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Is Algebra Necessary? - Page 28

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docvoc
Profile Blog Joined July 2011
United States5491 Posts
July 29 2012 18:57 GMT
#541
This should be taken with less than a grain of salt. I am not a math person, and yes I passed my math courses usually with A's, but the way most math is taught is not intuitive. It should be taught as a simple transative theory, A does B, B does C, so A does C. It should be taught in that kind of build up method rather than the way it is done now in most poorly taught schools which is a haphazard account of some parts of math and skipping the parts that may require some extra thought. Many people do not use math in their daily lives that is at the same level as Alg I and II, but they are necessary to have educated people. Sure maybe get a dialed down version for people who really don't do well at math, but getting rid of it is stupid. You can teach ALG I and II in an easier way by just giving easier questions on a test. You don't need to have super hard questions to prove that a student knows his material which is a something that most teachers believe in this country, and its dead wrong. The idea of school is to impart knowledge, not push the limits of students.
User was warned for too many mimes.
ticklishmusic
Profile Blog Joined August 2011
United States15977 Posts
July 29 2012 18:58 GMT
#542
This seems like the "its not me, its the curriculum" mentality.
(╯°□°)╯︵ ┻━┻
Sovern
Profile Joined March 2011
United States312 Posts
July 29 2012 19:05 GMT
#543
Of course Algebra is not necessary, neither are many other school subjects and things in life. Is art necessary? How about Science? Of course not, they're all human luxury's.
StarStrider
Profile Joined August 2011
United States689 Posts
July 29 2012 19:08 GMT
#544
If there is an excessive amount of dropouts from Algebra, the methods need to be reexamined. To consider eliminating the course because it is 'too hard' is the biggest load of bullshit.

While not used directly in many career fields, Algebra is one of those qualifying courses that lets students realize their potential for more advanced maths used in aviation, electrical engineering, and other advanced sciences. Without making it mandatory, students who excel in it will never have a chance to realize their potential, and programs will never have the opportunity to discover their future candidates. Removing the course appeals to the laziness in people... If it is optional, most people will take the path of least resistance and avoid it.

Algebra is not absolutely neccessary for everyone, but is absolutely comprehendable for everyone, if they aren't learning it they either aren't putting forth enough effort or the curriculum or method of education is poor. And the value it provides for, at very least mental stimulation and advanced problem solving, and at most qualifying more advanced math students, is superb. LONG LIVE ALGEBRA
Spontaneous Pneumothorax sucks, please keep MVP sC in your thoughts. sC fighting! 힘내세요
Rumpus
Profile Joined August 2011
United States136 Posts
July 29 2012 19:13 GMT
#545
Teaching methods need to change, not what we teach. In high school I can't tell you how many times I've heard "when will I ever use this!?" That needs to be done away with. Make these concepts and topics applicable to things kids enjoy. Instead of someone who has been teaching this stuff and knows it inside and out, walking into class everyday saying "Do this this this, hope we all got it! Class dismissed!" It has nothing to do with whether you deem it easy or not, I personally thought all math was simple until college but not everyone is the same. And throwing numbers around and doing tricks that some students might not understand makes them lose track quickly and subsequently harder to catch up and succeed.

Although at the same time, I am a proponent of "if your life doesn't require it, don't make them take it." I am engineer, why do I need to be well rounded in art and culture? I don't care and it doesn't help me. That stuff has always bothered me. There are some kids who will never have to paint a picture or memorize what happened in the Spanish-American War after the age of 17, don't waste their time and energy that can go towards what they like/excel at.
Grammin'
schben
Profile Joined June 2011
Germany60 Posts
July 29 2012 19:13 GMT
#546
On July 30 2012 01:37 jakeyizle wrote:
Show nested quote +
On July 30 2012 01:30 Silvanel wrote:
Since math in Poland isnt teached that way (we have classes in math in general) i dont really know what we are taking about. Anyone care to explain? What is level of mathematical knowledge that is required from a high shool gradute? A link to exampalary test or something would be nice.

