Ive been debating with a friend of mine on the subject of mathematics as a required class. Id like to hear what you all have to say on the matter.

I have taken calc 1 2 3 + differential equations...and i personally feel that i am 99.99% likely to NEVER use any of this in a real life application. Really...the only people who need to know this sort of math are engineer types.
(i used to be a mech engr major is why i even took those)
So anyhow, my friend, who is not going to be in that major or even try it on for size, has to take tests that involve mathematics of a lower level, but still a sort of math that the vast majority of the population probably will never use in their daily lives.
So...what do you think - should they force such 'high' level subject matter upon all students? or should it stop at the level of math actually needed by the typical masses daily?

After algebra, you aren't likely to use more advanced math. Unless of course you are planning to go into a math centered career. (i.e. Various sciences, architecture, engineering, etc.)

<font color = lightgreen>Well, I wouldn't say that the truly "higher" branches of mathematics should be required, but most people misunderstand the true nature of learning mathematics: math teaches you how to solve problems; not just numeric problems, but any kind of problem.

On the other hand, I am more than a little biased since my training is in math. [img]graemlins/petard.gif[/img] </font>

Indeed, mathematics is not all about learning special techniques to solve problems, it's more about just getting handy in solving any problem. Maths also increase your overall insight.

while I may never use the cylinder of revolution, I nevertheless think basic calculus, along with the ability to find the area under a curve, should be taught to EVERYONE. This of course requires basic geomoetry and pre-calc/advanced mat courses. As for Diffy-Q and advance algebra, I feel that gets into the field speciality level, and need only be taught to math majors/mionr and physics majors/minors.

Let's face it, to understand electromagnetic physics and to even have a rudimentary knowledge of what quantum mechanics is all about, you definately need basic calc.

And, in today's world, I think a basic understanding of what quantum mechanics looks at (without specific knowledge/applicability of it) is a BASIC. C'mon, we need to create Whole Citizens, in the Athenian spirit, people who can speak, at least generally, to the issues. If you don't understand, at least at a basic level, why punching a wall infinitely many times will sooner or later result in going *through* the wall, you simply are not fit to carry on higher level discussions combining physics and philosophy.

<font color=gold>
I think that the only reason why this is even a subject, is the fact that kids don't want to learn stuff like (higher) math. Today it's all about teach me barely enough to make loads of money, I don't care about the rest. Man, what stories I could give you about my college buddies, you'd be surprised Holland still has a relatively constant flow of graduates.... :(

So force it: yeah! It hope the kids might even enjoy it for a bit.
</font>

Well as an Engineer I can say that Maths gets a lot nastier beyond where you stopped. I know I am never likely to use anything from my advanced numerical methods classes. If I find the need to wade hip deep in Jacobi polynomials again I will simply hire "friend mathematician" to do the work for me ;) .

I don't see the lower levels of mathematics as a skill - it is more a training in rational thinking and reasoning. It sets people up with the confidence to approach any of life's problems in a logical and rational manner.

<font color = lightgreen>No, Davros, you do it the really easy way: you buy Mathematica, program what you need, go to lunch, then come back to see the answer on your screen. [img]graemlins/laugh3.gif[/img]

I agree, most people don't use anything about algebra in their daily life, but if we use that argument then school becomes nothing more than a job training center. Who would want that?

I don't use higher math in my daily life (one of life's little ironies), but I do enjoy a little analytic geometry now and then, as well as some numerical anaylsis. I designed a kiln for my psychotic ex using a hyperbolic cosine curve as the outer structure (think Gateway Arch in St. Louis; no lateral stress forces); one of the few things for which she was thankful during our time together.</font>

Well I went and did some research on this Mathematica thing - nice looking package, and it would be great for repetitive high level calcs. For single ones though, it would take more time to program the darn thing from what I read then it would for most people to write out the 4 or 5 pages of A4 to solve from first principles.

Besides, my Uni lecturer told me that life was full of "friend mathematicians & friend statisticians" to make all these worries disappear [img]smile.gif[/img]

I guess you have to fail something so they keep making you take math.

Maths is probably the single most important subject IMO. It won't do you any harm to excercise your brain and learn these higher level topics. Besides, as people have said, basic calculus is very useful - you use it all the time, even if you don't think about it - whenever you talk about the rate of change of something, you are talking about basic calculus. And then if you do ever do anything like chemistry or electronics you're going to need all that maths. Even if you don't use it, you will have trained your brain to think logically and understand difficult concepts. I know it's not fun and it's hard but in the end you're better off for it. As 2Pac once said (and probably others too) "That which does not kill me, can only make me stronger" and this statement is very true.

