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Preparation for the 21st C and the Information Era. What our kids SHOULD be learning! - Page 3

post #41 of 64
1/26/02 at 11:22am
Thread Starter 
Quote:
Originally posted by parisfrance
Alexander, regarding the book "Goedel, Escher, Bach" you said "never heard of them".
Silliy silly silly me.

In my semi wakefull state, I had mis-understood that these three people had each written a book!



a
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post #42 of 64
1/26/02 at 11:48am
Alexander wrote:
[Dot.Mom, you have no idea how close we really are. I hear you! My old man

Nice Link


quote:
--------------------------------------------------------------------------------
Dot.mom said

Alexander, do tell!!!!! Math and how it is taught is something that really interests me. My father is a mathematician and taught my brother and I in a way that made public school math seem ridiculously un-inspired and limited when we finally got there. Unfortunately, we then did very poorly.
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Alexander wrote:
-------------------------------------------------------------------------------
Once again, the term "math" which I see as a misnomer for arithmetic. Again, the methods refined over the last 150 years are probably fine. But mathematics? That is hard. To start with, kids have to have the right mind, the curiosity that leads them in this direction. If they do not have this, you have nothing.
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The semantics seem the least interesting part of this whole discussion, but I guess we have to agree somewhat on terms before we can continue the discussion (or I guess we can continue to discuss terms...)

I'll give an example of how my father "taught" us "math(s)": When I was fairly young, he challenged me to a race across a chess board. The rules were that we each started out in a corner and could move our piece, in turn, one space forward or sideways, not diagonally, and we were to race to the corner diagonally opposit us. After the first match, my father declared, "we won!" (meaning we tied). We tried again, and again, "we won". We tried several different routes, but to my amazement, it didn't matter what route each of us took. It was just as fast to tranverse the sides of the board as to move one up and then one over through the middle. When I tired of this, he left me alone with the chess board and a played with counting out the squares and seeing how many fewer squares were needed if moving your piece diagonally was allowed. I remember also around this time I became obsessed with measuring the sides of triangles with a plastic ruler, which I am sure now is related.

Unfortunately, the rote drill in public school left a bad taste in my mouth and I had no desire to learn anything about anything. I remember one teacher trying to teach subtraction ot the lot of us squirming kids on a beautiful sunny fall day. She kept saying "3 take away 2 is 1" and I kept asking what happened to the 2 she took away until she finally would no longer acknowledge my question. I hadn't meant to be obstinate, but I had already learned that things don't just "go away" or vanish off the earth. Eventually my parents pulled me out and sent me to a Free School (I think they're called Democratic Schools now-same concept). It was like those years in public school never happened and I was again motivated to learn. I did memorize there, but of my own volition because I wanted the information for something else I was doing.

Gotta run!
post #43 of 64
1/26/02 at 1:34pm
Thread Starter 
Quote:
Originally posted by Britishmum
Alexander - I don't follow the logic in waiting until you need to know something before learning it. Some things, like the abc, or number rhymes, or times tables, or a second or third language, . . .

So why waste a child's brain by waiting? Knowledge is often learned, then followed later by in-depth understanding. I'm not advocating rote-learning, rather that we tap into the natural propensity of young children to learn and use methods that are in tune with their natural learning styles.
Very briefly,

the issue is not whether or not you deny the child from experiencing these subjects, but rather:

1) that we can no longer assume that these subject will have any importance to that child's future.

2) that we must ensure that children learn the "new" skills, adaptability, motivation, be self-secure etc.


Next. Why do you think that children would be wasting their brains if they are not fed this stuff? I look at it from another point of view.

We are wasting children's minds by not allowing them to develop in the manner that evolution intended.

Play.

This is the method of neural programming designed for our species that has has enabled us to do what we can do.

a
post #44 of 64
1/26/02 at 6:44pm
Alexander,

You have misunderstood what I meant by 'wasting' brains. I'm not talking about 'feeding' children's brains this 'stuff' - I'm talking about learning the way that they learn best, (through play) at the time when they learn best (young).

You know that I would argue that times tables are a necessary skill for the future. You say that they are not necessary for everyone, so we should wait until the individual finds that they need or want to learn them. My point was that if we wait until later, when the child/adult may decide that they would be useful, we have missed a window of opportunity to learn with ease, and so the child/adult has to 'work' to learn something that he could have learned through play. Seems foolish to me.

The 'waste' I'm talking about would be in missing this opportunity, to learn young, through play - the way that humans are intended to learn. I believe that learning through music is a form of play.