In Florida, students graduating in 2014 or later are required to have 4 years of math. 1 year which must be Algebra I or equivalent (such as a year in Algebra 1A and a year in Algebra 1B) and 1 year which must be geometry or higher (pre-calc, alg 2, calc, maybe probability & stats).

Edit: students entering high school in 2012-2014 are required to pass Algebra 2 as well.
Edit 2: this is a practice Algebra EoC exam (end of course exam, passing it is required to get credit) http://www.flvs.net/areas/studentservices/EOC/Documents/Practice Test for flvs_net_Final.pdf

Sorry for being offtopic but how old are students that are taking this exam?
micronesia
Profile Blog Joined July 2006
United States24690 Posts
July 29 2012 19:21 GMT
#547
On July 30 2012 00:41 paralleluniverse wrote:
Show nested quote +
On July 30 2012 00:38 micronesia wrote:
On July 30 2012 00:29 paralleluniverse wrote:
On July 30 2012 00:22 micronesia wrote:
On July 30 2012 00:19 paralleluniverse wrote:
On July 30 2012 00:18 micronesia wrote:
On July 30 2012 00:10 paralleluniverse wrote:
On July 30 2012 00:06 micronesia wrote:
On July 30 2012 00:03 paralleluniverse wrote:
On July 29 2012 23:59 farvacola wrote:
[quote]
I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard.

Singing math is one of the stupidest ideas I've ever heard.

Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math.

I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations.

How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved.

I would also derive the formula.
You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread.

Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it.
Back to my first question of the current post.

Memorizing formulas has zero educational value.
Almost completely agree with you.

If you think math is about memorizing formulas, then I would direct you to Lockhart's Lament, which has been linked a few times already: http://www.maa.org/devlin/LockhartsLament.pdf

I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't.


Completing the square.

Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula?

We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student.

A good plan would go like this:
1) How should we solve (x+1)^2 + 4 = 0?
2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0
3) The problem reduces to writing 2) in a form like 1).
4) We work out how to do that, and hence solve 2).
5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation.

At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick.

I would like to see you attempt to teach completing the square to an actual class of average kids... because if you can pull that off well then your plan might work regarding the quadratic formula (I'm not confident), but we have gone away from the topic of singing to teach something.

It's OK 90% of the thread is still on topic.

Obviously the students should have some proficiency in symbolic manipulation before learning how to solve quadratics. But I fail to see your point. Do you have a better method?

Originally you asserted that a trick like a song shouldn't be used to teach formulas. In an ideal situation I agree... better to have people come up with things than give it to them (although I would argue that if you are already giving a kid a formula for whatever reason, then a song is no better or worse than another memorization method).

Here is the problem I have with your approach (and this is without going into the practical limitations as an actual teacher in a school): Kids who get completing the square will very possibly be better off dealing with quadratics than they would have been if you just gave them the quadratic formula itself after factoring was learned. However, kids who struggle with completing the square will have no way of solving quadratics (other than factoring). Should the kid not progress in their math career until they can complete the square? It's not necessary to understand where the quadratic formula comes from in order to be successful in math/life/work/college/etc. Remember, I agree that it's better to understand than to be given, but not always practical.

I didn't learn completing the square until precalculus, unfortunately.
ModeratorThere are animal crackers for people and there are people crackers for animals.
frogrubdown
Profile Blog Joined June 2011
1266 Posts
Last Edited: 2012-07-29 19:24:07
July 29 2012 19:23 GMT
#548
I'll quote a Facebook post I just saw from a Columbia philosophy prof I won't name:

"‎
" ... it’s not easy to see why potential poets and philosophers face a lofty mathematics bar."

What an appalling Op-Ed piece! Who the hell is this guy, and what makes him think he's qualified to opine on the subject of an appropriate education for philosophers?"

Not that that part in particular matters too much to the argument in the piece, but it struck me as well.