I have remorse at not going on to higher math than I did. College in general actually. Then again, at school age, I wasn't half as interested in learning. By the time I realized what I was missing, I was too old and had too many time consuming responsibilities for serious college classes. Take heed all you young folks, having kids, your own house, and a full time job will likely be the end of your educational opportunities. There are only so many hours in the day and everything demands them.

Yes I agree with this totally [img]graemlins/thumbsup.gif[/img]

I really think that there is too much focus on grades and rewards and getting something material at the end of school that kids aren't appreciating learning for its own sake. So long as there are material rewards for something, the intrinsic value of that thing will be lost. And so you get most students bemoaning the fact that have to learn 'useless' information - so learning is not an end in itself. They need to appreciate the fact that by learning, they're gaining something so valuable, NOT that it might be useful for something in the future.

Most students misunderstand the point of school. It is not to provide all the information that you will need when you go out into the workforce and get a job and no more. Of course, it could not! - that's what universities, tafes, apprenitceships, job training, etc are for. It is about providing kids with an education to make them full, well-rounded, knowledgeable adults. When you think about it, most of what we learn is 'useless'. You will never *need* to know anything about literature, most science, history, art, music. A large proportion of adults could have been taught to read and write, add, subtract, multiply, divide, the basics of replacing values with symbols, then some 'practical skills' - how to cook a meal, change your oil, manage a budget, use a computer, and then you'd be done! Don't worry about any of that other stuff - you'll never actually *need* to know about what cells are, or who Shakespeare was, or how to figure out the length of the hypotenuse. You could leave at maybe 12. My great-grandfather actually left school at 11 and worked on a farm. No worries at all.

But you can't go out into the workforce at 12 - you don't have the maturity or the endurance or the cognitive capacity. So you go to school and they give you - essentially for free, of course your parents pay taxes, but *you* don't have to do anything but turn up and learn - information and knowledge and skills in a huge variety of subjects. I've never been a big fan of the whole 'be happy because others are worse off', as it leads to stagnation of progress (gee I wish this technology was bigger, faster, more efficient - but can't complain! at least I have running water), but I really think that since it's there, why complain? Why would anyone choose to be ignorant when they don't have to be? It's not being forced on you, they're giving it to you, and you don't have to do anything but accept it.

It's funny how the irrelevance of 'fun' subjects like art and music are forgiven ;)

I do think that schools and teachers need to do a better job showing students the relevance and utility of a lot of the curriculum that is taught. Evidence shows that subjects that kids believe are useful or will help them later in life are more enjoyed and attended more often. For example, the LOTE (languages other than english) program that is used in Australia is hugely popular - on a par with 'fun' subjects like home economics and art, and disproportionately for a 'academic' subject and compared to other language courses in other countries - because it is actively sold to students as being interesting, relevant, and useful in their careers. A lot of stuff that is taught can be really difficult to grasp the relevance of - maths is certainly one example, but also literature (why do we have to analyse this poem?), science, history, etc. Partly because students don't really know what the breadth of careers and jobs are out there! I know I had no clue, and yet we were expected to choose appropriate subjects for senior that would help us enter university courses for careers which we didn't know about.

Sorry that turned out so long [img]graemlins/blush.gif[/img] ;)

Cough cough chuckle ;) - excellent post Aelia, and it is a sad state of affairs that I should so shorten it to a simple half sentence. I am risking copping a thwack on the head with a willow stick, but Aelia and I have discussed GPA's (Grade Point Averages) on more than a few occasions, and hers is way better than mine was :D .

In short the biggest single problem is that kids aren't wise or experienced enough to realise what to take away from what they are taught and what to choose to learn. As has been said: that's the teacher's job to somehow convince them of what is worth taking away and not to give up when something seems too hard. I know I hated maths until I actually started to get quite good at it and then I liked it more. The only reason I tried to get into it was that I knew that even though I hated it, I needed it. Also makes me proud when I learn stuff that say, only 1% or 0.1% or less of the population knows. :D

[ 11-12-2003, 06:59 PM: Message edited by: Vaskez ]

Well I still think that Math SUCKS :D
Especially Algerbra (Man learning that was taking a walk in Hell)
Sometimes when I do math I get frustrated. Not because the problem is too hard it's because I will never use this kind of junk later in my life. Unless I am going to become an engineer or something. Which I won't I have the same thoughts on biolgy. And besides as the years past my memory of the useless stuff I learned would get all blurry and forget some of it.

