In India for sure, the great majority of students > come out of school > > fearing/loathing math - which to my mind indicates > there is something > > profoundly wrong with the way the 'learning+ > teaching' of math is being > > done here. > > > > Of course. India derives a lot of its pedagogy from > Anglophones. English > is infested with classist memes and stereotypes. One > needs to be very > attentive if an English speaker as you will be > tempted into speaking and > thinking nonsense very easily.  I'm not saying > other languages aren't > riddled with pitfalls as well. Every language, one > may assume, is a > breeding ground for various characteristic > pathologies. > > > > (At least, that's my opinion - of the situation in > the USA and in India > > respectively). > > > > In the USA, I believe you recently had President > Barack Obama actually > > 'boasting' about his poor standards in math, which > fact (if it is a fact) > > also may indicate something to those who are able > to perceive what they > > need to. > > > > I don't know anything about this. He's probably just > trying to inspire > some hope in those who look up to presidents (I look > across at most > presidents, not up, not down -- my Quaker training > maybe). > > > > What, how come hardly anyone these days would boast > about being > > 'illiterate' - and how come it is perfectly > acceptable to boast about being > > 'innumerate'? (It was once, I believe, perfectly > OK to boast about being > > illiterate. I for one find it quite remarkable > that society has changed in > > this regard (in quite a short period of time). > Even in backward India, one > > no longer boasts about being illiterate. At least, > this is my opinion, in > > support of which I believe empirical evidence could > probably be brought > > forth [but not by me]). > > > > > These are cliche remarks though. I've heard this > point made too many times > to care anymore. > > > > (Perhaps the next big societal paradigm shift may > be that boasting about > > 'innumeracy' will no longer be acceptable - even in > the USA). > > > > Innumeracy is a form of illiteracy. Innumerate > people are only > quasi-literate. Most Americans are only > quasi-literate, just as most are > malnourished (seriously overweight). That's just the > way it is. > > > > The stakeholders in the school system (including > the students) do need to > > decide what they should learn through school. This > is my opinion, though > > I'm willing to concede that my opinion may be in > error. > > > > > > Schools tend to suck for the most part, because > > > e teachers are just given > > > monkey work, and students too. > > > > > Yes, I entirely agree with your opinion expressed > above. So then (in my > > opinion) the correct underlying questions to ask in > these circumstances > > would be: > > > > - -- "Do the teachers want to continue doing this > 'monkey work'"? > > > > - -- "Do the students want to continue doing this > 'monkey work'"? > > > > - -- "Why have they been doing this 'monkey work' > all this time?" > > > > It's a complicated history I'm sure. > > In my local sphere, I like to work towards liberation > from monkey work. > > I think the individual school is the unit to work > with. > > An individual school can become a center of > excellence with high standards > and committed teachers. > > But to focus on specific schools is different from > thinking > nationalistically about some vast mega-state like > "the USA" or "India". I > am skeptical that thinking in those terms is of much > help to anyone. > > What CCSS is doing is keeping a few more adults > thinking about curriculum > issues, standards, what should be taught. On the > whole, that's fairly > innocuous and probably improves living standards more > than it damages them. > > I scoff at most math curricula that have no > programming weaving in and make > no mention of polyhedrons and thinkers I consider > most relevant and > important etc. etc. But the CCSS doesn't hamper me. > It's just more "fast > food". No one forces me to eat at McDonald's > either. > > > > If "YES" to the first two questions, then - in your > opinion - what they > > should do is to continue what they have been doing/ > are doing??? Is my > > opinion correct about your opinion? > > > > If "NO", then perhaps it is time to think in terms > of working on those > > underlying systems a bit. (In my opinion). > > > > I think brave people should band together and fight > to create or continue > high quality schools. This is done by a few in every > generation. Most > people are not cut out for such work. They just want > some way to "earn a > living" (another stupid Protestant "work ethic" > idea). > > > > > As to the third question, perhaps they (or you) > might like to write a > > little essay about it. Some opinions elicited on > this matter may shed some > > useful light. > > > > > > As Clyde says, these are ultra-minimal > standards, > > > like you should also keep > > > the restrooms well stocked with toilet paper. > > > > > ABSOLUTELY right! > > > > So let's fundamentally define "school" as being > > > > "THE place where the restrooms are kept well > stocked with toilet paper" > > > > and then design the system to do just that in the > ultra-maximal case. > > > > All then will no doubt be well with your US public > school education > > system, no doubt, and there will be no