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Preparation for the 21st C and the Information Era. What our kids SHOULD be learning! - Page 2

post #21 of 64
I don't think we can ignore arithmetic, it is something that we use daily. And in the process of using it, the kids learn about it. When they are interested in it, they learn it quickly. No need to do all the drill and repitition. All the time can be much better spent!
post #22 of 64
wow! this is really exciting! this helps my mind so much! so, this means that, as unschoolers, my kids can learn arithmetic through our everyday activities as they need/want to, and if they have some brillant, genetically-suprising careers as architects/engineers/mathmaticians destined for them then they will naturally gravitate to these feilds without me nudging them towards formal "math" drills etc...

See, I've been so inspired my by study of "unschooling" except for this nagging fear that no math will ever happen in our house without some formal work on it, and then what if they never get to discover some great talent they might have in a math feild...

but I went up to calculus in high school, and have forgotten all but the most general of impressions of what it all was about, and not used any of it! what a waste!

i will not demand that dd spend a second of her precious life doing anything that she does not choose because it interests and empowers her.

and that's my feeling about our new age whatever you call it: now its more important to love learning in general than to have learned anything specific, because then you can always dive in and learn whatever arises that you need.

more important now to know yourself, know who you are and what you want each moment. instead of just knowing your tables and rules and facts which might not even matter to you ever.
post #23 of 64
Ok. So I'm compiling a list of books to read on the subject because this stuff is really compelling and I need to do a lot more reading if I'm going to really understand what you're talking about. So far you have...

Flatland
The I hate Mathematics Book
Math for Smarty Pants
The Book of Think

Any more? Any websites?
post #24 of 64
A very gentle reminder to all, to keep posts respectful and curious, especially when feeling frustrated or confused.

While I have no specific info. to add to this discussion of arithmetic vs. math vs. maths, it is a fascinating and eye opening inquiry. Let's continue to ponder it in the spirit of learning.
post #25 of 64
Thread Starter 
Quote:
Originally posted by Lucy
so is that your reccommendation, that we ignore arithmetic?

Absolutly. Unless a child either shows a natural inclination to do it, or towards methematics, or if that child requests such assistance.

Quote:

Do you teach math? Or do you discover this on your own?
Terminololy terminology.

Math=arithmetic (+ bits)
Maths=mathematics

You can teach Math.

You can't teach Mathematics. (Well not easily anyway)

People do discover it on their own. Even we ordinary mortals who are not destined to become Professors! We do it quite naturally.

a
post #26 of 64
Thread Starter 
Quote:
Originally posted by parisfrance
Alexander, have you ever read "Goedel, Escher, Bach"? It's about the connections between math, art, and music. I haven't read it yet, but my brother highly recommends it (and the authors second book whose title escapes me).
Never heard of them, and getting good books out here is a little hard. I'll keep my eyes open the next time I'm in the UK, or if I get to Boston this summer.

a
post #27 of 64
Thread Starter 
Quote:
Originally posted by larsy
I don't think we can ignore arithmetic, it is something that we use daily. And in the process of using it, the kids learn about it. When they are interested in it, they learn it quickly. No need to do all the drill and repitition. All the time can be much better spent!
Quite right. We do not drill our children to walk at 6 months so thaey can take the opportunity to become olympic runners!

The very fact that children face it everyday in their real lives means they will get a grip on it.

And if they don't encounter it everyday, then by default, no need to do it.

a
post #28 of 64
Thread Starter 
Quote:
Originally posted by Wildflower
wow! this is really exciting! this helps my mind so much! so, this means that, as unschoolers, my kids can learn arithmetic through our everyday activities as they need/want to, and if they have some brillant, genetically-suprising careers as architects / engineers / mathmaticians destined for them then they will naturally gravitate to these feilds without me nudging them towards formal "math" drills etc...

Snip. . .

more important now to know yourself, know who you are and what you want each moment. instead of just knowing your tables and rules and facts which might not even matter to you ever.
1 million exactly s.

Your post is SO brilliant, everyone should read it.

a
post #29 of 64
Thread Starter 
Quote:
Originally posted by k'smami
Ok. So I'm compiling a list of books to read on the subject because this stuff is really compelling and I need to do a lot more reading if I'm going to really understand what you're talking about. So far you have...
Flatland
The I hate Mathematics Book
Math for Smarty Pants
The Book of Think
Any more? Any websites?
Careful now. The thread was designed to look at the skills required for the Information Era, of which our comprehension of what mathematics or Math we should teach is a part. (not that I mind the current direction of the discussion at all)

What I want to say is that is is not only math (or mathematics) that we need to re-think when we prepare our children for the 21st C.

