Real Mathematics. (Not "Math") - Page 2

[Alexander]

Dear lilyka,

on: learning to add left to right=math
right to left (by yourself) = Mathematics:

Exactly! Which only goes to show how badly the Industrial Age School system dumbs down our children! Yuk.

[Alexander]

file d

Dear Sleepies,
on: If you don't teach "school Math" then what will your kids do when they need to take an ACT or SAT?

Uh oh!

This is "The Golden Key" trap. Once you fall into it, like Alice in Wonderland, your whole world goes mad, except here it is the educational world.

What you are suggesting is that it is ok to study something silly or useless, because if you get good at it, you can then get through the test and into further education. And this is what the test has become. Only an un-necessary door. We must do a test on something, even though it it quite useless, just because they put it there!

And why did they?

The US HS system lacks a national examination system that evaluates students in all subjects at the same level. The SAT and other multiple choice tests that are conducted in the US are a method of ensuring that students can comply with the minimum requirements of reading, 'riting and 'rithmetic required for the Industrial Complex.

But to address the question directly, if a teen wishes to go to collage, and do so, the SAT must be taken, then that student will face the fact in a timely fashion. There is nothing in that test that could not be learned (dare I say from scratch) in less than a year by some-one who has the motivation, and who has not been screwed up by the system.

a

[Alexander]

Originally posted by larsy


The difference between learning math and learning mathematics seems like a distillation of the problem of what good education for the information era vs what constituted a good education for the industrial age. The industrial age required people who could perform certain tasks and were willing to be controlled by the industrial complex, and schools were good institutions to burp out good citizens with those characteristics. Learning the right answer to the math problem worked for that society.

The information era will need people who can be self-directed and who can think...

LOL

ok, I mis-quoted larsy a little here.

But larsy, you've got it! And sure you (hope others) can see how this ties in with the way we as adults, and as authorities (Educational, Judicial and democratic) treat children, their education and their lives. It is no accident that these things are all connected. They are all of the same Era.

a

[Alexander]

Originally posted by Joan
This is interesting...that IS what turned me off of math when I was in school. Maybe some math-savy person here can expand on this---is math that rigid?

One of the reasons I loved English/literature was that there was room for debate and discussion and interpretation. I didn't think that was possible with math.

Math, you are learning a series of manuvers to achieve a task. There may well be many ways to solve the problem in Mathematics, but in math, a reliable system that gets people to produce the right answer is all that is important.

One of the reasons Mathematicians love Mathematics is because off all the debate and discussion that is possible!!! Like your Lit classes, it is possible, but if there was a formula for writing a "good" novel,(of course there are many), and the school was interested in getting everybody to follow that model, then of course there is very much less room for discussion.

On the intimidation you felt.

This would be funny if it were not so sad. That you felt intimidated by the possiblility that you might get the wrong answer is not only not un-typical, it is universal in the Industrial Model Schooling system.

As a matter of fact, in my school, making mistakes is actually in the school rules! Indeed, we go to great lengths to demonstrate to children that their mistakes are SO important, that we reward them, and we are not so interested in all their "right" answers.

When the kids "get it", there is no stopping them

Hope this helps.

a

[SagMom]

Alexander, your posts confirm what I've suspected. I sometimes wonder though, if my experince was so typical, where did today's mathematicians come from?

Incidentally, am I correct in thinking that your school is a free school? Is it for foreign students or Japanese or both? I recently read Summerhill... any connection to your school?

[Alexander]

Originally posted by Joan
Alexander, your posts confirm what I've suspected. I sometimes wonder though, if my experince was so typical, where did today's mathematicians come from?

Well I grew up with two. My father and my brother, (+all their friends : )

They are a "peculiar" group, who either absorbed all the methods faster than the teacher could provide them, ('cos it was so obvious) or did not pay any attention to the regimented classes because they were gliding over the whole thing, up in the clouds. They do not need to be taught how to add.

Incidentally, am I correct in thinking that your school is a free school? Is it for foreign students or Japanese or both? I recently read Summerhill... any connection to your school?

Well, the English as a second lang. is just a little school for once or twice a week lessons in the afternoon or evening, but we apply a goodly measure of freedom to the children within the framework of the course that we have designed for them. For example, the children themselves decide how many sheets of homework they take home, (although we do have an upper limit), they have a menu of games or activities (including drills and tests) to choose from, and we have a lot of "wierd" rules like "you must make as many mistakes as possible", something that Japanese kids are especially allergic to!!!

As for the other school, (the one to which you will be taken if you click on the www icon on my profile), this is a Democratic School in the making. It will (I hope) attract both Japanese and English speaking children between the ages of 6 and 18, (later 4-18).

Summerhill was certainly a model for Sudbury Valley School, and thus, indirectly mine. Additionally, a friend about ten years ago gave me a book on this school because I would not stop "going on" about how the Japanese had taken the American model to an extreme, and had both messed up a lot of kids, and accelerated down a blind alley, with the light turned off at the dead of night. Going in reverse seemed like such a good idea and it was the first incling I had that I could work out the form that a school specifically designed for the Information Era. It was not until I discovered Sudbury Valley School that I realized that my idea could become reality, (some-one else had proved it to me by starting "my" school 30 years before) and we decided to go ahead and start our own.


I find it very exciting that you are asking about this. I am stuck in glue, trying to create our homepage, which is currently under construction.

Hope this is interesting.

a

[SagMom]

"As for the other school, (the one to which you will be taken if you click on the www icon on my profile), this is a Democratic School in the making. "

I'd be interested in reading more about this, but the page that came up has many little empty squares, a few numbers and some other characters that might be Japanese, but could also just be gibberish.

[Alexander]

That's the Japanese encoding known as shift Jis. Depending on your system, you may well be able to select that on you browser.

Then you will be able to see the Japanese, which is, to you, probably just jibberish ('tis to me anyway LOL)

Eventually (like even this week?) I will get some English up too, if I can get off the MDC boards

a

[Alexander]

It's up!

Number one is now posted here: Lesson Plans for Mathematics.


Hope you all find this stimulating.

a

[Britishmum]

mistakes.....

Alexander, I wanted to pick up on what you said about making mistakes:

"As a matter of fact, in my school, making mistakes is actually in the school rules! Indeed, we go to great lengths to demonstrate to children that their mistakes are SO important, that we reward them, and we are not so interested in all their "right" answers."

Do you mean that you actively reward mistakes? I'm not a believer in 'reward' for anything, unless as a specific temporary behavioural strategy for an individual child.

I agree that mistakes should be recognised, acknowledged, talked about, and accepted as part of the learning process. Children should see that everyone makes mistakes. They need to learn not to internalise blame for mistakes (usually a female response) or externalise it (usually a male response.)

As for rewarding the actual mistake, is that what you meant? Or rewarding the process that may have involved making a mistake? Or rewarding the willingness to take risks, that means that you are more likely to make a mistake? And can you clarify what you mean by 'reward'?

[SagMom]

Hey, thank you to all who recommended the book, "Math For Smarty Pants." I'm having a blast with it--(imagine that!) What I find interesting is that, while I find some of it a challenge, my children "get it" early on. I may be quicker at the computation than they are, but they catch on to the patterns and such with less effort. (It could just be my rusty old brain, but I prefer to think that I'm thinking differently.)