Has anyone linked this relevant xkcd yet?
tuho12345
Profile Blog Joined July 2011
4482 Posts
July 29 2012 19:29 GMT
#549
Algebra is fucking easy, higher level or advance math is not necessary but Algebra is a must imo.
Enki
Profile Blog Joined January 2007
United States2548 Posts
July 29 2012 19:32 GMT
#550
He mentioned Germany's schooling where the grades 1-10 are the mandatory ones. Past that, you can get into vocational classes and start getting hands-on training which is what the U.S lacks dearly. Most high schools seem hell-bent on preparing the studends for college, shoving them down a path they don't really want. College is great and all, but we should be putting more emphasis on getting some of these kids into vocational classes and schools. You don't need high level math to do these jobs, they are in high-demand, and its a stable career that pays well. That's the first mistake the school system makes, they assume everyone want's to go to college after high school and thus forces the curriculum on everyone.

I don't think the problem is Algebra, anyone can learn it if they really wanted to (and they should, I still think everyone could use knowledge for basic algebra). Not everyone enjoys having it shoved down their throat though. Saying it is too hard is just bullshit. HS students couldn't give a fuck less about Algebra for the most part, it's a problem of motivation and that's a hard problem to fix.
"Practice, practice, practice. And when you're not practicing you should be practicing. It's the only way to get better. The only way." I run the Smix Fanclub!
ZeGzoR
Profile Joined April 2010
Sweden307 Posts
July 29 2012 19:36 GMT
#551
Wow, some people dont get why they teach math in schools. Its not because the math stuff have use outside of class, its for developing logical thinking,,,
yeah yeah im going
Kyrillion
Profile Joined August 2011
Russian Federation748 Posts
July 29 2012 19:36 GMT
#552
too many bad math teachers


I thought there was a general consensus on them being by far the best teachers, though. Unless it's not the case in the U.S. ?
If you seek well, you shall find.
radscorpion9
Profile Blog Joined March 2011
Canada2252 Posts
Last Edited: 2012-07-29 19:46:39
July 29 2012 19:41 GMT
#553
On July 30 2012 04:08 StarStrider wrote:
If there is an excessive amount of dropouts from Algebra, the methods need to be reexamined. To consider eliminating the course because it is 'too hard' is the biggest load of bullshit.

While not used directly in many career fields, Algebra is one of those qualifying courses that lets students realize their potential for more advanced maths used in aviation, electrical engineering, and other advanced sciences. Without making it mandatory, students who excel in it will never have a chance to realize their potential, and programs will never have the opportunity to discover their future candidates. Removing the course appeals to the laziness in people... If it is optional, most people will take the path of least resistance and avoid it.

Algebra is not absolutely neccessary for everyone, but is absolutely comprehendable for everyone, if they aren't learning it they either aren't putting forth enough effort or the curriculum or method of education is poor. And the value it provides for, at very least mental stimulation and advanced problem solving, and at most qualifying more advanced math students, is superb. LONG LIVE ALGEBRA


I feel like lots of people are misreading the article. Quoting from the end:

Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.


He's not saying that because its hard therefore we should eliminate it, people are turning into moral crusaders based on that simple misunderstanding. He's saying he doesn't think its necessary for people to go through training in Algebra if they won't end up using it meaningfully in their lives; and since it is obviously a huge stumbling block for many students according to the statistics and experts he cited, then it should clearly be reviewed for removal.

If it were absolutely necessary, like long division and reading and writing, then he wouldn't bring this up. If people would simply read the article more carefully I feel like most of the uproar would die down and we could discuss the substantive issue of how algebra is used in our day to day lives.

On July 30 2012 04:36 ZeGzoR wrote:
Wow, some people dont get why they teach math in schools. Its not because the math stuff have use outside of class, its for developing logical thinking,,,


Isn't the logical counter to this argument that math isn't the *only* subject that teaches logical thinking? I mean really, do you believe that you can't be logical if you don't learn math? Off the top of my head, what about philosophy class, or critical analysis of classic literature? Clearly you don't need math to learn how to think critically or logically; its just a useful tool towards that end. But if it largely teaches unnecessary things, then why not skip it and focus on things that are more relevant to students lives?

