Author Topic: Is Algebra Necessary?  (Read 4024 times)

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Offline Anfauglir

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Re: Is Algebra Necessary?
« Reply #58 on: September 05, 2012, 04:25:59 AM »
Our current system has been in place for over 80 years...

I think this is the major problem we have.  The system, and the main elements of the syllabus, were pretty much set out decades ago.   And when you left school, you worked in the factory, or the office, or you were an engineer, and for 99% of people that were pretty much the choices. 

Flash forward a few decades and the number of "things to do after school" has increased exponentially.  But the school system - and more importantly the basic syllabus - has not dramatically altered.  There's been tweaks, and the addition of IT units, but (although teaching methods may have changed), you still go to school and learn English, Maths, Geography, History, a Science, a Foreign Language.  Is that really still the best mix for the workers of the future? 

I've said before that there is a good argument for a broad grounding up to a point to determine your preferences and aptitudes.....but would it be better if that all happened at primary and first year of secondary education, and then you really DID have options as to what courses you would go forward with?  Not "English Maths History Geography and pick between Physics and Art for your 5th subject", but "will you take Maths, Physics, Chemistry and IT, or will you take French, Spanish, Latin and German?"  Or maybe be able to take History of Art, Photography, Graphic Design and Business Studies?"  In other words, really open up the choices a LOT earlier on to let youngsters really progress (and get qualifications) in the subjects that they excel at?

The caveat, of course, is that how many people know at age 12 what they want to do with their lives!  But better perhaps they leave fully qualified for something having spent several years doing things they like, than sitting for several years doing subjects they loathe, that they will never use again?
Just because you've always done it that way doesn't mean it's not incredibly stupid.
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Offline jetson

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Re: Is Algebra Necessary?
« Reply #59 on: September 05, 2012, 06:42:29 AM »
My suggestion is just an idea, and could easily be mixed with other ideas, done partially, or whatever.  I am not suggesting that privatization is the answer.  But I am also typically idealistic, so I don't generally take a paranoid stance about what the government may or may not do when I'm being creative with ideas.  Yes, privatization could be a disaster - but fear of privatization will prevent us from even trying.

Today we have a mixed system of public and private schools.  IMO, there are too many flaws with the current system, leaving many of our children behind in quality education.  And for some reason, many politicians seem uninterested in giving the matter much thought.  They fail to see the value in a quality education system, it would seem.

Whether we privatize, remove compulsory laws, or just roll up our sleeves and fix what we have, or do some compilation of things, we definitely could use improvements.  I know it's costing me more to homeschool than it would to send him to public school, and I was not interested in sending my son to a private school, most of which are religious institutions around here.  There has to be a better way.   

Offline HAL

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Re: Is Algebra Necessary?
« Reply #60 on: September 05, 2012, 06:58:33 AM »
These days, the answer to an algebra problem is only as far as your iPhone or computer anyway -

http://www.myalgebra.com/algebra_solver.aspx

Even if I had to solve a complex algebra problem around the house I'd just type it into the solver and use that answer. Why not?

Same as it used to be when handheld calculators first came out. Before that you'd have to solve math problems by hand. Now who does that? I don't know, perhaps at some point, for all practical purposes, you can stop teaching it. For example, who gets taught electronics in high school? Yet you use a TV and if it breaks you don't fix it, you don't know electronics, you don't "solve" the electronics problem and nobody expects you to. Same with algebra. If you don't get taught algebra some time in the future, so what? You just get the computer to solve it. There won't be a time in the future when you will be without a computer to solve algebra problems. Even if you didn't have your computer or iPhone, somebody else will and before you could solve the equation they'd already have the answer and would be laughing at you trying to solve it with pencil and paper.

Offline Anfauglir

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Re: Is Algebra Necessary?
« Reply #61 on: September 05, 2012, 07:51:24 AM »
These days, the answer to an algebra problem is only as far as your iPhone or computer anyway.....

True, but why single out algebra?  I recall an episode of the Simpsons where a new teacher tore into Martin Prince for "learning a fact that anyone can find online in 5 seconds".  Why learn ANYTHING when you can just google it?

It's a question I sometimes struggle to answer.  Best I can come up with is that without at least SOME basics in the field you are questioning - or perhaps a very good grounding in critical thinking - how will you have any basis for knowing if the answer you googled is correct or not?