I agree one thousand percent that children should be developing the way that evolution intended. And music is one of the oldest and most natural ways to learn something, which is why I recommended it to the mother on the times tables thread. Rhythm, movement, actions, dance, music, can all combine to help the child to learn naturally, the way that I believe nature intended.

Dd is sixteen months old and I unashamedly say that we have 'started' the times tables. We sing songs such as 'two four six eight, who do we appreciate? Mummy!" as we stomp downstairs. It's fun, it's play, and it's using her natural propensity to learn. We don't do it instead of anything else, it's just one of hundreds of things we do in a day. I think it would be foolish to waste the opportunity.
post #45 of 64
1/27/02 at 2:22am
Thread Starter 
Essentially I agree with what you say,

except. . . .

This window of opportunity that you describe. There is a window, I agree, but it is not a window outside which we can not learn anything. There is nothing theat can not be learned by a 12 year old in short time that 4-10 year olds take, well, between 4 and ten.

The window that you describe, (actually there are 4) are the periods that the brain develops in specific ways.

Up to about two, the brain is still in it's fetal stage, that is, not yet fully grown. By one the brain has doubled in weight, that is, doubled the number of brain cells. I estimate that this is at a rate of about 100,000 cell a minute! (this is all from memory, so forgive slight errors). By 2 it has doubled again to about 2Kg.

The next stage is the amassing many trillions of connections. (yes it is indeed in the trillions!). These connections represent the sum total of all the child's experiences, and from these, a model of the world is represented in their minds. However, many of these connections create "wrong" representations of the world, which is why children sometimes say such funny things. It is also during this time that certain neural paths are established, and are continuously re-used. These paths

Next comes the elimination of "wrong" or un-used neural paths,

and finally, between 12 and 16ish, the execution stage. This is where cells are eliminated.

If children are able to develop a model of the world in which they learn how to learn, then they are set up to learn anything, for the rest of their lives, not only in childhood. This has to happen before they are 12.

It is worth noting here that the same is true of emotions such as empathy, concern and love, and of abstract ideas such as justice, fairness and ulturism.

If these things are not encountered and experienced in spades by the "execution stage", the connections simply will never be made, as those cells that deal with those concepts will had been deleted as "redundent" by the brain itself.

As for music, yes kids enjoy it. Your child singing 2 4 6 8 tooty tooty tooo and stomping around the floor with you is another indication of what I am talking about though.

Human children are programmed to enjoy copying the older people around them. It is a successfull evolutionary strategy. (Are they enjoying the singing or the copying )

But the idea that we need to take the opportunity "before it is too late" (to quote a common phrase) is to mis-understand what it is that children actually learn while we think we are "teaching". Of course they might pick up tables along the way, (and I insist that this can be done at any time), but in the Information Age, children that have learned to tackle anything that they themselves wish to, will be more usefull than children that have been "pre-trained" with certain facts.

It is not "what you know" that will be useful, but "whart you are able to take on" that will be important.

This is already true. Job descriptions in many countries ask for "self motivated" people.

I've got to get the lunch on, but this is developing into some interesting interactions.

a
post #46 of 64
1/27/02 at 2:24am
Thread Starter 
Sorry dot.mom,

I've just seen your post. Gotta fly, but I'll have a look later.

a
post #47 of 64
1/27/02 at 8:19pm
Alexander, I have always been fascinated by brain development. Although I'm not sure that you are correct that the number of brain cells doubles after birth, I believe that it was only very recently that it was found that the brain is capable of creating any new neurons after birth, and that the number is small. I once calculated that the rate of growth, if averaged out, in the womb is something like 4,000 cells per second. Wow. However you represent the figures, it is amazing. Where did you get the info on the 'fetal stage' of the brain before age two, I'd be really interested in this as I'd never read that.

I do think you are making an assumption that if one believes in helping children to learn academic things (such as times tables) in their early years, one cannot also foster metacognition, and the development of emotional intelligence. I completely agree that these are vital for this century. One aspect of learning does not - and should not - preclude the other, in fact, I believe that they should complement one another.

You are right that there are windows of opportunity for learning, and nobody could surely suggest that it is impossible to learn outside those developmental stages.Otherwise we'd all have had it by age twelve! But the fact is that it is easier to learn some things when you are young. Why make something more difficult when you need not?

As for music, I would suggest that the child enjoys the music as much as he enjoys mimicking adults. Both are natural ways of learning. You would be hard pressed to find a culture, now or in the past, that does not have music and where music is not used for learning. Music can be very much a part of play.

