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Continuation on education

jd (1658) writes | about 6 months ago

User Journal 13

Ok, I need to expand a bit on my excessively long post on education some time back.

The first thing I am going to clarify is streaming. This is not merely distinction by speed, which is the normal (and therefore wrong) approach. You have to distinguish by the nature of the flows. In practice, this means distinguishing by creativity (since creative people learn differently than uncreative people).

Ok, I need to expand a bit on my excessively long post on education some time back.

The first thing I am going to clarify is streaming. This is not merely distinction by speed, which is the normal (and therefore wrong) approach. You have to distinguish by the nature of the flows. In practice, this means distinguishing by creativity (since creative people learn differently than uncreative people).

It is also not sufficient to divide by fast/medium/slow. The idea is that differences in mind create turbulence (a very useful thing to have in contexts other than the classroom). For speed, this is easy - normal +/- 0.25 standard deviations for the central band (ie: everyone essentially average), plus two additional bands on either side, making five in total.

Classes should hold around 10 students, so you have lots of different classes for average, fewer for the band's either side, and perhaps only one for the outer bands. This solves a lot of timetabling issues, as classes in the same band are going to be interchangeable as far as subject matter is concerned. (This means you can weave in and out of the creative streams as needed.)

Creativity can be ranked, but not quantified. I'd simply create three pools of students, with the most creative in one pool and the least in a second. It's about the best you can do. The size of the pools? Well, you can't obtain zero gradient, and variations in thinking style can be very useful in the classroom. 50% in the middle group, 25% in each of the outliers.

So you've 15 different streams in total. Assume creativity and speed are normally distributed and that the outermost speed streams contain one class of 10 each. Start with speed for simplicity I'll forgo the calculations and guess that the upper/lower middle bands would then have nine classes of 10 each and that the central band will hold 180 classes of 10.

That means you've 2000 students, of whom the assumption is 1000 are averagely creative, 500 are exceptional and 500 are, well, not really. Ok, because creativity and speed are independent variables, we have to have more classes in the outermost band - in fact, we'd need four of them, which means we have to go to 8000 students.

These students get placed in one of 808 possible classes per subject per year. Yes, 808 distinct classes. Assuming 6 teaching hours per day x 5 days, making 30 available hours, which means you can have no fewer than 27 simultaneous classes per year. That's 513 classrooms in total, fully occupied in every timeslot, and we're looking at just one subject. Assuming 8 subjects per year on average, that goes up to 4104. Rooms need maintenance and you also need spares in case of problems. So, triple it, giving 12312 rooms required. We're now looking at serious real estate, but there are larger schools than that today. This isn't impossible.

The 8000 students is per year, as noted earlier. And since years won't align, you're going to need to go from first year of pre/playschool to final year of an undergraduate degree. That's a whole lotta years. 19 of them, including industrial placement. 152,000 students in total. About a quarter of the total student population in the Greater Manchester area.

The design would be a nightmare with a layout from hell to minimize conflict due to intellectual peers not always being age peers, and neither necessarily being perceptual peers, and yet the layout also has to minimize the distance walked. Due to the lack of wormholes and non-simply-connected topologies, this isn't trivial. A person at one extreme corner of the two dimensional spectrum in one subject might be at the other extreme corner in another. From each class, there will be 15 vectors to the next one.

But you can't minimize per journey. Because there will be multiple interchangeable classes, each of which will produce 15 further vectors, you have to minimize per day, per student. Certain changes impact other vectors, certain vector values will be impossible, and so on. Multivariable systems with permutation constraints. That is hellish optimization, but it is possible.

It might actually be necessary to make the university a full research/teaching university of the sort found a lot in England. There is no possible way such a school could finance itself off fees, but research/development, publishing and other long-term income might help. Ideally, the productivity would pay for the school. The bigger multinationals post profits in excess of 2 billion a year, which is how much this school would cost.

Pumping all the profits into a school in the hope that the 10 uber creative geniuses you produce each year, every year, can produce enough new products and enough new patents to guarantee the system can be sustained... It would be a huge gamble, it would probably fail, but what a wild ride it would be!