It is everything that we currently describe as education.

Thus, a general case (Now that's mathematics ) needs to be understood.

As for books. . . I would sell you mine, but before I could finish it, I discovered someone else had already done the job :

this site to look at some online chapters

but you need to read Free at Last.

By the same author

http://www.mothering.com/14-0-0/html...hools103.shtml

Anyone who is reading this book could create a Discussing Free at last Thread. I'll join

a
post #30 of 64
Thread Starter 
Quote:
Originally posted by Just Wondering
IMO.........This whole discussion is a total waste of time, Alexander, until you define what you mean by REAL MATH. I tried to find a definition of this by reading through your verbiage in file a to file f. There was nothing.

Snip

So until you actually define yourself precisely, so that people can understand what you mean, the discussion is totally frustrating and confusing. To the point of being a waste of time, if nothing postive or useful can be taken out of it.
Well everything I snipped I basically agree with.

As for a definition, I want to start a new thread for that. This is not meant to be a discussion an what Mat or maths is per se. I am trying to keep up with all these wonderful posts!

As for it being a waste of time? No. We are just miandering to the right (or better) answer.

This is new ground for many. Not all our ideas are fully formed, and if I were to just jump to the end, I'd lose people.

That can easily happen.

But a definition. Yes. I'll set up a new thread soon.

a
post #31 of 64
Thread Starter 
Quote:
Originally posted by truly_sarah

Alexander, we want to see the lesson plan, or some other details of what you're talking about.


Sarah
OH Juice!!

OK. I have many. Can I get back to you on this?

Phew! I think I caught up

a
post #32 of 64
Alexander - I came over here from your link on the times tables thread, where you say that learning tables is time wasted in this day and age. I don't have time to wade through this entire thread; I tried but found it extremely dificult to follow!

Anyway, I just asked dh if he needs times tables in his work, which is at the cutting edge of technology. He laughed and says that he uses them all the time. Certainly, he could do his job without them, but he would be slow and ineffective and not contribute to the team in the way that is expected. (and would probably not be useful enough to the team to be employed by them!)

Apparently the mental dexterity to manipulate numbers is essential. Often he has to mentally computer a load of figures to decide which direction to take before calculating accurately. He uses times table knowledge to do this all day every day. If he didn't have the knowledge, he would spend more time calculating and less time being creative. In team settings it would be impossible to contribute if you couldn't just 'see' the approximate answers to these sorts of problems in your head.

I once went to a lecture once on accelerated learning with him. The speaker gave a quick maths 'quiz' where he demonstrated that the brain often 'tricks' you by seeing what it thinks it should see, not what the eye actually sees. Dh was the only person in the room who didn't get the wrong answer. He just 'saw' the correct solution, in the way that you say that you had a feel for CAD. He couldn't understand why others got it wrong.

I just can't see how knowing times tables along with understanding them cannot be an essential tool for this century. Even if you don't do the same sort of work as my husband, don't we all need to balance our cheque books, split bills in restaurants, work out how many potatoes we need for a dinner party, and so on and so on? I"m not advocating hours spent in drilling children in times tables, and believe that there are faster and more fun ways of learning them, but I can only imagine how incompetent we'd all be if we needed a calculator for all these everyday things.
post #33 of 64
Thread Starter 
Quote:
Originally posted by Britishmum
Alexander - I came over here from your link on the times tables thread, where you say that learning tables is time wasted in this day and age. I don't have time to wade through this entire thread; I tried but found it extremely dificult to follow!
No.

I didn't say that it was a waste of time for everyone. Just those who end up not needing it in the end ( almost everyone). My point is that we learn much that becomes redundant knowledge. We are able to learn what we need when we need it.

I think you'll find we are madly agreeing with each other.

The rest of your post concerning your DH, and his need to continuously use tables etc, nicely strengthens my point. Those that need to use them, do.

Indeed, the illustration you provide of the seminar on accelerated learning goes further to re-confirm my point. Those that do not continuously use a particular branch of mathematics (or music or literature or cooking) are not practiced, and struggle.

How much intelect does it really take to learn the tables? Almost nothing.

The knowledge gained concerning the intricate relationship between all the numbers comes from use, not pre-prepared lessons.

I sympathise with the fact that this thread is sooo long : Sorry about that

I too have mentioned that it was only a real life problem demanding real knowledge and practice that enabled me to achieve insite into trig.

So.

The argument is not that arithmatic, tables, physics, or anything is not needed in the modern age.

It is that it is not clear what we will need most of the time. Wait till you get there, and then expend maximum energy on what is entirely relevant.