You conjure up an image of my toddler ("Your child singing 2 4 6 8 tooty tooty tooo and stomping around the floor with you") that seems to indicate to me that you have an mental image that is not close to the reality. If it's OK to sing and dance to 'Three blind mice' or 'Five little ducks,' why is it not OK to do the same to number rhymes where you count in multiples?

Incidentally, I still question the assertation that times tables will not be necessary for everyone this century. Just after dh and I had discussed this last night (We're finding the debate very interesting and thought provoking) he went to get a yoghurt for dd. I had bought a different brand, the smaller 'baby' ones, which come in packs of six not individually. He asked how much I'd paid for them. We then both calculated that although they seemed cheaper, they were in fact a more expensive option. We had both used our times tables extensively to come to the same conclusion.

Will our children no longer need to work out such everyday problems when they become adults? Or will those who don't know their tables just pay more and not know it?!!

I fully agree that current systems of education often miss the point, that it is knowing how to learn what you don't know that is important. Metacognition is sadly missing in many of todays 'educated' people. However, on the bright side there are many teachers who understand these issues - you only have to visit the boards for teachers on brain based or accelerated learning to see the interest and expertise in our classrooms.

Also I agree about self-motivation, I think that Kohn hits the nail on the head, although I find some flaws in some of his reasoning. But that's a whole new topic............

fascinating discussion, by the way!
post #48 of 64
1/29/02 at 10:46am
Thread Starter 
file h

Quote:
Dot.mom Said:



The semantics seem the least interesting part of this whole discussion, but I
guess we have to agree somewhat on terms before we can continue the
discussion (or I guess we can continue to discuss terms...)
Terms now discussed here:

Real Mathematics. (Not "Math")

Quote:
Dot.mom Said:

I'll give an example of how my father "taught" us "math(s)": When I was fairly young, he challenged me to a race across a chess board. The rules were that we each started out in a corner and could move our piece, in turn, one space forward or sideways, not diagonally, and we were to race to the corner diagonally opposite us. After the first match, my father declared, "we won!" (meaning we tied). We tried again, and again, "we won". We tried several different routes, but to my amazement, it didn't matter what route each of us took. It was just as fast to traverse the sides of the board as to move one up and then one over through the middle. When I tired of this, he left me alone with the chess board and a played with counting out the squares and seeing how many fewer squares were needed if moving your piece diagonally was allowed.
Perfect. Funny actually. My dad did exactly the same thing!!! So good in fact, I will quote this in Lesson Plans for Mathematics.


Quote:
Dot.mom Said:

Unfortunately, the rote drill in public school left a bad taste in my mouth and I had no desire to learn anything about anything. I remember one teacher trying to teach subtraction ot the lot of us squirming kids on a beautiful sunny fall day. She kept saying "3 take away 2 is 1" and I kept asking what happened to the 2 she took away until she finally would no longer acknowledge my question. I hadn't meant to be obstinate, but I had already learned that things don't just "go away" or vanish off the earth. Eventually my parents pulled me out and sent me to a Free School (I think they're called Democratic Schools now-same concept). It was like those years in public school never happened and I was again motivated to learn. I did memorize there, but of my own volition because I wanted the information for something else I was doing.
Kids want to use their minds. They enjoy it. They develop that way. Your dad provided the environment. Unfortunately, the school you went to tried to "teach" you something altogether different. What a waste. Totally cool that you got to go to a Free School. My folks very nearly did too. I don't know why that did not happen.

As for Free School = Democratic School. That is not accurate. A free school is run by adults for children to do as they please. At a Democratic School, the children to do as they please, but the children run the school for themselves, and employ adults to help create and maintain the right environment.

Dot.mom, you're on my buddy list

a
post #49 of 64
1/29/02 at 1:53pm
Thread Starter 
Quote:
Originally posted by Britishmum
Alexander, I have always been fascinated by brain development. Although I'm not sure that you are correct that the number of brain cells doubles after birth, I believe that it was only very recently that it was found that the brain is capable of creating any new neurons after birth, and that the number is small.
I checked.

Brain weight is directly proportional to No. of brain cells.

Brain increases between 2 and 3.5 times between 0 and 2.

Brain cell production peaks at 250,000 per min!!!

The figures ARE amazing aren't they.

Quote:
BM said:

I do think you are making an assumption that if one believes in helping children to learn academic things (such as times tables) in their early years, one cannot also foster metacognition, and the development of emotional intelligence.
Unfortunately, not an assumption. The casually observed tendencies in children are all around us, (much resourses in the current bulky Industrial Model Education System is designed to either pick up the pieces where it fails with "special educators", drugs and theropists, or to co-erse children ever more effectively to comply with the will of the "Body Corporate"), and teachers whose eyes are still above the water know it.