There is perhaps less need to learn "facts" these days, as opposed to "working out which facts ARE facts", and "knowing how to put those facts into practice".  With reference to algebra, you need some grounding I think to be able to phrase the problem in a way that you can actually ask the internet - or even to know there would be a solution to search for in the first place! 
Just because you've always done it that way doesn't mean it's not incredibly stupid.
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Offline HAL

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Re: Is Algebra Necessary?
« Reply #62 on: September 05, 2012, 08:00:23 AM »
True, but why single out algebra?

Well, mainly because that's what the topic of the thread is.  :)

Offline screwtape

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Re: Is Algebra Necessary?
« Reply #63 on: September 05, 2012, 08:07:56 AM »
Maybe privatization is key?  I can't help wondering what the private market, minus compulsory laws would do for our overall education system? 

If people only got educated in areas they wanted - ie, a private market - education would go straight in the toilet.  I might support that if there were also educational requirements attached to voting rights, speech rights etc.  Democracy requires an informed electorate.  So if people are not educated enough to make a good decision, they should not have any say in government. 

That is what education in a democracy is for.  Do not confuse education with job training, which is what it has become. 

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Offline Boots

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Re: Is Algebra Necessary?
« Reply #64 on: September 05, 2012, 10:32:57 AM »
So I already stated one of the problems with the public education system (such as it is)--that teachers aren't given the time or the motivation to teach the ways that are most effective for learning concepts.  Another problem is the "that's the way it's always been done" syndrome.  Take grades/ages for example.  There is NO GOOD REASON to have an arbitrary cutoff age for any given grade.  It makes zero educational sense.

In fact, it makes little education sense to have, say, "first grade math" taught at the same time as "first grade reading" and "first grade social skills."  Not every kid is ready for 1st grade math at the same time as social skills.  We need to have developmentally appropriate subject matter taught--even if it means Johnny (age 9) is learning math with 12-year-olds and reading with 6-year-olds, IF THAT IS WHAT HE'S READY FOR.

tying what you learn to how old you are is stupid.  Assuming every kid can learn the same level of every subject at the same age is equally stupid.
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Offline jetson

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Re: Is Algebra Necessary?
« Reply #65 on: September 05, 2012, 05:27:42 PM »
Not a bad point boots.  And I would add that we are learning more about how the brain learns and retains information, for example, younger is supposed to be better for learning a foreign language.  And I have heard that this is the case with other topics as well.  Makes me wonder if just a few tweaks to the current model would gain vast improvements in learning, and retention. 

Offline jetson

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Re: Is Algebra Necessary?
« Reply #66 on: September 05, 2012, 05:31:29 PM »

If people only got educated in areas they wanted - ie, a private market - education would go straight in the toilet.  I might support that if there were also educational requirements attached to voting rights, speech rights etc.  Democracy requires an informed electorate.  So if people are not educated enough to make a good decision, they should not have any say in government. 

That is what education in a democracy is for.  Do not confuse education with job training, which is what it has become.

Good point.  But, a counter point might be that privatization could lead to innovative ways to improve the status quo, making societies better educated on average.  Today, I don't think we can argue that our education system is churning out an informed electorate!  But then again, much of the voting seems more hinged on emotion over facts, IMO.

I think the biggest challenge with privatization is that it might create a bigger divide between income levels in terms of education availability and quality.

Offline rickymooston

Re: Is Algebra Necessary?
« Reply #67 on: September 05, 2012, 05:45:34 PM »
So I already stated one of the problems with the public education system (such as it is)--that teachers aren't given the time or the motivation to teach the ways that are most effective for learning concepts.  Another problem is the "that's the way it's always been done" syndrome.  Take grades/ages for example.  There is NO GOOD REASON to have an arbitrary cutoff age for any given grade.  It makes zero educational sense.

In fact, it makes little education sense to have, say, "first grade math" taught at the same time as "first grade reading" and "first grade social skills."  Not every kid is ready for 1st grade math at the same time as social skills.  We need to have developmentally appropriate subject matter taught--even if it means Johnny (age 9) is learning math with 12-year-olds and reading with 6-year-olds, IF THAT IS WHAT HE'S READY FOR.

tying what you learn to how old you are is stupid.  Assuming every kid can learn the same level of every subject at the same age is equally stupid.