Hope this clarifies things.

a
post #34 of 64
just because you don't "USE" information.
doesn't mean it is a waste of time or a bad idea.

information is knowledge, knowledge is power.

i might not ever use a binary number system, but learning that was a great experience and i feel it widened my mind.

i think we should focus on teaching our kids MORE not LESS.

we only use a small part of our brains. I think we should try to find ways to use the entire brain and increase learning.

PS.
how do you "Think" we got into the modern age?

we didn't get there by not doing math that is for sure.

computers can break....and people are needed to put information into computers in the first place. if you don't understand your times tables, how are you going to program a computer to solve them for you?

im so confused by this post.
post #35 of 64
Thread Starter 
Quote:
Originally posted by Just Wondering
It's cheaper.
You don't have to buy batteries.
You don't have the problem of getting the thing, to find that the battery is flat.
No, we don't have solar ones....
anyway, the brain enjoys it....
They still make calculators that require batteries????




I don't know how seriously to take these comments. Either you are badly missing the wood from the trees, or giving me a good dose of sarcasm

I doubt you would stoop to sarcasm (hope).

Incidentally, there seems to be a mis-conception (not un-usual) that the Information Era = Technology.

It does not.

It is about problem solving, adaptability of cocepts, and salient ideas.

Hope this helps.

a
post #36 of 64
Alexander, regarding the book "Goedel, Escher, Bach" you said "never heard of them". "Them" who? If you've never heard of the books, you should definitely read them, I forgot to mention that my brother is a mathematician, just finished his PHD in math. He doesn't like any math with a practical application (read: someone will pay you to do it!! LOL my parents are SO sad). Anyway, he and many other people I know have said it's facinating, they never thought about math in the same way again. (I hate math, that's why I never read it). If the "them" you never heard of is the three guys in the name, Goedel was a mathematician, Escher is the famous artist who drew optical illusions (like two hands drawing each other), and Bach is THE Bach musician we all know.
post #37 of 64
JW, I thought your post was very funny. Sarcasm doesnt seem to be your style, am I right? I confess to not even having a calculator, I certainly have never carried one around with me.

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, can be learned easily through play in the early years, at the time when the brain is most able to learn. The window of opportunity then starts to close. There is no limit, as far as anyone can tell, to how much can be learned at that formative stage - it's not a case of 'learn your times tables and you won't have room to learn your alphabet or a second language.' (I have never understood, incidentally, why most schools start teaching a second language at the exact time that the window for language acquisition is closing.)

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.
post #38 of 64
Thread Starter 
file g

Quote:
sleepies said:

just because you don't "USE" information doesn't mean it is a waste of time or a bad idea.
When you say "it", do you mean

1) to study

2) The the information

3) learning the information

Any way, no, you are maybe right, but it does depend upon whether it was learned willingly or not, or whether it was enjoyed.


Quote:
sleepies said:
information is knowledge,

Ahh, come on sleepies! Information is only information. Data is just that. Data. It is context and relevance that turns it into knowledge.

Quote:
sleepies said:
knowledge is power.
Hmm. Application of the old cliche here eh!

No, sorry. Only relevant and timely knowledge is power, not knowledge in a vacuum..

Quote:
sleepies said:

i might not ever use a binary number system, but learning that was a great experience and i feel it widened my mind.
But did it have to be the binary system? Why not anything else? And who decided that you should study that? In the great plan of things, all subjects are worthy of study. What makes one more relevant or important than another in the Information Era is the decision of the student to study it, not the decision of the teacher, a school, or some faceless (and probably dead) beaurocrat.

Quote:
sleepies said:

i think we should focus on teaching our kids MORE not LESS.
More what? More . . . wax candle making (in case the lights go out)? How to tie a hog (so you can more easily take it to the market)? or sharpening a quill (in case biro doesn't work)? or pale mending (in case your pipes stop)? Shoe-ing a horse (essential if you it loses one on a long rocky trail, far from home)? (20th century one here) . . . using a slide rule for faster calculations. I doubt most readers even know what a slide rule is, much less remember how to use it's logarithmic functions to do multiplication?

The point is, time moves forwards, and certain skills and knowledge become redundant as technology rolls along.


Quote:
sleepies said:
we only use a small part of our brains. I think we should try to find ways to use the entire brain and increase learning.
Forgive me, but this indicates a common misconception that "the more brain you have, the smarter you are or the more you can do". This is unfortunately utterly wrong. Most of the brain (in functions, if not size) deals with basic functions such as sight, digestion and animal behavior. Only the frontal lobe helps us to be what we are.

