#40, you were done before you even started. You're still pushing educational agitprop since you're still denying the past ... which is well evidenced to the contrary to your assertion. I never said to teach the Calculus to a fucking TEN YEAR OLD, you immense donkeycock! I said repeatedly that with the dumbing down of our society we've removed rigorous mathematical instruction from children of all ages. Instead of seeing where children can naturally absorb Algebra, we push it off into the late teens on average. Too many children who SHOULD BE addressing the Calculus, simply pass it by during the grades 9-12 entirely.
Vicious fuckos like yourself have already CONDEMNED children in this magical 7-11 age group. Your contempt for their abilities (unknown until tested by trial, since Humans are different in how they achieve) is leading the tsunami of ghei-instruction which afflicts American students today. It's all watered down and nearly useless. The sheer repetition itself makes us the laughingstock of the civilized world.
Stop holding children back with your Neo-Regressive mentality and start expecting them to TRY TO PERFORM. Remember, fuckwad, that children are by law forced to attend some form of schooling for about 12 years while they are minors. Their time is already going to spent learning. Why not drop Piaget's cock, wipe his nasty cum from your mouth, and insist that children actually learn something during that period of time?
(I'd ask where stupid fucks like you become so heavily indoctrinated. However, I already know the answer: COLLEGE. American colleges prefer to manufacture obedience rather than critical thinking. Obedience is obviously much more controllable and fulfills America's rising Fascism.)
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Anonymous2007-07-22 1:12 ID:L1Af1AhU
I've asserted nothing other than before a certain age children are incapable of abstract reasoning. This is indisputable since a newborn is clearly incapable of this type of reasoning, whereas a fully developed adult is not. Therefore somewhere between these two ages a child must develops this ability. I didn't even go as far as to draw a single conclusion from that one fact. Everything else that you think I said is a product of your own insane delusions.
#42, as long as we both recognize there is a line, but that we're not sure where it's drawn, then sanity has been achieved. What all I've criticized American schools systems for, is still true. The danger of your attitude, is still true. Despite your assertions, you really don't know where any individual child lies on the spectrum of capability, UNTIL YOU SUBJECT THEM TO ACADEMIC TRIAL. An academic trial presumes to instruct. Only after they FAIL to achieve, do you have any rational basis for claiming said child is too young for the subject matter he was exposed to.
Of course, modern ghei-Liberal thinking demonizes any hint of passing on the concept of failure to children. Again, American children handled the concept of failure perfectly OK. It remains as an obvious conclusion that the modern population is simply coddled and mis-served thereby.
Bother to challenge your children, and with your loving support and intent, they'll be better off for it. Continue instead to follow some egghead's highly restricted ideas on child development (mental note: people usually enter the field of child development since they hate children!) and you'll end up undermining what your children are capable of. It's fucking elementary and it applies to all ages of people -- challenge is GOOD, pre-judging incapability is BAD. EPIC DUH!
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4tran2007-07-22 9:58 ID:alTBMYPe
>>36
Assuming he conducted his experiments well, it still only places a statistical limit on humans. Unlike iron spheres, humans have quite a large distribution of non negligible characteristics. It's rather hard to conduct the same experiment with the same 100 kids repeatedly. Each time the experiment is conducted is with a new batch of randomly selected children. Another variable you failed to consider is the possibility that early exposure can lower the age limit at which they can understand abstractions. On top of that, there are tons of other behavorial variables that can affect the outcomes in a very non linear fashion.
>>40
Somehow I'm not convinced that the ability to reason abstractly is a binary capability. Children are not going to wake up one day and suddenly be able reason in such a fashion. It almost certainly takes time for the progression from 0 capability to acceptable capability.
If it's a purely biological thing, please indicate the brain sections that are not properly formed/lacking in neurons/lacking in neuron activity/not chemically in the right state/etc... or is active research still necessary?
>>41
History shows that people were teaching children more rigorous stuff, but that doesn't necessarily mean they understood everything they were taught. Do you happen to have statistics on comprehension rates?
>>42
Your conclusion, or at least statement of current trends, is that all children should be taught according to the stastical average age of developing abstract reasoning.
>>43
You were probably better off not posting >>41 and instead just posting >>43.
