Kirby Urner posted Jan 31, 2013 1:12 PM (GSC's remarks interspersed): > > On Tue, Jan 29, 2013 at 9:24 AM, GS Chandy > <firstname.lastname@example.org> 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. > I don't quite know who "the governors" might be, unless you mean our Moderators. I observe you've not responded to my exclamation: "What, in your opinion, was the opinion I might have expressed by which I was "wasting their time"! - which really was intended as a question.
Yes - this is indeed 'the kind of thing we do'. Alas, almost all debates here do turn out to be (ineffective) "social discussions" - they may as well be tea parties or coffee breaks; in fact, we're on a perpetual 'coffee break', I find.
We do indeed "always continue and not 'arrive' at some terminus" - but there is no "must" about it, unless we actually prefer to 'do' these tea parties and coffee breaks.
This occurs mainly on account of the ineffective 'prose mode' of discussion to which we limit ourselves here. But it's also partly a habit of mind: these bad habits of mind are the very devil to overcome. See any of my posts where I've mentioned the issues of 'learning' and 'unlearning': the OPMS process, about which I often write, makes it *possible* to 'unlearn' bad thinking habits (though it is still not easy to do).
Partly, it occurs because we prefer to be intellectually too lazy to get down into the nitty-gritty of problem solving in complex systems - which, in final analysis and synthesis always depends on how the things we do from day to day may "CONTRIBUTE TO" or "HINDER" the things we believe we wish to accomplish. (Even the things we think are also a sort of 'doing'). It is not easy, at a start, to think in terms of "contributions". The ineffective mental habits that we have accustomed ourselves to because of existing societal systems are very difficult to break. > > Teachers should engage in it, but so should students, > parents, everyone. > Of course. This is precisely the point I've made time and time again, whenever I discussed "stakeholders" to the issue of education.
In fact, ANY issue under discussion (not merely education) should involve ALL stakeholders. To me, that appears to be the simplest of common sense: But that is rarely - if ever - practiced. > > 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. > Indeed. See any or all my remarks about "stakeholders". > > 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). > In fact, the 'voting bit' - though it IS crucial - is only one of the bricks in the structure of 'a democratic reality' (be that a nation or even just an organization running on the good ideas of its stakeholders). Much more important - to reach real democracy in daily practice - would be the continuing input of citizens (/stakeholders) into ongoing issues of concern.
Parliaments, Senates, Houses of Representatives, Boards of Directors, and so on are NOT adequate! This much should be entirely clear by now: our 'forms of debate' do need to develop quite considerably, if we are to resolve the problems and issues that confront us.
The sooner we realize this, the better for us.
That 'democratic' nations do not currently have effective instruments to ENSURE such continuing input from citizens - that itself is clear indication that true democracy is not in fact found in the ostensibly 'democratic' nations. > > 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). > It's not just 'people' (by which term I presume you mean adults).
That natural 'hunger to learn' actually starts in us when we're infants, even as soon as we are born into the world. See, for instance, "How a Child Learns", attached herewith. > > And there's some > agreement as well. Their job is to listen to the > adult babble for awhile, > and then to join in. > Indeed. (I observe that such 'adult babble' is precisely the training we provide to prepare our children for 'democracy'!) > > 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. > *Should*, indeed. But just HOW is that *should* to be accomplished, in practice, on the ground?
Check out the attachments to my post at http://mathforum.org/kb/message.jspa?messageID=7934528 for some practical tools for the purpose. (Repeat wherever, in practice, wherever the useful word "should" is used). > > In my view, mathematics as taught too often lacks any > historical perspective and that's much to its detriment. > Of course. > > One way to address this is to > open the classroom to more of the debates we're > having here. > What, in your opinion, would be the benefit to students to hear views like "PUT THE EDUCATION MAFIA IN JAIL!" (and other such manifestations as we see here all too often)??
Just what do they learn therefrom? But such views (or their 'near-equivalents') are seen all the time! > > 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). > Of course. As you seem to have many such good ideas as expressed above, why don't you get down and do precisely that? The attachments to the message noted above describes tools that could help, quite significantly.