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13 comments

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So it's a standard normal distribution (1)

smitty_one_each (243267) | about 6 months ago | (#45649099)

Creativity has a bell curve. The task is to excite people where they are, and drive them toward improving creativity, knowing that nurture can only go so far with a given natural set of chromosome pairs.

Re:So it's a standard normal distribution (1)

jd (1658) | about 6 months ago | (#45651331)

Which is precisely the point. I see no way of exciting creativity when the level of variation drowns out individual effort by the less creative and requires minimum exercise by the super-talented. However, you are correct that what I outlined is not enough to inspire.

Two people join a class, one from a poor school and is a ways behind, the other spent time in a crammer and is functionally a year ahead. The first person learns a lot more than average, but makes only an average grade. The second person does nothing but play games on their phone, but knows all the material and gets the absolute maximum grade with all the bonuses.

Clearly, the first is making the best use of resources and is highly adaptive. The hallmarks of intelligence and creativity. The second was able to learn fast, but they're a one-trick pony.

Putting these in the same class will dispirit the first, as they will remain invisible, but encourage the second because they're a superstar.

My approach is to say that years are an illusion. You start at a given point on the continuum, you proceed at your natural rate and in your natural style. If you can learn fast, then learn fast. If you can learn deep, learn deep. If instead of learning isolated facts, you can discover underlying patterns never seen before and interpolate the facts correctly, then do that instead.

A test for any one of these, or geared in their direction, will be failed by the others.

What is the purpose of testing? In the real world, mostly school PR and student PR, standardized tests have no functional worth. In my imagined school, it fine-tunes the experience, each student gets a completely customized schooling based on where they are and what they can do.

But this gets back to your point. That, alone, is not enough. It removes friction and inaccurate perceptions of failure, but where is the inspiration? In part, it would come from teachers/lecturers who aren't trying to deal with all types but know exactly what the score is. In part, it would come from the flexibility produced, allowing projects and contests designed with the students in mind and not diluted to cope with other types of mind.

There may need to be more besides. I am not sure yet. These 15 streams would diverge, never to reconverge. Creatives create, thinkers think, creative thinkers creatively think, and nobody gets in anyone's way.
People should have a broad enough base that they have a real, meaningful, functional choice of careers.
People should have enough research skills that they can realistically switch career paths midstream.
People should have the deepest knowledge in each field that the above constraints permit.
People should develop their own methods of learning, memorizing and understanding, so as to maximize all three.
People should never be satisfied with the old for being old, or the new for being new - age is not an interesting property.
People should invent what they lack, if they can, or request it of those that can.

Meeting these constraints is hard, and there are probably many I am missing. But, as you can see, my idea is very different from any existing system.

The objectives are to increase personal freedom to make use of talent, better meshing with less office politics between different people (nobody needs to feel threatened, because cogs don't get replaced by axles - even the perception of a threat is reduced), less friction and more traction in the arts and sciences, more real progress and less smoke-and-mirrors illusions of progress.

Well, those are the primary objectives.

The secondary ones are a superior match to Plato's requirement for functioning democracy, the tackling of issues rather than assuming they are too hard to solve, and the closest approximations yet to Homo Universalis, as determined in the Renaissance to be the ideal due to the interconnectedness of life. (ie: Because all the sciences make reference to all the other sciences, you can only partially understand a science in isolation. To completely, 100%, understand anything in all aspects and at all levels requires that you understand everything. This is impossibl, but how much to learn? Pick the must-haves, then maximize across them. It's about all you can do.)

Re:So it's a standard normal distribution (1)

smitty_one_each (243267) | about 6 months ago | (#45651899)

Part of our challenge is that, just as you can't take the square root of 9 without roots of +/-3, the idea of making the individual the unit of analysis implies that some people are going to "fail", according to some measure of success.
So much of our contemporary society is predicated upon attempting to factor out the -3 of reality (at least, according to materialistic scales) that we're now watching a global economic system consume itself with debt.
Education is a seed scattered to grow where it may, not a magic absolute value wand that can wish away -3.