Another added bonus is that teaching everybody a standard curriculum is far cheaper and easier than adjusting standards according to a child's capabilities.
For the same reason university students do calc before group theory or lin. alg.: it's a little more work, but it's less abstract and gives them the experience in dealing with functions that they'll need for algebra: more of a comfort thing than a theoretically required pre-req.
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Anonymous2007-07-22 16:05 ID:9+EH4bEN
um i hope you know that the maths curricula is more demanding in other countries, and is successful.
that said, one can only lol at some of the ideas on here. algebra should be started in the final year of primary (elementary school). i think, at least in the uk, the key is to do more once kids are in secondary education. it could easily be more demanding - a sensible target would be to properly start calculus by at least year 11, and preferably year 10 (grades 10 and 9), rather in the final two years. anything else is unneccesary dilution of the curriculum.
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4tran2007-07-22 23:18 ID:mCM0zcei
>>47
Yes, we do know that; that is part of the reason we are condemning US educational policy.
I had calculus in grade 10 and got As in the class by playing Phoenix on my calculator during lectures lol.
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Anonymous2007-07-23 22:29 ID:c+bgrvCA
This is anecdotal, so grain of salt and all that, but there is NO. FUCKING. WAY. I would have been able to do some of the shit you're talking about at those ages.
It's nice to say, "Oh, 4th graders can take algebra no problem! Hell, throw some trig in there! They can take it!" Thing is, I remember seriously struggling with fucking long division in 4th grade. I just didn't get it, and there's no way I could have handled full-on algebra.
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4tran2007-07-23 23:11 ID:6gstW6zj
>>49
Trial and error. If the kid can take it, give them something harder. If they are phailing, then give them something easier.
Long division is just a mindless algorithm. Nobody ever explains WHY it works, which might contribute to a lot of people struggling over it.
Well, #49, that's too bad. Humans are intrinsically fairly bright and in supporting environments they can generally achieve strongly. In your case, you may have been incapable, or the environment was poorly supportive, or your teachers were not good, etc. But in all those cases, the idea of letting achievers ACHIEVE has not been falsified. We can change our educational systems to stop classifying and limiting so much, and become more enabling and unleashing. Stopping the monopoly of the public schools in America is a good way to move towards such an organization.
The entire idea of challenging students to thrive (and FAIL, if necessary!), left the public schools in America about a generation ago, if not longer ... which has all been well enough documented by Charlotte Iserbyt and John Gatto.
Let's see if more students can accept higher reasoning by trial and error, not by resolutions crafted by a professional class with a large conflict of interest.
Sorry, 4tran, I was composing my reply while you were posting yours. You've said the same thing in a more succinct form than I did.
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4tran2007-07-24 1:49 ID:ONVSkfMQ
>>51
Unfortunately, we're still uncertain about the real average capability of humans (I'm not very optimistic), but you are right that everybody deserves a chance to prove themselves capable. Assuming stupidity is a little too contemptuous of children.
>>52
lol, it's all good. Coincidences on 4chan are rather rare these days.
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Anonymous2007-07-24 12:58 ID:AS03LE5M
>>49
>Thing is, I remember seriously struggling with fucking long division in 4th grade. I just didn't get it, and there's no way I could have handled full-on algebra.
That's because you're an idiot.
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Anonymous2007-07-24 13:13 ID:L8IiPbUl
VECTOR CALCULUS
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Anonymous2007-07-24 13:35 ID:ec3KnTN8
>>54
More likely because he hadn't been taught it correctly or wasn't sufficiently prepared, or forgot what he had been taught (which is common because of how we're taught now.)
I think what you're saying is on the mark. Looking back, the way that it was taught was abysmal.
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Anonymous2007-07-25 4:38 ID:pCb8S8Nt
I don't remember if I was taught why it works, but since I explain it often to others, I eventually figured out the whole rationalle myself and how to move from a basic principle to the common algorithm when training others.
To begin, note that multiplication can be understood as repeated addition, and so division can be understood as repeated subtraction -- once that idea is solid, no one should have to ask, "I don't remember, what do I do in this step, add or subtract"
I can't tell you how many times I've seen people forget that the long division algorithm has subtraction in it.