[ 11-12-2003, 07:23 PM: Message edited by: Sythe ]

I forget who said this quote: "youth is wasted on the young". However, it is absolutely true. When you are going through school, you trudge through most of the subjects wondering what you will ever use any of it for. When you get older, you look back and wish you had applied yourself more in school, and took the time to retain a better portion of it.

I use math every day. This is the case even if I am not dealing with a single number. Every day, I come across the same old situations everyone else does, but regularly I get complimented on how much I can accomplish compared to other workers. The reason? I took higher level math classes. I couldn't tell you how to do an integration problem anymore, but I learned the lessons underneath the math. I learned how to break down the big, chaotic situation into the elements that are important for what needs to be done, then how to plan my course of action by setting up these elements in the way that allows me to grasp the problem as a whole much easier. Then, I come up with the best solution given the elements of the problem, and implement the solution. The simpler math classes gave me the basic knowledge of how to do that, and the more advanced classes grilled me on that sufficiently enough that I can do it quickly and without second-guessing myself. You may not use the math in your career, but think about how many times good planning and analytical thinking skills help you, both at work and at home.

I'm not sure who originally said it, but the first time I heard it was from King Picolo from the Dragonball series.

I once put the same question to a teacher of mine and his answer was "It expands the mind". I accepted that at the time but given further years of experience and thought I have come to the conclusion that it does not. Maths is simply memorization and application. It does nothing to broaden the mind...the memory yes but not the mind.

[ 11-12-2003, 09:13 PM: Message edited by: SpiritWarrior ]

Sythe - i hope you can see from the comments of people who've left school that it is pretty common for people to find that they actually did need some of that stuff they thought was a waste of time, and to wish to have those lost opportunites back again.

Spirit Warrior - unfortunately, your comments regarding "memorisation and application" are only too true, but only in as much as they represent poor teachers. or, to put it another way, ANY subject that relies on memorisation and application is bound to be dull and not actually encourage learning.

some of the earlier comments about how mathematics teaches logic and problem solving are spot on. the point is that the content of the material that's taught (eg a-squared equals b-squared plus c-squared) is only a small part of what you're learning. the best teachers know this, explain it to their students, and inspire them with stories and anecdotes and a personal affinity.

given my, and others, advice to sythe about taking advantage of learning opportunities, i'd recommend that you, spirit warrior, not let your teachers get in the way of your learning. in the long run, the only person that suffers is you.

on a more personal note, i've always felt the learning of maths and science would be better facilitated using personae from history to teach the evolution of thinking in a story-telling fashion. [img]smile.gif[/img]

Exactly. I had good teachers in that regard, and I left the math major behind once I started getting a bunch that were the opposite (actually, I had fallen out of love with math as a major before then (just wasn't the right path for me), but that was the last straw).

I remember hating word problems, because they never started you with the equation (you had to actually review the problem, and set up the problem based upon the situation; you were not "spoon fed" the equation). Now that I look back, I now know why teachers force fed you so many of them. Being able to look at all of the facts (many of which are irrelevent for what you are doing) and weed out the important facts for consideration is a valuable skill. All situations you run into in the real world are usually clogged up with facts and events that, if you boil the problem down, really have no bearing on the problem other than to confuse you.

Kind of like that movie Teachers. One of the subplots involves a guy escaping from an asylum, and posing as a teacher. The big thing is, he actually dresses up as the historical characters that he is talking in the history class, and goes full out into the role. However, as he is in role, he is interacting with the class, asking them questions and making statements in character about the important facts. The tragic part is that he is exposed and taken away; he turns out to be an outstanding teacher, because he gets everyone involved in his roleplaying, and as such they ended up learning and retaining that knowledge (classic scene: he is playing George Washington, and has all of the desks moved to the outer edges of the room. All of the chairs are in the center of the room, in the shape of a rowboat. He is standing up in the center of the chairs, while he has given paddles to each of the people in the class, who are sitting there rowing away (taken right from that old painting of Washington crossing the Delaware). The whole time, he is talking like George Washington, asking questions about the war and why they are crossing the river).