Re:So it's a standard normal distribution (1)

jd (1658) | about 6 months ago | (#45655011)

I absolutely agree. My idea of having a symmetrical arrangement for speed and creativity is that there will be brilliantly creative people who need a lot of time, and amazingly fast people who have the creativity of a lettuce leaf.

In terms of +/-, because this is 2D, I would describe these as -3 + i and +3 - i.

Now, because everything is done per subject, you can be -3 -i in absolutely everything but basket weaving, where you might be +3 +i. Would you be a success or failure? Broad society would probably say failure, but I can absolutely guarantee you would have a very successful, highly profitable business and international acclaim in the art world. That sounds like a more interesting measure.

Ok, what about those who are truly doomed, negative in every aspect in every subject, learning slowly no matter what you do?

Well, one aspect of streaming is that nobody holds anyone else up, so such people aren't inhibited further by even slower people. In turn, they slow nobody up - a significant cause of classroom disruption that hurts those who are struggling even further. So these people certainly exist, but should fare a lot better.

With customization of style as well as speed, those "not getting it" because the presentation is wrong for them rather than any lack of ability should be running much closer to their natural speed. You have to introduce a third dimension to the streaming to tune the style better, but a mere 3 styles takes us from 15 streams to 45, and the total cost jumps from 2 billion to 6 billion. You might be able to do this - the law of diminishing returns won't kick in until classes (or buckets, if you like queue theory) cannot be kept full OR your research division (the actual end product as far as economists are concerned) have saturated the market, there just isn't any way to absorb the extra products.

Ok, but even when you have siphoned off all those doing badly for extraneous reasons, and got them where they can progress naturally, there will still be people who do badly. Some may even become politicians. The system I have outlined allows any one of these people to change gears. (In fact, it allows anyone to. Shifting down can help avoid burnout, shifting across can help avoid getting into a rut, shifting up can really stretch the mind.) So those who circumvent neural challenges (I'm one, so I know it can be done) can experiment. They can test any or all adjacent streams, without risk. They should be encouraged to, the differences in perspective may help solidify the person's methodology and lead to ever-increasing confidence and ability beyond the genetic baseline. Again, this is true of everyone.

Those who cannot beat the limitations should not, as often happens, be dumped by the system. Those who are slow should be allowed to continue schooling even to degree level or beyond, just at a pace they can manage. Those who have difficulties that mean they cannot learn certain skills at all, ever, at any pace, should nonetheless be encouraged to master what they can, as far as they can. I am stuck on ideas on how to help them further, suggestions are welcome. But what I am proposing is a definite improvement on what they have. Nobody gives up on them, as happens so often today, and because it's ok to suddenly "get it" at any time, nobody feels like they are necessarily marked for failure.

Added to which, you don't need to be a genius to be a lab assistant, and lab assistants are just as entitled to flashes of insight and inspiration. Such insights may lead to even better solutions for struggling minds. After all, rote memorization has little to do with ability. Indeed, very little memorization is needed. Those with poor memories but brilliant idea engines need a way to offload the part they will never be able to do, to nurture and turbocharge the things they are great at.

Ok, this pushes us into computer augmented learning. This isn't a new axis, since these are prosthetic aids that let you take advantage of your strengths. These aids should never be such that natural ability ever decays through under-use, but they should supplement those abilities so that people aren't disadvantaged by the irrelevant. Anyone can - and should - look up facts, because human memory isn't reliable. Memory is useful only as a temporary work buffer to learn skills. So if a computer provided that temporary work buffer, index and, indeed, knowledgebase, it does not reflect one whit on your skills or ability to utilize them.

There is currently no way to plug a memory expansion pack into the brain. It should be possible, though. Once it is, that kind of neurological disadvantage can be eliminated. Would it provide an unfair advantage? No. Because you can train a decision tree with facts, and train a rat brain to respond to stimuli to operate controls, a rat wired to an expert system can pass a traditional exam even though they could do nothing else. (It does prove that we are in a rat race, though.) Ergo, you need an exam that tests current understanding and usage of that understanding.

