Is Algebra necessary?

[BlackShinobi]

I proof and edit papers for my friend in grad school, his writing skills are pretty terrible.
I had a debate with him a couple of months ago very similar to this thread when he said there was no need for anyone to know anything that they don’t use in everyday life. He wasn’t just talking about advanced math he was talking about common knowledge, history, current events, politics, advanced science etc his basic argument was that as long as you can look it up online you no longer need to know it. Did I mention that he works in a hospital?

[HoneyBBQGrundle]

What the fuck is wrong with this thread?
So a country that is already behind in math should further hinder students who want to go into fields that need math? You can’t let kids graduate high school at a math level that is multiple years behind that of kids from other major countries and hope they catch up by the end of college.

In our supposed golden age jobs were done locally, business owners were confined by local talent and people willing to relocate, which wasn’t too bad when America was on top of things; now employers have no need to deal with this type of limitation, if Americans aren’t smart enough to do the job it will be outsourced to someone who is.

So there are just hundreds of thousands of jobs waiting for Americans to get smart enough to do? That’s the reason for outsourcing? Or is it because most jobs are designed to require little intelligence and critical thinking and can thus be done anywhere on Earth, preferably by people who will do it for almost nothing in awful conditions?

And do you have any idea how much of an improvement it would be if American students **actually learned **geometry and algebra by the end of high school? You act as if it’s a step backwards! Some other nations aren’t just multiple years ahead of us, they’re infinitely far ahead because our students don’t even know arithmetic, let alone algebra, very well. Don’t ignore my parenthetical remark either; any student who wishes to learn more math should be able to, but this insane competition to teach every student algebra 1 by eight grade is only going to make things worse.

[tolore]

But if they know algebra by 8th grade people can actually start learning the coveted practical applications in highschool.

[Negative-Zer0]

I proof and edit papers for my friend in grad school, his writing skills are pretty terrible.
I had a debate with him a couple of months ago very similar to this thread when he said there was no need for anyone to know anything that they don’t use in everyday life. He wasn’t just talking about advanced math he was talking about common knowledge, history, current events, politics, advanced science etc his basic argument was that as long as you can look it up online you no longer need to know it. Did I mention that he works in a hospital?

Which one? Free malpractice suits.

[BlackShinobi]

So there are just hundreds of thousands of jobs waiting for Americans to get smart enough to do? That’s the reason for outsourcing? Or is it because most jobs are designed to require little intelligence and critical thinking and can thus be done anywhere on Earth, preferably by people who will do it for almost nothing in awful conditions?

2 Things

1. No, the jobs aren’t waiting, thats the problem, once they leave most aren’t coming back.
2. The two things you described are two different types f jobs and you can’t lump them together just because both are being outsourced. Outsourcing a call center and outsourcing engineering jobs aren’t the same thing.

And do you have any idea how much of an improvement it would be if American students **actually learned **geometry and algebra by the end of high school? You act as if it’s a step backwards! Some other nations aren’t just multiple years ahead of us, they’re infinitely far ahead because our students don’t even know arithmetic, let alone algebra, very well. Don’t ignore my parenthetical remark either; any student who wishes to learn more math should be able to, but this insane competition to teach every student algebra 1 by eight grade is only going to make things worse.

I am painfully aware of how many high school graduates don’t know algebra or geometry, but the few kids who pay attention do, because it was taught. Your suggestion of not teaching it doesn’t do much to hurt the kids who were going to graduate and still not know it anyway, it only hurts the kids who actually wanted to learn and use math. You can’t make basic functions optional so that only the kids who want to learn them have to because most high schoolers are too dumb to realize how big that decision is until 10 years later when they are stuck in a low paying dead end job.

[pedoviejo]

I can’t believe some of you are actually insisting that it should be up the kid or not if he learn Algebra. For fucks sake, what kid in today’s age, where the internet is only a tap away is going to want to do Math.

Face it, MTV won.

[factory9]

I’m just reading through this thread and

I

WANT

TO

CRY

I thought my school was pretty bad (not too terrible though), but we were always calling ourselves “the best high school in the nation”.

No fucking kidding.

It kind of hit me hard enough that our standards are too low, but seeing personal testimonies about it here is just…I can’t even think of a good word for it.

