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Math education

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EricL:
I'm on page 10.  My pushback was to Nums and Shasta's posts.

W.r.t. the article, I'll agree with author's point that mathematics in it's pure form is an art and I agree we should perhaps supliment the teaching of formulas and math-derrived facts with the art and freedom to discover for one' self how those things were derrived.  Certainly the joy of discoverry is missing in today's math education.

But for the sake of argument, I'll push back here too.  First, how do you measure this?  Everyone gets an A in art class.  Building one's intutition for the beauty of math is a wonderful and necessary thing for mathimaticians, but few people will become profesional mathimaticians in the same way few people become professional artists or musicians.  Sure, I would love a world where the pusuit of math for personal pleasure was appreciated and respected in the same way as the personal pusuit of music or art.  I'd love to stroll down to the math-walk on Sunday mornings, gazing out at the eligant works of struggling mathimaticians hocking their wares for $20...

The talented artist stands out head and shoulders above most of us in art class but most people end up painting walls not landscapes.  Contray to the author's statements, carpenters really do use triginomitry, people really do need to balance their checkbooks.  Most people don't need or care to pursue pure math principles to do these tasks in the same way I don't need artistic talent to paint my daughter's room.    I'll all for supplimenting math education with a more artistic, discovery-based approach and perhaps we would see more mathimaticians as a result, but I fear such would provide about as much value to the majority of students as art class.

abyaly:

--- Quote ---First, how do you measure this? Everyone gets an A in art class. Building one's intutition for the beauty of math is a wonderful and necessary thing for mathimaticians, but few people will become profesional mathimaticians in the same way few people become professional artists or musicians.
--- End quote ---
Measuring mathematical ability really is a problem. In order to make schooling 'fair' we need to adopt a quantitative method for measuring results. This usually amounts to testing. However, testing detects side effects of mathematical ability rather than mathematical ability. It is far easier to learn the side effects in order to test higher in the short run even though it is damaging in the long run. I don't know how this can be solved. Some teachers assign grades qualitatively - they use their best judgment. But since we want our teachers to be accountable for their consistency, we can't really allow this.

--- Quote ---I'd love to stroll down to the math-walk on Sunday mornings, gazing out at the eligant works of struggling mathimaticians hocking their wares for $20...
--- End quote ---
It seems you're implying that if math was taught more like art then mathematicians would not get paid as well. Do you really think so?



--- Quote ---I'll all for supplimenting math education with a more artistic, discovery-based approach and perhaps we would see more mathimaticians as a result, but I fear such would provide about as much value to the majority of students as art class.
--- End quote ---
Mathematical ability is useful outside of the field of mathematics. That's the premise under which math is made a required topic. The LSAT is a test that measures reasoning ability - it's no surprise that math students tend to get the highest scores on it. Reasoning ability is something that makes a person not only able to argue better, but also make better life decisions.

Numsgil:
I'm not saying you shouldn't learn how to long divide.  But we spent months and months and months on it through 3, 4, and 5th grade.  Maybe in to 6th, I don't remember.  A month would have been sufficient.  Yep, hmm, that's how you long divide.  I don't need to practice it.  The computer does it better than I ever will anyway.  Take those months of learning to long divide (which I'm pretty sure is universally despised by teacher and student) and let's spend it doing something applied or fun or something.  Play Monopoly with more complex math (Billy is staying in 2 rooms of your 13 room hotel which costs $485 to maintain.  Determine an appropriate price).  Heck, we could put up dry wall.  Anything is more fun than long dividing!

Anyway, how humans do things by hand is usually totally different than the way machines do things anyway.  Addition involves bit identities, for instance.  Not really the way I long divide.

asterixx:
First of all, I know I'm "new" here, but I won't let that discredit me.

Second of all, I'm being careful not to generalize and say that all schools aren't teaching mathematics. There are many schools across North America that have used what EricL is referring to as a discovery-based approach, and such schools have seen the benefits of such a style of teaching and learning. The point is, we ALL learn things better if we can find meaning in our own lives through that selfsame learning.

Thank you for sharing the essay

Moonfisher:
The whole concept of education is relatively new in the west, it used to be reserved for the rich and the church, teaching the whole population hasn't been done long enough for us to find a propper way.
The root of the problem is that you have one teacher and 20-40 students depending on funds... and the 20-40 students all have different skills and interests.
It's obvious that if you allowed the students to spend more time on the areas they like and have the skills for, the time would be better spendt, you could be done with the university before you turn 18 and you would probably be better at what you do, the only downside being that you would have less "basic knowledge" and therefor wouldn't do well in gameshows.
I know I've never used and never plan to use aproximately 80% of what I've learned in school during my life.
When people don't know much they tend to focus a lot on whether other people know the same things, and if they don't they must be realy stupid.
And I'm not saying that if you're good at math and computers you don't need to learn anything about history and geography, since if you have the right to vote you should have some basic knowledge to understand what's going on in the world. Ofcourse personaly I would say history is being taught the wrong way in most places, trying to glorify people or periods or nations through time, and neglecting the history concerning religious powers out of fear.
But a lot of the time it will be painfully obvious that trying to teach certain people certain things is a complete waste of time.
Trying to teach a fanatic kid about biology or history is a complete waste of time if he's already got his mind set that the earth is 10000 years old and all the stuff that goes with it... is a wate of time.
Trying to teach me how to spell right, or form readable letter using a stick of ink with a hole in one end, or the world cappitals, or memorize dates of important events, or anything else that never caught my interest.... also a complete waste of time, for me, for the teacher, and for everybody who ever had to wait while someone explained it to me...
I don't think we realy spendt much time on long division where I come from, but in general there is a tendency to force whatever you where forced to learn against your will on the next generation. Otherwise you would be admitting that all that time was wasted, that several years of your life where spendt making no progress, as if a small chunk of your life is suddenly worthless.

Anyway you can argue forever about whats important to learn and what isn't, but in the end you need to consider if the person you're trying to teach can and wants to learn it.
You can't force people to remember, and if they're not interested they WILL forget eventualy.
You just can't cram 30 people into a room, hold a lecture and then believe you actualy taught people something. If you forget the fact that people only have a 15 min attention span, peple will still have a different pace which varies over time and according to the subject, they will have different skills, they may get different things from what you said, some will misunderstand what you said or just not understand it and you'll never know, because noone wants to make 30 people sit and wait around for you to ask a question.

IMO you need computers, one for each student no less can ever be acceptable, this way you can use software to assist in the teaching.
Lectures should be banned or reserved for freaks that actualy like those. Teachers should be more like tutors, walking around helping peope with their problems.
This way people can learn whatever subject they feel like today (And haven't completed) at their own pace, they can ask questions without disturbing the entire class, they can explore subjects far deeper than normal education would ever allow, they can test their own skills when they feel ready for it, asf asf....
(Ofcourse there would still be other classes without computers, personaly I would want to add one teaching social skills and manners and generaly how to live in the country you're in without upsetting the local population. IMO if in Rome learn to do as the romans or go back where you came from, I can't even believe integration is a real word, what the hell is it suposed to mean ? People don't need help to get integrated, that's something that happens naturaly over half a generation if you don't fight it.)

I know money is a big issue here, but if poeple finish school sooner they will also work for a longer part of their life, so for countries with socialist education systems it would still add up in the long run...
But I'm hoping we'll see this evolution in the near future as there will be more teachers who actualy know how to use a computer...

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