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

[Alexander]

In another thread, this subject cropped up. It is something that I believe is too important not to have it's own thread.

I hope it will be a place where those not yet familia will be able to ask questions or post their own observations.

Originally posted by larsy

Alexander, I for one would be glad to hear more about the skills needed for the Information Age over the Industrial.

Origionally posted by Wildflower
I could go on, I've been doing a lot of research on unschooling and its benefits over public ed lately...Alexander, I'm also interested in what you mentioned about the Information Age...

Hi guys,

sorry for the delay in reply.

Actually I consider it to be the Information Era, not Age, because, as I understand it, an Age is shorter than an Era. What we are entering now, is surely to last longer than the Industrial Age, which really started only in the mid 19th Century, and is all but over in the US and Western Europe.

As for the skills that are required, they are things like:

Problem Solving,

Being Self Motivated and Self Directed,

Being able to set your own goals,

Being able to take Responsibility for things,

Being able to Identify Choices,

Having Interpersonal skills, (negotiational skills, bargaining skills, team-work and management skills, and family skills)

Being able to take on New Skills easily and quickly, that enable you to achieve your goals.

And if you are not a speaker, English, todays "lingua Franca".

There are more, and I have written about it before, so I'll see if I can find it and post it. Anyone got any other ideas?

BTW, you will notice that I do not include things like reading, writing, arithmetic, computer skills, science or knowledge of the internet. The assumption that these are needed is an Industrial Age mind-set.

The truth of the matter is that these may, at the moment, be important skills for survival and day to day living, but non of them are certain to retain any relevance in the Information Era. Indeed, I am not the only person to argue that what is mis-named as "Math" in modern American schools, is an acute waste of time. Real Mathematics is found almost nowhere in any curriculum in most of the Industrial world. UK schools made a brave attempt in the late 70's and early 80's, but it did not penetrate everywhere, and it was soon diluted. The worst culprits, (or victims) are the Japanese, Koreans and the Singaporese.

Looking forward to more comment on this.

a

a

[Lucy]

ok, so whats wrong with the math? I would love to know since I have been doing singapore math with dd (5), we homeschool. It looks very real to me, hands on, real world stuff so far, but of course this is a very early level.

Would love to hear what exactly you mean.

Thanks!

[truly_sarah]

Alexander, yes. I'm very interested too to know what's the matter with the Singapore Math. Your ideas are usually well presented and thought out and have a firm foundation, so I will consider very carefully any facts/ideas you have to offer.

Why are these countries both victims and culprits simultaneously? How should math be taught ideally?

I am always tinkering around in my head with a number system that is based on a spiral number line instead of a straight line. When the teacher first presented the number line in first grade (I remember well the day) I found it suspicious, since in the real universe there are no straight lines. But it was intellectually challenging to go along with the mental gymnastics and computations of the system presented and it has of course served me well - my checkbook computations match up pretty well with the ones suggested on the back of my monthly statements!

I'm thinking about reading Flatland with my son...isn't that the name of the book that shows everything in 2 dimensions? I would someday like to explore different numbering systems with him and math as logical thinking instead of just numbers and rules/axioms/theorems. Is that what you mean?

Sarah

[Dot.mom]

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 rediculously uninspired and limited when we finally got there. Unfortunately, we then did very poorly.

[Alexander]

OK.

I can't just give "the" answer straight and complete, it is too boring to just have to wade through. (+ time. I'm really busy trying to start the home page for our school )

But I have read you posts, and would love to find time to address you all.

But to come back to the subject. Math isn't Maths. What you are dealing with is arithmetic. Got that? The manipulation of numbers, (angles for geometry).

And if you wish to ensure that your children learn to do that, then it is a noble cause, and I for one will not critisize it at all.

But it is arithmetic.

And this will do little for someone growing up in the Information Era.

Mathematics is not only about the relationship of ideas, and how these inter-relate, but also about the way people discover and internalize these concepts. Notice the word "concepts" here, not numbers.

There are 2 ways to "teach" too.

1) you can show by demonstration that something is true / exists / is beautiful etc, or

2) you can create an environment inwich a child "comes across" the same.

1) Industrial. Easy. Done for a purpose.

2) Information. Hard. done only because a student's nose takes them there.

How can we have maths with no numbers?

How do I count the ways? LOL (that was a joke ok! )

Take prime numbers.