The only way you csn really improve on that is home schooling. Few ppl have the time for that.

Private schools demand MORE, of Johnny. If he cant keep up, they kick him out.
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Offline Noman Peopled

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Re: Is Algebra Necessary?
« Reply #68 on: September 06, 2012, 02:35:28 AM »
Again, don't be impatient with me, because these are honest questions. But aside from certain more technical career fields, what might be an example of a situation where the lack of a firm grasp of something beyond basic math would really leave someone at a loss? What would you need that you couldn't work out with paper, pencil, and an understanding of addition, multiplication, subtraction, division and how decimals & fractions work?
Well, that depends on how much algebra we're talking about here. Basic algebra is nothing more than you describe in your last sentence plus the not-so-confusing leap of substituting one number with a variable. So yes, if you can do those plus a bit of basic logic like realizing that dividing both halves of the equation by anything (except possibly zero and infinity? dunno) will still result in an equivalent equation, you're pretty much set. (And no, you don't have to know the vocabulary either.) A lot of algebra, when applied to everyday life, seems like nothing more than common sense - but I find it only all the more troubling that kids appear to have so much trouble with it in the US.
Teaching a formalized version allows people to see that thourough understanding and logical application of some relatively easy-to-grasp base knowledge will help them immensely when solving some otherwise very hard problems.

I mentioned computer games specifically because nobody needs them and lots of people play them. Maximizing my character's capability in D2 was more fun then actually playing, and now I can work out which perks in Fallout 3/NV or Skyrim I can skip without losing too much oomph. Granted, I could probably figure those out without algebra as such, but it is so much easier when you know and have some practice with it - plus, as I said, for D2 you'd need some crazy math I was not prepared to elarn for a game.
For a maybe more serious example, I started working with Blender, a 3D modelling freeware, and I quickly realized that the best approach to having all the walls and roofs and whatnot of buildings fit together the way I want to, I really need to figure them out beforehand. Lots of it is quadratic equations, which are not really all that intuitive. I could do it all in blender, but then I'd have to readjust dozens or even hundreds of vertices,

My point is mainly that algebra may become useful unexpectedly. Ignorance of algebra is not likely to leave someone at a loss regularly - if they don't have a job that requires it (and they won't think of getting one if they don't know algebra), opportunities to use it will still pop up, but will be ignored in pretty much the same way I ignore the possibility of applying chemistry to cooking. It simply seldom enters my head as an option.



As for teaching it, I have forgotten a lot of math in my life, but whenever I needed or wanted it, I had only to retrace what I once knew, which was much easier than learning it from scratch, pretty much like a basic, confused understanding of 20th century history still gives you a frame of reference.
One point that I think wasn't mentioned explicitly yet is that I find it very important for people in general to know the basic principles of very important things. I advocate media criticism/applied rhetorics and science theory (Oh, and logic. Economy may be a good idea too.) in school for that very reason. So many people have no bloody clue what tricks politicians use on a daily basis, so many people think that scientists are educated guessers. It is important to know where civilizational accomplishments come from in order to appreciate their fragility and make informed decisions. Which, in a democracy, should be self-evidently desirable. Broad education for everyone may be a hard or even (easily) impossible task, but it's well worth it to try.
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Offline Boots

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Re: Is Algebra Necessary?
« Reply #69 on: September 06, 2012, 07:07:40 AM »
The only way you csn really improve on that is home schooling. Few ppl have the time for that.

Private schools demand MORE, of Johnny. If he cant keep up, they kick him out.

Not sure I agree, Ricky.  If you give pre-assessments to each kid in each subject, you can determine what they're ready for in each subject.  Their results (assuming solid assessment techniques) for the year determine where they are for the next year.

Then, we need to get rid of that assenine summer vacation. :-)  Let's do several 2-week vacations throughout the year instead of a 2.5 month break--where it's proven that the kids who need the most help, are the ones who lose what they've learned over the summer!!
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Offline screwtape

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Re: Is Algebra Necessary?
« Reply #70 on: September 06, 2012, 11:26:23 AM »
Good point.  But, a counter point might be that privatization could lead to innovative ways to improve the status quo, making societies better educated on average.

I don't buy into the idea that only privatization will lead to innovation.  The only thing privatization guarantees is someone will make a profit. 

http://www.csmonitor.com/USA/Education/2010/0629/Study-On-average-charter-schools-do-no-better-than-public-schools

Today, I don't think we can argue that our education system is churning out an informed electorate! 