What is the purpose of an exam? In most schools, it is a barrier to the next level, where parrots and cyber-rats have all the best seats reserved. Here, the purpose is to see if a student is matched up correctly to a stream. There are no quantum leaps, no years in the classic sense, but an approximation to a continuum, enough gear ratios that you can slide smoothly around with minimal repetition and minimal synchronization issues.

Since there are no years, exams cannot be at the end of them. I picture exams as being an educational version of dynamic probes - if a bug in the process is detected, you test to see if the bug can be patched (extra help) or if there is a mismatch between student and environment (ie: stream). The student can then be matched better, re-learning only the bits not quite grasped.

The "final" exam, when the student transfers out of the system (regardless of when) would be intended to translate the level of ability in each subject into terms that can be understood outside. Thus, a person with the knowledge, proficiency, experience and demonstrated skills equal to a doctorate would have a doctorate. Time spent in the system would not matter, nor would a formal designation of being in a doctoral program. The exam would not be "for" something, in the ordinary sense, it would merely establish a level of competence, where the label is decided by what that level is.

Re:So it's a standard normal distribution (1)

smitty_one_each (243267) | about 6 months ago | (#45655503)

You might find Glenn Reynold's [amazon.com] upcoming book of interest.

Re:So it's a standard normal distribution (1)

jd (1658) | about 6 months ago | (#45655935)

Thank you for the link. It looks intriguing.

Basically, my assumption has been that you can treat education as being a problem in multi-variable space, that it cannot be reduced until all the variables have been identified together with their relationships and interactions, but that once reduced to the simplest elements, those elements should naturally form a very simple pattern or weave. If my reduction is inaccurate, the weave I have produced will be flawed. Threads will tangle, patterns will become disjoint or incoherent. The same is true if any of those three core assumptions are wrong.

This book you pointed me to, along with any others I find, will definitely give me different perspectives. If my three assumptions are correct, all perspectives should reduce to exactly the same atomic components. If they do not, the idea of atomic components must be wrong.

It is also the case that a different perspective might lead me to reject utterly my entire line of reasoning (won't be the first time, won't be the last) and adopt an entirely new outlook. That can be a very good thing. Never be afraid to learn. I have an interesting mind but far better ones exist for this sort of work. It would be foolish to ignore the ideas of others.

And if it kinda goes along with my thinking? My ideas evolve constantly, even during a post. The very worst that can happen is that I'm inspired and correct mistakes in my thinking. As tragedies go, that seems acceptable.

I look forward to the book, and hope I find many more.

Re:So it's a standard normal distribution (1)

smitty_one_each (243267) | about 6 months ago | (#45656001)

The point isn't that you're wrong; it's that, if correct, the situation is far too complicated to be "solved" by government.
The best government programs are going to do is provide substrate and catalyst for the more complex, individual reaction.

Re:So it's a standard normal distribution (1)

jd (1658) | about 7 months ago | (#45656367)

I would concur with that. What I have proposed is at the upper limits* of what can be achieved by a single entity running a single entity. If you need finer granularity, more dimensions or greater timelines to give everyone a fair chance in life, no single entity (corporate or government) could do it.

*It may actually be beyond. Not financially, but organizationally. To predict the optimum path for each student individually, track that, and correct at a moment's notice, no entity has shown the capacity to do that. To perform a travelling salesman heuristic for that many people, remembering that exactly ten people with identical requirements in a subject can enter a location simultaneously and that people of different needs should never enter the same location simultaneously at all, and all the other constraints...

It is possible that the problem is too big, that it must be distributed somehow. The internet is a powerful tool for that, but it has to be used correctly.

I have worked with computer aided learning, in the sense of designing it and experimenting with its limits, back in the 90s. It was grossly underutilized, people looked at it only as a book with clickable images and audio. Internet whiteboards, collaborative tools, shared documents - all existed back then. So did multi-way videoconferencing, telerobotics and all kinds of other nifty teaching aids. Almost none were used then.