Whether or not it is a straight line graph, or gradual decline with a catastrophic fall in the middle, I don't know, but one thing is for certain. More study does not equal better accedemic results, or better understanding, but you do get kids with NO motivation, and ofter little or no empathy, tolerance, creativity or common sense.

This is the story everywhere in Japan, where the Industrial Education Machine has been taken to an extreme.

Quote:
BM spake:

You are right that there are windows of opportunity for learning, and nobody could surely suggest that it is impossible to learn outside those developmental stages. Otherwise we'd all have had it by age twelve! But the fact is that it is easier to learn some things when you are young.
1) The windows that exist do close. But they close, not for learning "things", but for "how to learn how to do things", which is what I want people to realize is one of the most important skills to have in the InformationEra.

2) otherwise we would have to have it by 12. Exactly, but I take issue with this idea that it is easier to learn "things" while you are young. It does not. Children are patient learners while they are interested.

"If it's OK to sing and dance to 'Three blind mice' or 'Five little ducks,' why is it not OK to do the same to number rhymes where you count in multiples?"

I have never indicated this. But I know you would agree that you would stop immediately that he wanted to. A child in "class" at school does not have the same power, or choice. Secondly, songs and stomping are perhaps non-effective methods of teaching older children everything that is considered important to children in the age range, say 6 - 12!!!

"Incidentally, I still question the assertation that times tables will not be necessary for everyone this century."

There is no such assertion. The idea is that there may not be and there may well be requirements for many other "facts". The ability to re-train, adapt, land recognise what the relevent facts are, are the skills our children need.

On your yoghurt story, I can only say that you are products of the Industrial Age. It might be posible for an Information Era person to do the same calculation in the same way, but more likely it would not matter that he could not. What matters is the they are able to find a way to get at the same result. And a calculator might very well be the implement used, (or it could folding bits of paperor who knows???)

Of course our children may need to work out such everyday problems when they become adults. But the methods of solving will be designed by them. It may even be that they find it easier to do all this stuff by learning their tables tables, but I think it more likely they will just pay more, and not care.

"However, on the bright side there are many teachers who understand these issues"

This, unfortunately goes nowhere to enlightening the parents, the school boards or the State Education Councils. We are lonely soldiers, fighting to keep the children thinking. The course I designed is to get children thinking again. Once they are doing that, they learn English all by themselves. It's magic. It works. If parents "discovered what I was doing, or what I was not doing, I'd go bankrupt in a week

a
post #50 of 64
1/29/02 at 3:57pm
Quote:
Originally posted by Alexander
[As for Free School = Democratic School. That is not accurate. A free school is run by adults for children to do as they please. At a Democratic School, the children to do as they please, but the children run the school for themselves, and employ adults to help create and maintain the right environment.


a [/B]
I never new there was a distinction, which I guess is proof how well our Free School did. I thought we did run the school!!!! But now that you mention it, we did not practice voting for any major decisions, only minor ones (like naming the guinea pig-"Stench" poor thing, or where to go on field trips). I do wish we had either a Free School or a Democratic School in this area for our daughter.
post #51 of 64
1/30/02 at 3:36am
Alexander,

Do you have a link for the info about brain cell growth? My searches only throw up the recent research showing that the brain can grow new cells, which challenges the old assumption that all, or almost all, cells were in place at birth.

I entirely agree that the ability to learn and to know how to learn is more important than the content of what you learn. Also I am convinced that emotional intelligence is more important than IQ. However, I am still not convinced that this means that learning things such as the times tables precludes a child from becoming emotionally intelligent. I believe that is is how these things are learned that is of vital importance.

As I said, I do not advocate 'stomping' around the room chanting times tables! I'm talking about tapping into the natural way that the brain learns. That means using multi-sensory means and being mindful of all forms of intelligence (Gardner's multiple intelligences being a good model here.) Using music is a part of this, but not stomping and rote learning! It's called 'play' - which we both agree is vital for effective learning.

Music is also used effectively by many teachers with older children in the age range you talk about, ie 6 to 12. Physical movement is sadly not used enough in many classrooms, ignoring the brain's need for movement. Again, I am not advocating the learning of times tables in place of investigations and practical maths, but I believe that things like this can be incorporated into a child's day in a way that gives movement, a break, and FUN!

You say that your assumption that helping children to learn academic things precludes them becoming emotionally intelligent or metacognitive, is not an assumption: "The casually observed tendencies in children are all around us"

Can the apparent lack of emotional intelligence in children around us be attributed entirely to the content of what they learn, or maybe to the way that the learning occurred? Personally, I think that the method of learning is the deciding factor. I'm sure that a lot of inappropriate material is covered in schools, but it is the method of delivery that is more likely to lead to poorly motivated children.