> > 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. > Agreed. I want to note that - when I say/write "the USA" (or "India", for that matter) - I ALWAYS mean the 'integration' of all the needs, desires, wishes, aims of its individual people and variety of groups therein. THAT'S my "aggregate"! > > "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". > See above. > > > 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. > Of course. So how do we train our own (individual and group) minds to avoid/ escape the inbuilt pathologies of each/all of our languages? I suggest we need to take a couple of simple steps in understanding what precisely we want to do when we communicate. I suggest a simple extension to our conventional language: prose + structural graphics. > > > (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). > I'm not certain that Obama actually said that. (Seems very sloppy - which is uncharacteristic) It WAS, I believe, something I read somewhere - but I'm unable to locate the precise place/time where he might have said it. However, the rest of my complaint holds true - that it IS generally acceptable (in the USA and in India as well; and probably in most nations) to be 'innumerate'. > > > 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. > If most of you in the USA believe they are 'cliche remarks' - then that state (of imprisonment in that cliche) will continue. I am acting here in India to change that state. In a generation or so, I would predict it will NOT be acceptable (though I for sure will not be around at that time!) > > > (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. > I agree. But it IS often acceptable to boast of being 'innumerate'! But it is no longer (since the past 50 years or so, I'd believe) to boast of being 'illiterate'. The issue is somewhat deeper than you make it out to be. > > Innumerate people are only > quasi-literate. Most Americans are only > quasi-literate, just as most are > malnourished (seriously overweight). > Indeed. Likewise in India. But: > > That's just the way it is. > This is where we SERIOUSLY differ!!!
I claim there are specific and definite things we can do to change "the way things are".
Some of these changes may take generations to come about. However, one basic fact is clear: It is no longer acceptable, NOW, to boast of being "illiterate"! (It was acceptable [here in India at least], just a few decades ago, to my very clear memory). > > > 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. > It is MUCH less 'complicated' than you would make it out to be. It was, earlier, a lack of needed tools. Then Warfield initiated our understanding of "CONTRIBUTION" through the modeling tools he pioneered.
As I understand, in another instance, it took a couple of generations for people to shift over from 'Roman numeral arithmetic' to 'placeholder arithmetic'. But it did happen - and it is placeholder arithmetic in even the most backward of countries!
Likewise to change from accepting 'illiteracy' as being something we could boast about - this change has already occurred in society practically everywhere in the world.
Also, quite similarly, the shift from accepting 'pure prose' as being the ONLY way to discuss complex issues - to a stage where people realize that we do need something more than that 'pure prose' to discuss and arrive at an effective understanding of the complex issues we do need to deal with all the time. > > In my local sphere, I like to work towards liberation > from monkey work. > Excellent. In several of your ideas expressed above, you have enough to help liberate entire generations from 'monkey work'. > > I think the individual school is the unit to work > with. > To some degree. The fundamental unit has to be the individual 'individual'. The individual school is a collection of such individuals. > > An individual school can become a center of > excellence with high standards > and committed teachers. > Yes. See above. Even the teachers are 'individuals', whose aims, desires, prejudices all come into play - separately and integratively. > > But to focus on specific schools is different from > thinking > nationalistically about some vast mega-state like > "the USA" or "India". > See above. The nation is an 'integration' of vast collection of 'individuals', EACH of them having very complex intents, desires, needs, aims and so on. > > I am skeptical that thinking in those terms is of much > help to anyone. > Well, just learn to start thinking of the nation as such a collection, as indicated above, of 'complex individuals' - and your scepticism may reduce significantly. I too used to be sceptical, not very long ago. Then I carried out a number of 'practical experiments of mind' and my earlier scepticism has changed a bit. > > 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. > Possibly. As noted, CCSS is just one 'thing' that *may be* useful to work on within a much larger goal. The real 'potential' utility of CCSS is probably a long distance from being understood. > > 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. > Agreed. So why not actually work out (much more specifically than I've seen you do here) your ideas about "polyhedra and thinkers" that I've seen you put forward at these interactions of ours? I believe you would find the graphical 'structure-conceptual' tools of Interpretive Structural Modeling' (ISM) and Field Representation (FR) Method to be useful tools. It'll take some doing to "do the demo" - but you have to be the person to do it. > > > 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). > I believe we should primarily try to band together and fight to help develop *high quality individuals*. I believe *high quality individuals* would develop by quite *ordinary individuals* working with high quality tools on their own minds. Our minds can - and do - develop.