[HoneyBBQGrundle]

I am painfully aware of how many high school graduates don’t know algebra or geometry, but the few kids who pay attention do, because it was taught. Your suggestion of not teaching it…

What the? When did I ever suggest not teaching algebra and geometry? That’s the opposite of what I’ve been saying. Yeah, piling on extra subjects and topics for the majority of students would be a great idea if it had any hope of working now, but it doesn’t. The first priority should be to teach better, not more, although like I’ve said numerous times, successful teaching of algebra and geometry is actually more than what we’re doing now. Then once we figure that out we can push for teaching every high school student calculus, but first things first. I’m talking in general here. There will always be students taking advanced math in high school, but it’s not for everyone nor should we expect it to be.

Don’t underestimate what can be learned in four years of college with a solid foundation. What kind of math are the engineers and computer programmers in this thread using? Vector calculus, differential equations, linear algebra, discrete math at most? I don’t think it’ll take more than four years for someone with solid geometry, algebra, and hopefully trig to get to that level. And for those who struggled with those subjects, where was the difficulty? I bet calculus was hard because of weak algebra, right?

[alejandrosh]

Math is logic, and then you apply that logic to build systems/models to do what you need it to do. Then you use known logic to expand on that logic to build even more complex rules which you can use to explain more complex things like rate of change.

http://en.wikipedia.org/wiki/Mathematics

its something, but Math is built of logic.
of co

Godel’s incompleteness theorems proofs that no axiomatization of mathematics can proof every statement and still proof it’s own consistency. While logicism itself is not a dead philosophy in mathematics the statement “Math is logic” is far from being a fact.

[fishjie]

Are you talking about when russel tried to prove 1 + 1 = 2?

Sent from ur mom using my penisTalk

[Warrior_s_Dreams]

Are you talking about when russel tried to prove 1 + 1 = 2?

Sent from ur mom using my penisTalk

I think this is the basic idea he is referencing
http://n4bz.org/gsr11/gsr1102.htm

The success of epistemology, the philosophy of knowledge, as a branch of philosophy probably owes more to Bertrand Russell and Alfred North Whitehead’s Principia Mathematica than to any other single work. What we are going to discuss now is the first international epistemological school of philosophy, the Logical Positivists. Without the “Principia” and the impact it had on the philosophy of the turn of the century there would probably have been no successful logical Positivist school, and modern analytic philosophy might never have developed. ** What Russell and Whitehead attempted was a complete reduction of mathematics to logic. And the attempt was nearly successful. Whatever the shortcomings of the work, it, and Russell’s own manner of speaking, were undoubtedly part of the kindling that set off the Positivist movement. Russell and Whitehead’s Principia failed to accomplish what they attempted, the reduction of all mathematics to logic simply because it was impossible task. Godel later showed that no consistent set of logical relationships could be proven within the system itself. To do so would add another proposition outside the field which would then create another set which could not be proven without stepping outside that. ** Bronowski applied that to scientific knowledge. He explained it using the analogy of a paradox presented by the ancient Greek Epimenides. What Epimenides said was “All Cretans are liars.” But, since Epimenides himseelf was a Cretan, if the statement is true, then his making the statement makes it false. Therefore you can neither prove the statement to be true, nor show it to be false. The problem comes up whenever you try to prove the truth of any scientific statement. As Bronowski put it, whenever you use the phrase “the statement is” you are no longer using the language to describe things. You are in a different universe of discourse about statements about things and you can never get out of it. This fact, Bronowski said, was proven by Alfred Tarski in 1931.

Essentially, he took issue with pedoviejo saying that math is logic. I think he would have been satisfied if instead pedoviejo said “math uses logic”

[BullDancer]

The whole system is broken. I’ll have Ken Robinson say it for me:

I liked what I saw of the video…

But I kinda wanted to cut it off when he said ‘ADHD has increased with the introduction of standardized testing’:wtf:

Umm, prove it? How the fuck are these two things related?

I liked the video, but that aside about ADHD needs to be taken out lol…

Even though I personally believe this stuff can be changed, it would take more money… college/university level teaching is not like this, but it is private education, and done on the students own dime…

I’m not trying to go back to the days where no one but the middle class and rich have access to education… however superior it may be…

[Legendary_Hoamaru]

even if you are an engineer, no one does actual math. takes too long. it’s all done by computers and programs that can solve equations and do simulation. i’d say i only encountered only one equation i had to solve by pen and paper as an engineer.