more calls > to "PUT THE EDUCATION > > MAFIA IN JAIL!" > > > > No one is taking those calls seriously. True, a lot > of Americans think > "jail" is a great solution for all kinds of social > ills. The USA (yes, > I'm back to speaking in close-to-meaningless terms) > is hugely into prisons > as a way of life, almost more than schools. A lot of > it has to do with > taking away voting rights. If they can get you on a > felony, just once, > that's enough to keep you from voting in many states. > It's a post Civil > War thing (if we agree the Civil War ever ended). > > I do think prisons should be more educational since > that's where we're > starting from. > > > Do tell me: just what, in your opinion, was the > whole point of my post(s) > > on this thread, to which you seem to be responding? > Or were you responding > > from something drawn out of your imagination? > > > > > > > I'm just having deja vu as we plow through all the > same positions and > posturings that we went through with the new NCTM > standards awhile back. > It's all so predictable. > > I only have a few years left and I'm eager to see > more interesting > developments than watching mediocre thinkers writing > pabulum and then > arguing about it. I don't begrudge them their corn > flakes and beer (their > incomes) in exchange for these paltry efforts, but I > hate to see our > debates dragged through the same dreary twists and > turns, like a bad movie > you've already seen too many times. > > What are the CCSS people doing with fractals I > wonder. They're pretty to > look at, they exercise programming skills, and > there's lots of complex > plane mathematics one can learn from exploring them. > I'm going to guess in > advance that none of the high school level standards > mention fractals. > > ... Well, I was wrong. Colorado mentions them, as an > "application" of > complex numbers, but with no suggestion that students > be able to generate > them. After all, there's no programming happening. > In my book, that means > few real / relevant numeracy skills are being > developed. Par for the > course. > Mathematics - Colorado Department of > Education<http://www.google.com/url?sa=t&rct=j&q=&esrc > =s&source=web&cd=6&ved=0CFwQFjAF&url=http%3A%2F%2Fwww. > cde.state.co.us%2FCoMath%2FDocuments%2FMath_Standards_ > 2010.pdf&ei=eQgKUa72FOWgiALC24DQCw&usg=AFQjCNHpdbzVJdO > RHSonhOdF8gxXmZl8xQ&sig2=bZiAJIARhV6fuxR-ZAtwzQ&bvm=bv > .41642243,d.cGE> > www.cde.state.co.us/CoMath/.../Math_Standards_2010.pdf > > File Format: PDF/Adobe Acrobat - Quick > View<https://docs.google.com/viewer?a=v&q=cache:jrOGKA > PhQzMJ:www.cde.state.co.us/CoMath/Documents/Math_Stand > ards_2010.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESiMy4peEG > yXPLfbqkxVYUAHhkM0_6bWp58jYjQhqMi1P83Lj4awIWZKFH4e8QGs > 68T-eryubkPcAyIoGHCCBpGOVhJZg0EAQKkd_HokktiEE2f9BPBQHw > -Sk_llBWdJoLQq1uGg&sig=AHIEtbRlcWSj_AHnWOZhRr6vOQyuhRo > eXQ> > *Mandelbrot fractal* is the *Mandelbrot* set graphed > on the complex plane. > Nature of Mathematics: 1. Mathematicians build a deep > understanding of > quantity, *...* > > Inquiry Questions: > > 1. When you extend to a new number systems (e.g., > g., from integers to rational > numbers and from rational numbers to real > eal numbers), what properties apply > to the extended number system? > > 2. Are there more complex numbers than real > eal numbers? > > 3. What is a number system? > > 4. Why are complex numbers important? > > > Those questions look pretty desultory and insipid, > but that's what standards > are like. > > > But then the latter aren't qualified to set > standards > > > regarding food > > > either, so lets give them their innocuous busy > work. > > > > > If that is the way you want to utilize your > resources (of money and human > > resources of various kinds), fine, do go right > ahead and give them that > > innocuous 'busy work'. > > > > Possibly that is precisely what in fact is > happening right now, which may > > be why you are getting calls to "PUT THE EDUCATION > MAFIA IN JAIL!" > > > > > > > You should just ignore those calls. You make a big > deal out of them. It's > just a lot of shouting. You waste a lot of time > repeating these silly > slogans, as if they were meaningful. > > > Possibly. So why do you not address Domenico Rosa > and Clyde Greeno about > > this matter? > > > > I have, many times. Dom Rosa is nostalgic for > textbooks that leave out too > much of the mathematics / geometry I consider > important (e.g. fractals). I > am not as nostalgic for those books. > > > > Would that not be more useful? > > > > Or do you believe that it is useful to insist on > soliciting my opinion > > regarding the CCSS (about which I know rather > little - and care rather > > less)? > > > > No, I don't think it is useful to insist on > soliciting your opinion > regarding the CCSS. > > I already said I agreed with Clyde. Let these people > have their fun. > They're not hurting anyone. As long as schools are > free to exceed these > standards, leave them in the dust, they're not a ball > and chain. > > The better schools have their own resources and > thinkers and don't need > some silly state called "Colorado" to tell them > what's what. That these > fifty states think they should become authorities > about math curricula is > somewhat touching and cute, but no one with a serious > brain needs to waste > much time immersing themselves in this kind of > writing. It's "make work". > > But we shouldn't be stingy with "make work". Vast > amounts of work fall > into that category, including 99% of what's done in > such bloated > over-funded bureaucracies as the NSA (where we take > math pretty > seriously). > > I'm not calling for cuts because I don't begrudge > people their living.  > > > > Further, in regard to your last, possibly you are > correct (if you are in > > the rain-fed farming business or are addressing > someone who is; I am not in > > that business at all). > > > > As you are responding to messages in a thread on > educational systems > > containing a fair number of posts, you might like > to do yourself the > > considerable favor of checking out the messages you > are responding to with > > a bit more care and accuracy than you have shown > here. > > > > You've spent a lot of time defending yourself in this > post. I skipped > commenting on most of that, but I did read it. > > > > That (in my opinion) would be at least as useful as > inquiring about > > whether it is due to rain. > > > > Cordially > > GSC > > > > Kirby > > Notes: > >  Of course the rhetoric of many here is > anti-polymath, > anti-generalist. No way should a math teacher impart > any history. They're > supposed to be "subject specialists" and according to > these dweebs it's not > *any* teacher's or course's job to really integrate > or help fit together a > bigger picture. That's left to the media or to no > one in particular. > > This emphasis on specialization and making teachers > be narrow in what they > teach, as defined by standardized tests, is a > terrible disservice to > everyone. Over-specialization is the cause of so > many of our woes. As a > liberal arts type, I despise this "only people with > degrees in math should > teach math" idea. > > To help provide historical perspective, it would, for > example, make lots of > sense to dig up arithmetic books from the 1860s in > the US and say "here's > what kids your age were working with in the 1860s." > We'd do some problems, > learn some concepts, see how they were teaching these > concepts, and then > contrast this with other curricula in different > places and times. > > Given the Internet, it's so much easier to access > these resources. > > http://archive.org/details/schoolarithmeti01ellwgoog > (available online) > >  > http://controlroom.blogspot.com/2013/01/towards-anthro > pology-of-geekdom.html > (about laziness) > >  Not that I speak anything else fluently. Just > I've cultivated an > attitude of great suspicion towards English and that > has served me well in > terms of improving my powers of thought. We should > all learn to be > critical of our mother tongue and explore other > languages for contrasting > heuristics. Anthropology is as important as any > subject (in my version of > STEAM, the A is for "anthropology", not just "art"). > >  A lot of people in those prisons were put there > for dealing in > marijuana (Thomas Jefferson was a grower), which some > states are starting > to legalize (Washington most recently). Imagine > spending years in jail for > something the society that put you there has > subsequently legalized. And > yet they still won't let you vote, those monsters. > >  My answers:  that depends  complex because > reals are a subset, > but it's not a well formed question (I'm not a > Cantorian in that regard) >  I don't think anyone has a simple answer, which > is why  is > ill-conceived  because they associate > multiplication with rotation, > because they help systematize our numbers games. > >  The Mayor of Portland wants to cut the benefit > where a high school > student ID card is also a bus pass. The high schools > don't have bus fleets > and kids are supposed to get to school on city buses. > Their ID card was > also a bus pass. A one way ticket is $1.65 or $3.30 > a day or $16.50 a week or > $66 a month not counting after school events etc. > What a horrible thing > to have a mayor like this. Everyone I'm talking to > is quite upset that we > have this mayor and they're ready to vote him out > tomorrow, even though he > just got in. Such a cruel, stingy, nasty society, > this one. I feel so > sorry for the kids born in the USA today. It's a > really militaristic ugly > place. > > On TV today these talk show hosts were talking about > how this soldier who > had just had two arms sewn on (an arm transplant) now > couldn't wait to > get back to his buddies participating in some > nebulous occupation. The > audience was encouraged to clap at this and to > demonstrate support for the > troops. Woo hoo. Send kids off to get their arms > blown off in some stupid > misguided fiasco and then applaud when they say they > want to go back for > more of the same because they're loyal to their > friends. That's pure > exploitation, child abuse. A little American flag > was sitting there on the > desk. People were being told what to think and how > to react, yet they have > no clue "why we fight" **. And this wasn't even Fox. > Pure propaganda of > the most transparent kind, extremely disgusting and > offensive. The prouder > America I once knew has been transformed into this > more putrid one, with > far less to be proud of. > > http://www.tv.com/shows/live-with-kelly-and-michael/ja > nuary-30-2013-2656958/ > > ** http://youtu.be/i2uAc4HkIAM > > > Message was edited by: kirby urner