Smarts and the amount we are able to hold in a function of the way our brain cells are wired together, not the amount we have. Indeed, I would suggest that one day, it will be shown that too much brain in certain places actually makes people less smart. This is because the processing that is done in the parts of the brain with which we think is terribly local, and to reference to other parts that have more data or computed concepts is made harder by the fact that linking through too much brain is all but impossible.

Thus it is possible for people to use large amounts of their brain, but be quite dum, or use small parts of the brain, extremely efficiently, with wonderful models of the world in which they live, and be very smart.


Quote:
sleepies said:
PS.
how do you "Think" we got into the modern age?

we didn't get there by not doing math that is for sure.
Brilliant point, which wonderfully re-illustrates the point that I make. Namely that the "Modern World" (Industrial World) was established and maintained by a rigorous process "pidgin holing" a number of vital skills (vital for the maintenance of the Industrial Economy) and ensuring that as wide a variety of people were exposed to this as possible. And you are right, Math (arithmetic) was an integral part of that process.

There is only one thing though.

The Industrial Age began to end in the late 60's in the US, 70's in the UK, Late 70's in Europe. In fact, out of all the industrial powers, only the Far East has yet to catch up. Now the world is moving through a kind of "overlap" time, where the "old Industrial Model Society" has to co-exist with the new "Post-Industrial or Information Era Model Society".

One of the deepest ironies of this transition is those economies that have benefited the most by using the Industrial Model for their Society and Economy, are the worsed placed to take advantage of the Information Era. This is because the mind-set required is so utterly different. In fact, I can not think of how opposite they could be!

But more on that on another post.

Quote:
sleepies said:
computers can break....and people are needed to put information into computers in the first place. if you don't understand your times tables, how are you going to program a computer to solve them for you?
society will not collapse because a computer breaks, I assure you. There are all kinds of back up systems in place in case of that eventuality.

Also, I promise you, you do not need your times tables in order to be able to program well, and if you did, most programmers would find it a trivial matter to learn, or use the calculator found inside every computer


Quote:
sleepies said:
im so confused by this post.
Er, thread you mean

And of course. You and most of the people who live contentedly in the Industrial Economy, oblivious of the storm that has already hit the shores.

Hope this helps

a
post #39 of 64
Thread Starter 
Quote:
Originally posted by Just Wondering
Yes, my calculator requires batteries.
No, I kid you not.
WOW! Really! But this explains alot about how ou see the world.
Quote:
JW
why should I stoop to sarcasm?

I appologise. I was not sure. Many who encounter this thesis react in many kids of negative ways, sarcasm being second only to straight disbelief, which is understandable given that everything they know to be true, that works for them, the "solid ground" so to speak is threatened.

Forgive me.

Quote:
JW
Anyway, see my post on "tables".
By the way, a penfriend in Japan just sent me a fancy one. But its so small my fingers get claustrophobia.
Stop it! You are making me giggle

Quote:
JW
My husband says that if I bothered to go to Auckland and look in a fancy business store, I could get one.
I guess people here of my age, just don't use them that much..
And there, unintentionally, you beautifully illustrate the problem facing people who have grown up successfully in the Industrial Age, facing the idea that what worked for you should not work for the next generation. Not even to use or need a calculator demonstrates clearly that you are of the generation that did not require one, due in part because of the training you underwent.

Another generation along, and we may have kids who don't even have to use a calculator, even to get sophisticated calculations done.

But, just as surely as the knowlegde of lighting coal gas lights (essential in Victorian England) has become redundat as a life-or-death skill, so to will much of what we now regard as essential learning.

a
post #40 of 64
A perspective to consider...

The above discussion about calculators reminds me of when the young me discovered a slide rule and instruction book in my mom's math teaching bookcase in our basement. I undertook to learn it, and there was a HUGE discussion in our house of whether I should be WASTING my time on that, because this wonderful NEW DEVICE (called the calculator) had just been invented. My dad said, well, calculators are expensive, we can't get her one, so she can use the slide rule, it's easily replaced. My mom said, well, we SHOULD buy her one because she will NEED it. But I don't think they had the money. In a year we were amazed...you could get one for FREE at Radio Shack.

My prediction is that this discussion will be replaced in another decade or sooner, by a discussion of whether our kids should get a wearable transmitter that will enable their brains to become instant calculators...whether it is OK to bypass learning arithmetic of any sort with an artificial device and whether the dependence on it is OK or not...and whether job applicants/university applicants can be asked if they have such device. Then there will be all sorts of discussions about public funding such as we are having here in Maine with the laptops in the schoolrooms and only a few pilot classrooms getting them. I have yet to see even calculators being issued to students...yet all of a sudden they are talking about issuing laptops. Well HELLO! What's up with that?

Sarah
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