People have to continue to create and improve on those programs…cutting back on math, and potentially killing more interest in that area, doesn’t really help with that. I guess other countries can pick up the slack though.

Once math is nerfed, what’s next? Will we continue nerfing subjects that many people may struggle with or not need as much of in the future? We should probably nerf (world) history some more then, since most people aren’t concerned with what happens/happened outside of their time/city/state/country anyway (even though you can learn a shit load from it).

It’s crazy…we’re talking about Algebra here, not Trig or Pre-Calc…

Yea technology and how incredibly fast we get information compared to before would have more to do with ADHD than standardized tests.

[pedoviejo]

ADHD is just kids not wanting to pay attention because there is to much to do, and to much to keep their attention. IDK why people act so suprised when men in white coats say there is a lot of kids with ADHD/ADD. There has to be a consequence to effects of over saturation of information in a child’s developing mind, and ADHD seems like the consequence.

[Matriarch]

Hold on for a damn second. You are asking psychologists, fucking psychologist? those are the last people you should ask whether or not Algebra is needed, and if it can be substituted by other classes.

Yeah, you know those people who specialize in human behavior, development, and learning. Obviously you know more than they do.

You insist that you can simply substitute “logic” class, but fail to realize that Arithmetic and Algebra are nothing more than pure applied logic. In a logic class, you can rationalize all the crap you want, in Math you cannot. Algebra or Arithmetic does not give a crap about what you think, its pure simple logic at its core.

Math isn’t true logic, but many of the skills it teaches are very similar to logic. It will never perfectly reflect anything in the real world because it’s an approximation. And that’s why there will always be engineering disasters.

For example, because all numbers are infinite it can’t really measure anything. It might get ‘close’, but it’s always an approximation. We have to round any number into a tiny chuck of what it really is because we can’t calculate infinite numbers, despite the fact all numbers are in fact infinite. If this concept is confusing to you, just remember that all numbers exist in an infinite number of decimal places in both directions.

In addition, any answer you get merely has a probability of being right. And even then that probability is only relevant if all variables have been properly accounted for and measured (which as was said before, is impossible).

Also, if math was true logic we wouldn’t have multiple possible solutions, and there are many situations where this happens.

Math has its limits, and I personally feel students partaking in rational logic and debate will be far more functional in the world than a bunch of math geniuses.

BTW, if you where to pair Math with a tangible subject, it would not be possible until the completion of Intermediate Algebra. Chemistry uses a lot of system of equations, quadratic functions, rate of change (Calculus), etc. Physics needs an even stronger foundation in Algebra and thorough understanding of Calculus as well. Computer programming needs the student to understand Intermediate Algebra.

Therefore teaching math through science is not possible.

Not possible is a pretty strong statement. Sure some sciences can use very complex equations, but aren’t they capable of also being used in conjunction with simpler functions?

Practicallity means nothing.

If practicality means nothing, why are you even talking about this at all?

Just because it isn’t practical for you does not give you the authority to dismiss a subject you find boring/useless/impracticable/repetitive.

Of course it doesn’t. I’m stating an opinion. If I was actually going to try and implement my views I’d conduct a study with a control group and compare their abilities. My own opinion of what is practical wouldn’t be an issue. However, advancing scientific knowledge doesn’t necessarily mean it’s going to impact public policy, as that is largely the job of politicians.

It’s been shown in a wide variety of studies that when a student can apply knowledge it increases retention. So I’d say practicality does matter. Or at the very least, it sure as hell helps me and seems to greatly assist the students I’ve had.

And just because you find no use for the answers that are achived by factoring a quadratic equation does not mean they are useless. Solving a basic Algebra function is a test of simple logic. There are no opinions or feeling that you have to worry about. Math doesn’t give a damn about that, all it cares is whether or not the answer is a logical solution to the given problem.

I just feel things could be more conducive to teach people. You seem to think that we’ve reached some math nirvana. I hate to break it to you, but the education system is failing at an alarming rate and I feel that many subjects, and especially math, needs to go back to the proverbial drawing board. Clearly what we’re doing now isn’t working out so well.

Fishjie addressed this point really well.

That’s an opinion.

Wouldn’t that tell you that there is a problem with the way teachers are trained? This is nothing but a red herring, and an appeal to people’s emotions because so many of them can relate easily. Please try again

lol, right.

Relevance means shit in the world of Academia, especially in the years leading up to their decision about what they want to do in life.

