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.
1. When you extend to a new number systems (e.g., from integers to rational numbers and from rational numbers to real numbers), what properties apply to the extended number system?
2. Are there more complex numbers than real 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 >
 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.
 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.