Anyway I don't have any conclusive opinion on this issue, but it is good to review what is being taught and how useful it is.
IceCube
Profile Blog Joined June 2009
Croatia1403 Posts
Last Edited: 2012-07-29 19:44:42
July 29 2012 19:43 GMT
#554
Only thing you learn from Algebra is that nothing in life is simple as it seems.

What I mean is that if your good at Algebra your most times good than not good at solving difficult problems in life if you apply what you have learned in life to it.
That is why and only why I think learning that in high school (any part of your schooling) is really essential, because you can simply apply it later in life, on any part of your life.

So, for me, learning at least basic Algebra or math or any type of problem solving programs is essential part of teaching in a young persons life.
Forever Vulture.. :(
tokinho
Profile Blog Joined December 2010
United States792 Posts
July 29 2012 19:50 GMT
#555
This is the dumbest thread ever.. please stop with your lowest common denomator.. now is the first time ever kids are dumber than their parents. I could hire 10 people right now.. if they knew pde and complex fucntions and were willing to work for less that 70k a year.. but honestly i think if they are not willing to struggle through it.. they don't deserve the degree
.. the degree requires work and practice. like starcraft who is good without practice.. so if they don't practice. they don't get the reward
Smile
nennx
Profile Joined April 2010
United States310 Posts
Last Edited: 2012-07-29 19:52:55
July 29 2012 19:51 GMT
#556
On July 30 2012 04:36 Kyrillion wrote:
Show nested quote +
too many bad math teachers


I thought there was a general consensus on them being by far the best teachers, though. Unless it's not the case in the U.S. ?


i dunno iirc my high-school math teachers were all pretty bad except one, and this was doing AP classes and all where you'd think teachers would be able to teach better. when i retook calc 2 at community college (and when i did later math at uni), i realized how shitty my high school math teachers were.

you might be able to make the argument they were better than other high school teachers though, so i guess they "win" at being not the worst
Sup
DeadEyE X
Profile Joined July 2011
United States23 Posts
July 29 2012 19:53 GMT
#557
So like... math is important mmk
nennx
Profile Joined April 2010
United States310 Posts
July 29 2012 19:56 GMT
#558
algebra is increasingly important because we live in the information age were science and engineering are playing more important roles in our lives. the purpose of school should be to prepare you to enter the next level of education or to start working. since math-based jobs are becoming a larger share of the job market, it only makes sense to expect students to have a higher understanding of science/engineering (and fundamentally, math) than we previously did.
Sup
Servius_Fulvius
Profile Joined August 2009
United States947 Posts
July 29 2012 19:59 GMT
#559
On July 30 2012 03:57 docvoc wrote:
It should be taught as a simple transative theory, A does B, B does C, so A does C. It should be taught in that kind of build up method rather than the way it is done now in most poorly taught schools which is a haphazard account of some parts of math and skipping the parts that may require some extra thought.


What you're describing relates specifically to "sequential learners". These people learn best when there is a linear progression of the course material. Your appeal of A= B, B = C, so A = C is the logical progression best understood by "thinkers".

As I mentioned before, this means global learners, "feelers", "sensors", and "perceivers" are at a natural disadvantage. This can be overcome with a lot of hard work and individual effort, but it is a whole lot easier to reach for the C and never think of it again.

This thread seems to expect a lot out of teachers. I've been a guest science teacher for underpriviledged high school students and the job is overwhelmingly hard. You can be the best teacher in the world, but if your students don't care, no matter how good you are at motivating them, then there's truly nothing you, as the teacher, can do. Poor US performance in high school STEM fields is as much a reflectance apathetic high school students as ineffictive teaching.
Kyrillion
Profile Joined August 2011
Russian Federation748 Posts
July 29 2012 20:03 GMT
#560
On July 30 2012 04:51 nennx wrote:


i dunno iirc my high-school math teachers were all pretty bad except one, and this was doing AP classes and all where you'd think teachers would be able to teach better. when i retook calc 2 at community college (and when i did later math at uni), i realized how shitty my high school math teachers were.

you might be able to make the argument they were better than other high school teachers though, so i guess they "win" at being not the worst



Then I guess it's a country thing.
If you seek well, you shall find.
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