First, is it important that any child MUST know what these are?

2nd, does it have to be numbers that are covered in a curriculum? (the concept can be covered spacially)

3rd surely, the thoughts of a child that recognised what they (primenumbers) are, through their own volition, and can recognise any connections to anything else, is deeper than that of a person that has simply been told and remembered what they are?!. . . Indeed, such a child has indulged in mathematics, not "Math".

Suppose I presented a lesson on prime numbers that invoved NO NUMBERS! Would that be acceptable to those teaching "math"?

I have actually created such a lesson. And thus far, found Industrial Age "Math" teachers very uncomfortable with it.

I even "gave" the lesson to a Junior Professor of Mathematics here in Japan, and it took a goo hour (and some hints, coaxing and prodding) before he saw what he had been studying. Of course when he understood that we were dealing with primes, he could use his own internal model to quickly solve all the problems, and my little "lesson" became redundant.

BUT the style gave new insite to this gentleman, and he loved it.

So, I say that real Mathematics is about the discovery of manipulations and relationships, not having them presented to you so you don't have to think about too much. Anything that is given to you that becomes self evident is junk.

Of course I have heard many argue that in the "real world" we don't need that many mathematitians.

Well, in the "Information World" we sure don't need people that rote learn their times tables!!!!!

Get real guys, even the Japanese use calculater to add up the price of your coffee and cake!

There is much I have not addressed. I'll get round to it.

I am very aware that not everything I have written is clear, and I appologise. Please DO bug me about the bits that come across lumpy. (It's 1:30 am now, so I must get to bed).

Truly Sarah:

Spiral? Wow! Internalized or what. Great!

Dot.Mom, you have no idea how close we really are. I hear you! My old man

Hope this begins to help, but if not, feed-back please.

a

Edited slightly for grammatical clarity.

a

[sleepies]

WoW that post went right over my head
guess it is a good thing im not home-schooling.
maybe it was the fact i got only formula and not breastmilk....that i don't understand.

what are you talking about?

oh. im sure it is me and not you.

but, im lost

[truly_sarah]

Reading a book like Flatland might be a start...but Alexander, we want to see the lesson plan, or some other details of what you're talking about. My imagination won't stretch that far today and I'm going to accuse you of maliciously teasing us...oh far worse than the scent of mere chocolate or coffee!

Thanks in advance.

Sarah

[Lucy]

sleepies, oh no its not just you, unless its just me and you. lol!

If you could be a little more precise Alexander I would love it!

btw I use my memorized times tables all the time to calculate stuff in my head, like at the store ect.

Now if by creating the environment where a child can learn a fact you mean for instance, letting them help you bake a cake and measure the ingriedients and as a result learn fractions, instead of learning from a worksheet, than I understand and agree with you that much. Is that st like you mean?:

[larsy]

hey, Alexander, thanks for posting on this! I agree! It's great to see this articulated- I'm been stumbling around in this and not seeing the forest for the trees.

short on time now- I just got a copy of Flatland, thanks for reminding me of it! We just got a hold of 'The I hate Mathematics Book' and 'Math for Smarty Pants' and 'The Book of Think' and various others by these same authors. I think these are definately going in the right direction! We have devoured these and use the concepts daily. What fun!

gotta run, thanks!
larsy

[dfoy]

Alexander,

I'm a teacher, too. Taught "math" to special education kids for years (I am in collaborative classes all day teaching high school science now and making the regular curriculum accessible to students with special needs). I agree, its the concepts that count (no pun intended). Same thing with grammar. Do kids really need to know what a gerund is to write a good paragraph? Of course not!

Students do need to know that the answer that they get on their calculator makes sense for the information they are asked to get. You teach that through concepts, not repitition or drill.

Mathematics is patterns. I learned a lot about math when I was little through music (time signature, augmented 5ths, etc) since my mother was a musician.

[Alexander]

Originally posted by Lucy
sleepies, oh no its not just you, unless its just me and you. lol!
If you could be a little more precise Alexander I would love it!

Precision is on it's way.

btw I use my memorized times tables all the time to calculate stuff in my head, like at the store ect.

and I question if that is needed in this day and age. Should we be allotting a good part of childhood to this activity?

I say no. In fact I say ABSOLUTLY NOT! We are wasting life no less.