That is, in fact, the underlying point of the OPMS - always!!!
Check out those attachments and, in particular, a whole variety of 'individual Missions' that arise. Try out a few Missions of your own to convince yourself. > > > 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. > Well, I don't take them very seriously - they are merely something I can enjoy poking fun at. > >True, a lot > of Americans think > "jail" is a great solution for all kinds of social > ills. > We have much the same kind of thinking here in India, on a whole variety of issues.
For instance, you would know about a recent horrific rape case in Delhi, mid-December 2012, where 6 men (one of them a 'juvenile' of about 17-odd years in age) assaulted and raped a 23-year old paramedical girl student; she later died in Singapore after truly terrible suffering.
Now, most of India seems to be convinced that putting those 5 1/2 men to death will cure the Indian male's need to demonstrate his power over women who are (very slowly) trying to liberate themselves from tyranny of a patriarchal mindset that has enslaved women's bodies and minds for generations. Even many women are calling for the death penalty to be applied! In point of fact, if we were apply the death penalty to tackle the 'mindset issue' that leads to such rapes, I would believe that a sizable percentage of Indian men would actually have to be executed! Alternatively, we could work to develop a sizable number of *higher-quality individuals* than we currently have around us. This is the approach I recommend.
(I personally have no objection at all to the death penalty being made mandatory for proven rape of any kind - I just think that the death penalty really does not work as a deterrent to men who are seeking to demonstrate their 'male power' over women. The death penalty as a 'societal instrument' to enforce any societal norm does not really work in ANY case - in my opinion. Most people here seem to think otherwise). > >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. > Indeed: but that's a long, LONG way from happening in most any country in the world. Well, perhaps some of the Scandinavian countries may have achieved a more civilized way of thinking in regard to 'crime and punishment' (in some or many respects: I'm interested in India). > > > 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. > Of course. But see the attachments noted above, for practical means to avoid having to keeping plowing through these positions time and time and time again! > > 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. > Well, see above. > >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. > Indeed. > > 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. > I'm pretty sure not. > > ... Well, I was wrong. Colorado mentions them, as an > "application" of > complex numbers, but with no suggestion that students > be able to generate > them. > That IS interesting! We should perhaps urge/ help some of the Colorado curriculum people to move further along? > >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, *...* > I shall check out those websites in due course. I do have a fair bit of material on the Mandelbrot set and frractals - which I must investigate much more deeply than I have managed to do thus far. > > 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? > Excellent! Why not work to put such ideas into the 'regular curricula'? What would be needed to accomplish that? Who to discuss such matters with? HOW to do this discussion??? Etc, etc, etc. > > Those questions look pretty desultory and insipid, > but that's what standards > are like. > Nope: you are wrong. Approached *properly*, these are very real questions indeed - and they could lead to quite profound investigations into the field (of "'learning' and 'teaching' math" - by a person who is qualified to do - capable of doing - such investigations).
In more or less such context, I recall that someone called "Leah", right here at Math-teach, had pointed out a quite interesting 'discipline'issue' - which could lead to very productive work and investigations indeed. (See http://mathforum.org/kb/thread.jspa?threadID=2431841).
It ALL depends on the connections you are able to make: for practical tools to investigate 'connections', see those attachments that I'd mentioned.
Your ideas above are in fact most useful - but "approached more creatively and productively" than is the norm in our conventional discussions: that is key. > > > 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. > I do get my (not-so-innocent) fun out of teasing the people who put up such slogans. I do deserve my relaxation! However, such slogans do indeed represent the ideas of a fair segment of the population (in the US/ in India).
> > 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. > Well - the underlying idea is to create the right math/ geometry textbooks. Nowadays, with computer software and internet, it IS, I believe, much easier to accomplish. (But I do approve of Dom Rosa's dislike of 'door-stoppers' serving as learning tools for kids). > > > 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.  > I may, later, respond further to some of the very important and useful issues you have raised in this post: specifically, I could try and show you 'action structures' developed from some of your ideas, which could help bring some of them into play in practice on the ground.
Now, I have to get going to a workshop I'm conducting.
GSC POSTED WITHOUT PROOF-READING! > > > 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