Today, some of these are used, but the technology has not stood still. Not just data but entire applications can be pushed from machine to machine. Sensors can track hand motions, allowing instructors in music, sculpture, painting or, indeed, archaeology to know precisely what is or is not happening, instant by instant. Simulators can compare expected results with the actual, long before anything is finished. In science, DIY spectrometers can tell chemistry lecturers everything they need to know.

There will be ideas I haven't even stumbled upon. My knowledge is broad, but technology is broader by far.

But these aren't being used. Computer Aided Learning remains 20 years behind the curve at best, 40 years behind at worst. (80 if you include YouTube videos of lectures, Open University was providing that sort of material a long time ago.) If you want a revolution at the level of individuals running the show, that is where to start. You need between quarter to half a century of development to be factored in. That is a lot and inertia is high. If MIT can't be more original than a video camera, an achievement sci-fi conventions could boast of even in the 80s, the people with the knowledge will not adapt to new methods by choice.

Re:So it's a standard normal distribution (1)

smitty_one_each (243267) | about 7 months ago | (#45657151)

I'm waiting for computer games to merge with History and let students really step into some ancient contexts.
Of course, there is going to be some shock as people discover some of the airbrushing that's gone on. . .

Re:So it's a standard normal distribution (1)

jd (1658) | about 7 months ago | (#45657353)

I'm working on it. Seriously. They dug up an Iron Age settlement not far from where I used to live. My father was one of the scientists on the team, providing magnetometry, ground penetrating radar and mass spectrometry. One of his colleagues from the university provided geological analysis and a colleague from another university handled conservation of things like amber artefacts.

I have all that data (not all of which was released to the public) plus the archaeological reports and a decade of photographs of the site from over a dozen people, plus photographs of very nearby contemporary monuments.

My plan, from the very start, has been to turn this into something educational. My thought has been to construct a virtual reality, much like Virtual Rome (dunno if that is still being run), so that people could see a reasonable reconstruction of what the site looked like - not just in one era, but in each of the eras for which sufficient data exists.

Admittedly, this has turned out to be a very difficult project - well beyond my artistic skills and a very tough challenge for the virtual reality software that has been open sourced. Any help - any at all - would be gratefully received. I tried to get kickstarter funding, to hire the necessary talent, but kickstarter rejected the project outright as too freakish.

If that project fails, I am looking to see what other educational uses I can put the data to.

Re:So it's a standard normal distribution (1)

smitty_one_each (243267) | about 7 months ago | (#45657501)

I can't believe there aren't historians who would totally groove on the project.
Get some English majors to contribute historical fiction.

Re:So it's a standard normal distribution (1)

jd (1658) | about 7 months ago | (#45657593)

As for airbrushing, there was an interesting story run by the BBC a month or two back. Apparently Queen Elizabeth I signed into law the right for theatrical companies to kidnap children off the streets without limit or redress in law. It was apparently boasted that not even the children of nobility were safe.

This isn't the sort of thing that gets a lot of mention in productions set in that period.

Norse-style grave goods were also still deposited at the time, apparently some Londoners considered themselves the true descendants. Probably a bit like modern Wiccans, except with big, sharp pointy swords and large quantities of booze.

Other cults doubtless existed before, then and after.

As for medicines, the oldest actual medical book (not a reprint or modernized version) is from 1772. It isn't old enough to get a feel for really old cures, but it is certainly old enough to get a feel for what people were trying. Hemlock (as a drink and a poultice) is well-known, as was the use of mercury. Tea made from ground ivy doesn't sound good and the treatment that calls for the patient to down half a dram of antimony probably wasn't one that encouraged people to call on the doctor very often.

Fireworks listed in a book from 1776 could not be used today - the compounds and gasses produced are too carcinogenic. Companies hiring pyrotechnic experts back then presumably didn't have to worry about sick leave or pensions.

Head lice, tropical diseases brought in by sailors, personal zoos of deadly animals, cholera epidemics, the occasional plague, religious extremists... No, wait, that's modern life, isn't it? When was the Children's Crusade, anyway?

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