I also think that there are also a lot of other factors that lead to unmotivated youngsters, other than the failings of a school. There are many many reasons for a child lacking in emotional intelligence - not least, being raised by parents who lack it themselves! Maybe home schooling is ideal, but what about children whose parents lack this motivation or emotional intelligence? Which children will end up with a lower EQ, those who are raised by parents with low EQs, or those attending imperfect schools?

You are right that children in schools do not always have the opportunity to say no to the learning diet being offered themm and you paint a sad picture of schools. I am more of an optimist, and believe that there are some amazing teachers out there who do strive to understand these issues. They have to work around increasingly stringent legislation nowadays, which makes their job harder, but I believe that it is still possible to deliver a curriculum in a way that fosters the qualities that I think we both agree are essential for the adults of the future.

Maybe children in the future won't care that they can't work out things like the cost of their groceries,or how to split the bill in a restaurant. How sad! I cannot imagine anything more frustrating than being unable to do such a simple calculation in my head and having to get out a gadget to do something that my brain could do with ease if it had been given practice.
post #52 of 64
2/1/02 at 7:27pm
Alexander, I've searched some more and still can't find a reference anywhere to brain size being proportional to the number of brain cells. Every reference I have read states that all neurons are in place by birth, or 'almost all', or 'essentially all'. Hence the excitement of last years research showing that the brain can form new cells, and its implications for treatment of conditions such as Altzeimers.

I thought that brain growth (ie size increase) after birth is due primarily to continued myelination and the phenomonal rate of synaptic connections being made.

I'm happy to be corrected though, do you have a reference for your theory?
post #53 of 64
2/2/02 at 5:35am
Thread Starter 
Quote:
Originally posted by Britishmum
Alexander,
Do you have a link for the info about brain cell growth? My searches only throw up the recent research showing that the brain can grow new cells, which challenges the old assumption that all, or almost all, cells were in place at birth.
No, you are right. I may have made an incorrect assumption that increased weight = increased number of cells. Why should it not? but anyway, a quick search thew up this:
Neuroscience for Kids - Brain Development

a
post #54 of 64
2/2/02 at 5:47am
Thread Starter 
I still think the number of cells increase, because the fetal brain is capable of cell division.

a
post #55 of 64
2/2/02 at 1:31pm
Alexander, thanks for the link.

That confirmed what I thought, that there may be a very small increase in neurons after birth, but essentially they are all there. Their job after birth is to get to work, or to die off.

Phew, I thought I'd been getting it wrong all these years. Just like those scientists who just found out that the adult brain DOES produce new neurons anyway!
post #56 of 64
2/13/02 at 10:26am
Hey, I found this book at the library yesterday and immediately thought of this thread. The book is: The Five Faces of Genius--The Skills to Master Ideas at Work by Annette Moser-Wellman.It is geared toward the business worker and the "thinking skills" that one needs to be sucessfull. Is anyone familiar with this book? According to the jacket, the author owns a consulting firm that "offers workshops in creative business thinking." The "Five Faces" that she writes of include things such as: being able to visualize in detail, being able to observe details in things around us, finding connections between seemingly unrelated things, having perseverance and taking risks, being able to simplify or "distill ideas to the essence."

It amazed me that adults were getting together to be taught these things...to me, it all boils down to creativity and problem-solving. It would seem to me that life, in general, would offer us many opportunities to develop these skills and that classes to learn these skills wouldn't be necessary. However, some big name companies are using her services and her book got published, so I may be wrong---what do you all think? Are these skills that need to be TAUGHT?
post #57 of 64
2/13/02 at 7:27pm
Joan, this book sounds interesting.

I think that these are skills that should be fostered, rather than 'taught'. I don't think you can teach things like perseverence, or resilience, or visualization. But you can foster them - or not - in a learning environment, or in a work environment, as this author writes about. With regards to education, I think that teachers need to be mindful about these sorts of qualities when they plan lessons. Content can be delivered in numerous ways, only some of which will foster these lifelong qualities in students.
post #58 of 64
8/17/02 at 10:17pm
im just being a trouble maker today and bumpin stuff
post #59 of 64
3/7/08 at 1:52am
Yes, very old thread!

subbing so I can come back and read
post #60 of 64
3/10/08 at 7:31am
Old thread,but info that needs to be restated OFTEN!

www.keypress.com Offers miquon,algebra and geometry from a deductive rather than inductive approach.
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