I don't disagree.  But I think that stems more from the way repubs have mistreated public education over the last 30 years.  It has been refocused on job training and not general education and critical thought.  This makes it difficult to justify curricula like history, art, music, which are important.  When I was in engineering school about 80% of my peers would have dropped English lit if they were able.

Education is one of the first areas to get cut when budgets are tight.  And repubs have made sure budgets are tight.  Repubs consistently say the way to better education is not to throw money at it.  I sort of agree.  That is, only throwing money at it won't solve anything.  We as a nation do not actually take education seriously.  There are countries where they only accept the top 25% of graduating students as teachers.  Is that how we look at it?  Nope.  In order to get the best, you have to offer better pay. 

There are other major differences as well. Look at Finland:
http://www.theatlantic.com/national/archive/2011/12/what-americans-keep-ignoring-about-finlands-school-success/250564/

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Offline jetson

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Re: Is Algebra Necessary?
« Reply #71 on: September 06, 2012, 02:01:16 PM »
Wow - thanks for sharing that Finland article!  I was just talking to my wife about countries that are more successful, generally speaking, than American schools in education.  Still reading, very interesting!

Offline jaimehlers

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Re: Is Algebra Necessary?
« Reply #72 on: September 06, 2012, 03:21:00 PM »
That article makes good points.

There's some areas where competition is beneficial, if not essential.  Education is not one of them.  For example, there's an anime called Baka to Tesuto to Shoukanjuu (Idiots and Tests and Summoned Monsters) which is built around the premise of a school where the students compete with each other in order to be in the best classes - literally.  The students in the A-ranked class get the best equipment, the best teachers, the best of everything; the students in the F-ranked class are in a dilapidated schoolroom that's practically falling apart.  The idea is that the students will compete so that they can be in the best classes.

What really happens is that the students focus on beating the other classes to either retain their existing privileges or to to pull the other class down a run or two.  The lowest-ranked class, the 'idiots' referred to in the title, are in such a bad position that it's almost impossible for them to get ahead - they simply don't have the resources to really compete, and it takes a miracle for them to ever win any of the periodic test battles that the school uses to determine placement.

Yes, it's a completely silly premise, but it illustrates the point that education shouldn't be competitive.

Offline shnozzola

Re: Is Algebra Necessary?
« Reply #73 on: September 06, 2012, 04:56:50 PM »
I always thought there are basically 2 types of education systems being used.  The “educate as many as possible pretty good”, and the “push the very best far” system that doesn’t mind leaving some way behind.  And I always thought the US has been  on the side of “as many as possible pretty good.”  Finland blows my view of our system out of the water.

This is not the first time I’ve heard the US out USed by Finland.  Humanoid, a fairly new member, wondered why government is bashed constantly by so many Americans when the government itself is the people.  Finland is doing things right.  They understand democracy better than America.

By the way, what a great conversation this has turned into.  I still lean towards kids being pushed uncomfortably into Algebra.
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Offline rickymooston

Re: Is Algebra Necessary?
« Reply #74 on: September 06, 2012, 09:09:42 PM »
If you give pre-assessments to each kid in each subject, you can determine what they're ready for in each subject.

In many cases, different kids are held back for different reasons. They need personal attention.
You may classify a bunch of kids as being the same level but they arenot all held back fir the same reasons

Furthee more, paer of learning involves "stretch" and this involves challenging them.

With advanced students, without giving them personal attention, yiu may not necessarily challenge them or rgey may miss developing other key skills.

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Offline darkdragon46

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Re: Is Algebra Necessary?
« Reply #75 on: September 06, 2012, 10:55:11 PM »
Our education system is based on the theory of humanism, which came from the Renaissance.  And that came from the Roman latin word Humanitas (Cicero made the word up actually), which came from the Greek idea Pedia.  It was the basic system of education to create the prefect citizen.  Arithmatic, rhetoric, grammar, geography, natural history, history combined with ethos (ethics) to create the perfect citizen.  Our model is the same as theirs, only updated with our new ideas and information.

I will always stand by the fact that learning has more to do with teachers than lesson plans.  Good teachers can teach, bad teachers can't, so it really doesn't matter what lesson plan you throw at them, if they can't teach, not many people will learn.  That said, teaching is the most under appreciated profession in the U.S. at the very least.  And they don't get paid squat.