Now if by creating the environment where a child can learn a fact you mean for instance, letting them help you bake a cake and measure the ingriedients and as a result learn fractions, instead of learning from a worksheet, than I understand and agree with you that much. Is that st like you mean?:

No.

This is a good environment for teaching arithmetic, not mathematics, although some mathematics will creep in by itself, but not because of the adults or the corse, but because of the child's observation of the natural world around them.

Gotta fly.

a

[Lucy]

thanks for responding Alexander. I still do not have a clear idea of what you mean by real mathematics. I must say I do not feel a lot of my childhood was spent memorizing times tables, it was relatively easy for me, and I am glad I have them memorized. Too often I have been in a checkout where the register isn't working properly for some reason, and the poor clerk has to do the math herself. Most times it has been a painful struggle. I appreciate when people can add, subtract, multiply and divide properly. I still think these are valuable skills. Now how much time should we devote to them? I don't think its the ? of too much time in the public schools being spent on arithmetic, I think there is just too much wasted time, where the kids aren't doing anything of value, waiting, ect.

What would your alternative approach to mathmatics be?

Forgive me if this is tiresome too you.

[Alexander]

File c

lucy said:
ok, so whats wrong with the math? I would love to know since I have been doing singapore math with dd (5),

Nothing is "wrong" with it, but you are deluding yourselves if you think you are teaching mathematics.

lucy also

It looks very real to me, hands on, real world stuff so far...

Yes, but is arithmetic.

Hope this is starting to help

a

[Alexander]

file d

truly_sarah said:

Why are these countries both victims and culprits simultaneously? How should math be taught ideally?

Victims because they can not let go of the Industrial Age Model, for which "Math" (note no 's') was seen as a necessary component. Not only that, but in the race to be the best, children are force fed this tripe at a rate that is far quicker than they are really able to digest. Ask any adult or teen to solve problems commonly given to 10 year olds, and they will fail miserably. This begs the question, why were they taught the stuff in the first place???!

Culprits because they not only waste the life of children, but they are neglecting to equip these children with the skills that are really needed in the Information Age, beginning with creativity. Not only that, but they continue to help perpetuate the misconception that all that Math is really necessary.

truly_sarah also said:

I am always tinkering around in my head with a number system that is based on a spiral number line instead of a straight line.

This is most interesting. It demonstrates a most un-usual internalization of numbers. It is a shame that that was not understood as your model by your teacher and cultivated. That would have been the "ideal" way to do Maths (note the extra 's' to denote "mathematics").

truly_sarah also said:

my checkbook computations match up pretty well with the ones suggested on the back of my monthly statements!

A common enough sentiment, if not comment! But the fact is that you use arithmetic for that, not mathematics. And it may be a stunning revelation to many, but you do not have to begin teaching children this (arithmetic) until they become teenagers, if at all. They will all get there on their own, with or without wasting many hours of their lives in class doing it.

truly_sarah also said:

I'm thinking about reading Flatland with my son...isn't that the name of the book that shows everything in 2 dimensions? I would someday like to explore different numbering systems with him and math as logical thinking instead of just numbers and rules/axioms/theorems. Is that what you mean?

I am unfamiliar with the book, but the title strikes great resonance with me. As a child, my brother and I talked at great length about what it would be like to live in "flat-land" and what the experiences of beings in such a place would be like. We even drew pictures of what they could look like, and their insides an' all.

Exploring numbering systems? Hmmm. It depends on how you approach this. I'll come to this in a mo.

Math maybe logical. Mathematics (is rarely?) is not always (only the proofs are). Mathematics often gut instict, guess, idea, image and trial and error. It's more like composing music. When you get it right, it is beautiful.

In fact that is a good analogy. Mathematics is like composing music. What you teach as "Math" is playing it.

As for covering the different ideas in Mathematics (dimensions, geometry, bases, number theory): that is more like getting someone to be able to sing along with a bit of Mozart, or recognise that is Beathoven, or play Smetina well.

You don't need Mathematics to balance your books, you need arithmetic (commonly called "Math").

Getting there

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[Alexander]

file e

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.

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.

I had an unbelievably bad teacher in HS, and I dropped out of Math. My teacher would not listen, had an agenda, a time table, and wanted to be the "star" in his own class. Ironically, leaving probably saved me, though I had to do much of this stuff again to solve dynamic circuits in collage, but it was quickly forgotten, as soon as the tests were over!