Here is a list of the types of math I use daily:

Algebra
Geometry
Trigonometry
Calculus
Statistics

My job is managing a group of accountants (statistics and algebra play major roles here). The rest of the math plays a part in my every day job when I am responsible for procuring a projected profit and loss statement for my department quarterly, based upon 50 years of sales data. Welcome to executive management, the last place I would have expected to find math of this level necessary.

i somewhat enjoy math more than other subjects (such as english) but still believe it is next to useless in the real world once you get past that level that isnt used by anyone but certain professions.

The method i learned math was prety much memorize formule A, reasons why to apply formula A, and then doing problems involving that formula till i worked out the various 'kinks' that they like to throw in to make it more difficult. This didnt teach me anything about analytical thinking or good planning; i learned these things in the real world (games!) i mean really, untill college every single class seems to be just memorization of a technique or information temporarily. Heck, a lot of college courses are like that. there are very very very few classes that focus on you thinking for yourself, coming up with your own answers, planning/analyzing situations etc.

Science courses in college *really* try hard to screw you up; most will not give you any problems even remotely like the ones you see on the homework. they are *real* challenges to solve since you are supposed to be able to by connecting the various techniques learned to solve other problems and using common sense. Really, physics based courses teach you to think (or fail you!); its too bad most other classes arent like this; course if they did id be willing to bet most people would fail since they dont generaly teach you to think earlier. I suppose if they taught this way from day 1 in kindergarden we would end up with a heck of a lot more thinking oriented people and much fewer memorizers.

that sounds awesome - thanks! something to rent for the weekend :D

You said it there. The kinks are like red herrings which cause many to peceive maths as difficult. Difficult is not the right word as the only time you cannot do maths is when you have not memorized the formula and become familiar with these kinks. There is nothing difficult about that - you either know it or you don't.

Hmmm... who uses math?

Programmers
Accountants
Engineers
Bankers
Lawyers
Doctors
Scientists
Managers
Carpenters
Stonemasons
Bricklayers
Special effects guys in movies
Artists
Consultants
Analysts
Pizza delivery guys
Inventors
Roller coaster designers
Rocket scientists
Rock stars
Authors

And the list goes on. Maybe a better question is who DOESN't use math. Any takers?

Some people may argue against some of these. I'll defend all of them, so long as you let me address any jobs you think don't use math... :D

I believe I agree with what's been said thus far -- you may not use all your math skills all the time, and some but rarely, but the more you have, the more you can handle everyday situations without a worry.

Majority of these professions incorporate basic calculations. This is something that is taught in schools yes but is actually part of our own instincts. Even animals can do these basic calculations. The rest of them, well...they use calculators to save on time [img]smile.gif[/img] .

Bungleau, I don't know if I missed a post somewhere, but I don't think anyone claimed there was a job that didn't use math. Only jobs that didn't uses higher maths. All occupations, and the vast majority of basic daily activities incorporate some level of basic math.

<font color = lightgreen>My question is "why haven't you broadened you mind yet?"

I don't know if you study martial arts, but if you do then you know that when you are first starting that all you are really doing is memorization: hold your hand/wrist this way when punching, keep your toes curled back when kicking, the sequence of moves in the basic kata, etc. As you progress you understand more of the true nature of the moves you are doing and they become instinctive and natural.
This same process occurs with mathematics (or any topic of study)--the basics like the soltution of the general quadratic equation must be memorized; only after you reach a certain point do you begin to understand what the solution really means and how to apply it more generally.

Memorization has its place in learning. The true key to learning and understanding is when you are able to apply what you have memorized to more general problems/situations. [img]graemlins/petard.gif[/img] </font>

I'm not familiar with american math courses, just what are these "kinks", an example perhaps? ;)

An interesting suggestion! [img]graemlins/thumbsup.gif[/img] . When I was in high school, I did two maths subjects, in one the teacher showed us how the formulae were derived and where they came from. In the other we were given the formulae and showed how to use them. The difference in interest was palpable even with that small change in teaching style!

Unfortunately, I think the problem isn't necessarily the teachers, but the whole mentality of school and maths in particular. Students don't WANT to know background or context - they just want the formula and its application. I think one of the most frustrating questions for teachers is 'is this going to be on the exam'? Otherwise they're not interested! I was talking with my supervisor the other day (a university lecturer), and she was discussing how frustrating it is that a lot of promotional and salary is tied up in student evaluations at the end of semester. And the only way to get really good evaluations is totally spoonfeeding them.