I'm always amazed by the system we have that awards having great knowledge and experience, but fails to even blink at the very people that helped us get there. 

Offline Mr. Blackwell

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Re: Is Algebra Necessary?
« Reply #76 on: September 07, 2012, 01:58:34 AM »
Our education system is based on the theory of humanism, which came from the Renaissance.

First time I've heard that theory...care to back it up?
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Offline darkdragon46

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Re: Is Algebra Necessary?
« Reply #77 on: September 07, 2012, 12:37:08 PM »
Our education system is based on the theory of humanism, which came from the Renaissance.

First time I've heard that theory...care to back it up?

Humanities 101.

Humanitas, coined by Cicero in the 1st century BC, as I said, is based on the Greek idea of Paieia. 
There's the wiki: http://en.wikipedia.org/wiki/Paideia

That was taken by Francesco Petrarch to sell the idea that having a well rounded society is better than a simple tradeskill one.  Thus was born the well rounded education of the renaissance, which in turn gave birth to our education system.  In fact, its pretty much word for word.

It should be noted that the word 'humanism' has changed some what into a philosophical term.
The wiki: http://en.wikipedia.org/wiki/Humanism

Basically, the renaissance took their love of all things greco-roman, including the shunning of a tradeskill education, and made them stick.  Even today we compare ourselves to the democracy of Athens. 

Offline Mr. Blackwell

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Re: Is Algebra Necessary?
« Reply #78 on: September 11, 2012, 01:29:05 AM »
I thought it had to do with Horace Mann and the Prussian model...are they the same?
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Offline darkdragon46

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Re: Is Algebra Necessary?
« Reply #79 on: September 12, 2012, 03:23:45 AM »
Horace Mann was more to do with how subjects were taught than what was taught.  His goal in his education reform was to create disciplined, upstanding Republicans.  If you look at his six principles, they have more to do with who is teaching and how.  He wanted public education, professional teachers and education for all.

The prussian method is very similar in that it focuses on how education was to be carried out.  Compulsory attendance, trained teachers and standardized testing with a national curriculum.  It does not state what this curriculum is, however.

Again, these are dealing with the how not the what, but yes, our education model is based on these.   But what we teach is still rooted in ancient greece and rome.

Offline Anfauglir

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Re: Is Algebra Necessary?
« Reply #80 on: September 12, 2012, 04:53:26 AM »
Again, these are dealing with the how not the what, but yes, our education model is based on these.   But what we teach is still rooted in ancient greece and rome.

I think that's where the confusion sprang from.  Humanism today tends to be pretty much exclusively referring to the philosophical position rather than Renaissance Humanism.  Humanities as you note would be the more widely referenced term, so far as education is concerned.

That said, it may be that on an education-based forum, use of the word "humanism" would be taken by most as the Renaissance Humanism you mean - but given that we are a philosophical forum (with a number of (philosophical) humanists in the membership) I'm not surprised we presumed it was the philosophical usage you were talking about....hence the confusion!

You'd think with such a huge language like English we could manage to have one word just have one meaning!   ;)
Just because you've always done it that way doesn't mean it's not incredibly stupid.
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Offline inveni0

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Re: Is Algebra Necessary?
« Reply #81 on: September 21, 2012, 08:23:48 AM »
The greatest benefit of "higher level" math is the training it gives us to think logically and problem solve.  When you're given something like: 8^(6-(7/4)*3) - 6^5 = 9x, solve for x, you are being taught how to logically analyze a problem and develop a method for how to solve the problem.

Believe me, if more Walmart associates had knowledge of higher level math, I wouldn't get so frustrated with them every time I go to the store and ask a simply, common sense question.
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Offline none

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Re: Is Algebra Necessary?
« Reply #82 on: October 27, 2012, 03:55:41 PM »
The greatest benefit of "higher level" math is the training it gives us to think logically and problem solve.  When you're given something like: 8^(6-(7/4)*3) - 6^5 = 9x, solve for x, you are being taught how to logically analyze a problem and develop a method for how to solve the problem.

Believe me, if more Walmart associates had knowledge of higher level math, I wouldn't get so frustrated with them every time I go to the store and ask a simply, common sense question.
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