When I was brought to Japan, I was sent to the Computer Aided Design Dept. and became involved in writing CAD software. And look! I could not remember a single trig formula

So I started working from first principles. Boy I was slow! But, unlike the other engineers (who were coding much faster than me because they could recite all the formula and just type out the code), I also thought about how the curves on the screen would be translated to the final machine cutter. I doubt I would have done this if I had been just typing out the code like everyone else. This "other thought" saved us from a monumental error.

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[truly_sarah]

So, you are saying...it is OK to teach the Arithmetic when the kids do need it...my son at 11 has a checkbook and uses it, and he cooks, and does other stuff - ie figuring out how much food his dog needs for his weight, and so forth, that does require Arithmetic. He is really good at figuring discounts in his head, doing exchanges of money from US-Canadian and back, computing interest and ROI, and figuring how much time it will take to bushwack at x kph distance Z1 versus follow trail at y kmp distance Z2. For his life, which is still pretty far away from a lot of technology, it makes sense for him to be able to do calculations. He is interested in maps and is my navigator on road trips. If he couldn't do the figuring, we'd literally be lost. His knowledge is such that oftentimes, I do not even bother to consult the map, I just drive and he gives directions, complete with ETAs to landmarks. That is great.

There is something else going on in there though, because when he does his Singapore Math (no S!) I look at his workbook, and many times, for a word problem, he will have an answer, and nothing else. They are problems that I would probably have to write down simultaneous equations for! (And I am not what you would consider mathematically challenged.) I have to check my impulse to ask him to do it the 'correct' way, and thinking 'oh, he will get into trouble when he comes up against more complicated problems and needs to know how to write and solve simultaneous equations. Somehow, he "sees" the answer and has a worthwhile system of deducting the answer. (This is a book with no answers in the back, so I know he's not getting it there.) That was a BIG LEAP for me. Leaving WELL ENOUGH (or MUCH BETTER) alone because it didn't jive with what I believed internally. I don't actually teach him with his curriculum, he's a self-learner...I give him the book and he is motivated enough to do it...if he has a question, it's answered the way my brain works, not necessarily his, and then he knows me well enough to understand how I see things, then he somehow translates into his way of thinking, and eventually, 'gets' it.

I know that he has some roller coaster programs that he plays around with, and has been reading up on G forces and velocity and doing some experimentation. At some point, he is going to get bored with the canned packages and we will have to get him a CAD program to play with.

OK all you math and music people...I have had an idea about a statistical package that incorporates both, for looking at complex data sets...I would call it the statischord! Basically, you could load your data set into a big solution space (that does not have to be, and is better if it is not - symmetrical, or even a matrix), and select a 'harmony key' that best suits your brain's natural resonance. Then you could select different instruments for each variable, and navigate through the solution space listening for concordance/discordance or interesting sequences...the idea being that where there is some sort of basic correlation between states of variables, you would hear a 'theme' and where there are interesting spaces or points of intersection, you would hear something different, and would be able to intuitively tell (because it is 'tuned' to your own resonance) which variables were involved and in what state. Personally, I think it would be much easier than poring over printouts...and if you wanted to share with someone with a different resonance, all you would have to do is switch keys. In the same way, somebody who deals better with color could use colors instead of sound (but colors HAVE sound, right, in the way they affect your brain, they do produce waves that could be translated...) I know I'm not the only person who's ever had this idea! I wonder if anyone knows if there is anything like this in development or even available now? It would be fun to try it out!

Alexander, yes, that's what Flatland is about...just like you imagined as a child.

Still interested in that lesson plan though!!!

Sarah

[Alexander]

file f

sleepies said:

WoW that post went right over my head guess it is a good thing im not home-schooling. maybe it was the fact i got only formula and not breastmilk....that i don't understand.

what are you talking about?

oh. im sure it is me and not you.

but, im lost

It is certainly not you. The difficulty in understanding what mathematics is, is shared by those purporting to be educationalists in your local and state government. And they haven't got it right either. Not even close. :

It is hard. So don't think any the less of yourself for struggling here.

As for not Home schooling. Sadly, I think that it would be much better if you were to. Then you could just ignore the whole subject.

a

[larsy]

re: homeschooling, Alexander, amen!

[Lucy]

so is that your reccommendation, that we ignore arithmetic?

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

[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).