We have two types of math classes here at university, and the lack of interest in the theory one and the interest in the application one is likewise as the one Aelia Jusa talked about.

No actually it was the other way around ;) . LOL I didn't explain it very well. We were shown in both how to apply the formulae. But in one we were just presented with the formulae and off we'd go. In the other we were shown how it was derived and how it was developed. That provided context, and also helped in using it. The class where we were shown the derivation was much more attentive.

LOL at Davros and his GPA :D . I tell you, if I'd done engineering, I certainly wouldn't have been getting 1st class honours. I got a 4 for multivariate calculus and differential equations - and that was a 1st year subject! My only 4! :( ;)

We actually get one class where we only get the theory and provings of it, which everyone hates because it gets boring after 5 minuttes, and in the other one we just use the theory to resolve problems.

Davros whistles to himself - did someone mention that all the focus and way too much emphasis is placed on grades :D

PS : LOL - you got a 4 [img]smile.gif[/img] .

PPS : If it helps, I can mention I got one for Thermodynamics II - I don't know how it was a 4 - by all rights it should have been a 3 ;) .

I'm taking an Auditing class right now, and I hate it for that reason. It only talks about the broad theories; they never show how to apply it in a real-life situation. Just listening to him spout out "in this broad situation, you want to do one or more of these X things" gets old really quick. If he didn't give a quiz every single class period I would never go to class; I learn more from the book than I ever do from him. You know how much of this I'm going to retain? Probably nothing. Meanwhile, I'm taking a COBOL class where we are doing a bunch of programming projects; all of the projects are real-life situations, where you apply the stuff she is lecturing. You know how much of that I am going to retain? A whole bunch, and even though I can't stand the archaic language it holds my interest due to the fact that I am actually interacting with the subject matter and seeing how it actually works to resolve problems.

and perhaps the best reason to keep studying your maths: being able to get jokes like these!

-----------------------
The Top 10 reasons to become a statistician:

1. Deviation is considered normal
2. We feel complete and sufficient
3. We are 'mean' lovers
4. Statisticians do it discreetly and continuously
5. We are right 95% of the time
6. We can legally comment on someone's conjugate priors or posterior distribution
7. We may never be normal, but we are transformable
8. We never have to say we are certain
9. We are honestly significantly different
10. No one wants our job

------------------------

Three statisticians went bow hunting for deer. They spot a big buck and take aim. One shoots and his arrow flies off ten feet to the left. The second shoots, and his arrow veers ten feet to the right. The third statistician jumps up and down yelling, "We got him! We got him!"

kinks are the little tricks that make a problem appear to be harder (or make it actually harder)
its kinda hard to give an example...after all, unless youve worked a few problems without the kinks you wont recognize it as a kink.

usually, a kink will be something that makes a problem on its face appear unsolvable, and the resolution in general is applying a secondary formula to help simplify the equation and make it possible to solve.
For example, cos^2 + sin^2 = 1 could be the secondary equation used to simplify a difficult looking expression that involves sines and cosines.

prety much every level of math has these kinds of things added to try to trip you up; and the solution to the kink in general is related to the chapter your studying or has been taught in a previous chapter, or is just common sense.

<font color = lightgreen>My question is "why haven't you broadened you mind yet?"

I don't know if you study martial arts, but if you do then you know that when you are first starting that all you are really doing is memorization: hold your hand/wrist this way when punching, keep your toes curled back when kicking, the sequence of moves in the basic kata, etc. As you progress you understand more of the true nature of the moves you are doing and they become instinctive and natural.
This same process occurs with mathematics (or any topic of study)--the basics like the soltution of the general quadratic equation must be memorized; only after you reach a certain point do you begin to understand what the solution really means and how to apply it more generally.

Memorization has its place in learning. The true key to learning and understanding is when you are able to apply what you have memorized to more general problems/situations. [img]graemlins/petard.gif[/img] </font> </font>[/QUOTE]For martial arts this is true. There is a practical method in the application of what you memorize. This thread however argues whether higher mathematics has a practical application in everyday life. The answer, for most people is no.

<font color = lightgreen>I must unfortunately agree. Most people, it seems, are content to be able to balance their checkbook (assuming that they bother) or count change at the store.

Oh, well...I enjoy having an understanding of higher mathematics, even if others choose to miss out on the experience. [img]graemlins/petard.gif[/img] </font>