Did it ever occur to you that maybe, just maybe, this discounting of relevancy is a major fuck up?

If Algebra was not a requirement, then students would not be exposed to Chemistry, Physics, or Computer Programming. leading to an even bigger shortage of students in those fields.

On the contrary, if math was more closely paired with these subjects I feel more would be exposed and retention would be more succesful. However, this, like your statement, is an opinion. I’d love to have the opportunity to test this out someday.

Wrong, read above statements.

You sure like to call other people wrong. Especially considering this is ultimately about education and development, something that you don’t really seem qualified with at all. I’m not going to say my points are irrefutable facts, but you sure seem to think highly of yours when you flat out just tell people they’re wrong.

[Sleazoid]

Math has its limits, and I personally feel students partaking in rational logic and debate will be far more functional in the world than a bunch of math geniuses.

clearly you underestimate what math geniuses contribute to this world

this is the first and only time i am responding to matriarch because his posts are so naive i feel like i am being trolled

[Matriarch]

clearly you underestimate what math geniuses contribute to this world

this is the first and only time i am responding to matriarch because his posts are so naive i feel like i am being trolled

I feel like when people make statements without backing up their points I’m being trolled.

[Matriarch]

I see where Matriarch is coming from and I think her statements are being misinterpreted or exaggerated.

Thanks for noticing. They’ll argue against virtually anything I say. Sometimes I feel as if they want to skew my views into something bad just so they can argue with me.

I really don’t think your explanation would interest a 9th grader at all, as you still just kind of handwave and refer to “some phenomenon”. Why not just show them specific ones? Physics is a goldmine of interesting applications. I know you actually would do that, since you understand math, but it seems that’s all Matriarch is really saying. Give them interesting examples and applications and don’t divorce math from the sciences. Morris Kline would certainly agree.

Exactly.

I really hope a lot of people in this thread never become teachers. They seem to REALLY lack empathy and understanding, especially towards uneducated minds.

Actually, it seems like almost everyone posting does agree more than we think. I don’t see any contradiction between saying that math is important but overemphasized and taught poorly.

Again, thank you.

This fear mongering has just led to pedagogically questionable programs with no logical structure, way too many topics, and no motivation or application. But education departments, textbook publishers, and those making the latest technology fad for classroom use are loving it.

This. So much this. The amount of politics that are behind the structure of our education system is staggering.

[LoyalSol]

Hell as a chemist we don’t even explain our math till your junior year in college because it was derived from some really heavy math.

[Matriarch]

Wow, this Morris Kline guy is amazing. He’s written a ton of math books across most of the last century:

Introduction to Mathematics (co-author), Houghton Mifflin Co., 1937
The Theory of Electromagnetic Waves (editor), Inter-science Publishers, 1951
Mathematics in Western Culture, Oxford University Press,1953
Mathematics and the Physical World, T. Y. Crowell Co., 1959
Mathematics, A Cultural Approach, Addison-Wesley Publishing Co., 1962
Electromagnetic Theory and Geometrical Optics, John Wiley and Sons, 1965
Calculus, An intuitive and Physical Approach, John Wiley and Sons, 1967
Mathematics for Liberal Arts, Addison-Wesley Publishing Co., 1967
Mathematics in the Modern World (editor), W. H. Freeman and Co., 1968
Mathematical Thought From Ancient to Modern Times, Oxford University Press, 1972
Why Johnny Can’t Add: The Failure of the New Mathematics, St. Martin’s Press, 1973

Reading through his last book, ‘Why Johnny Can’t Add: The Failure of the New Mathematics’ I’ve found myself happy to see my views are strongly supported.

TLDR: This guy kicks ass and you should find out why.

The new mathematics presents the subject as self-sufficient. Presumably mathematics can feed on itself to grow and offers values when studied in and for itself.

Historically this approach to mathematics is certainly false. The significant concepts, operations, theorems, and even methods of proof were suggested by real situations and phenomena. Mathematics grew out of our experiences in the physical world. For example, as we have already noted in another connection, our method of adding fractions was adopted because the sum so obtained represents what results physically when fractional entities are put together. We could instead add the numerators and add the denominators so that 1/2 + 1/2 = 2/4, but this result does not apply when 1/2 of a pie is added to 1/2 of a pie. Likewise, the properties which mathematical operations possess are not dictated by extending the associative, commutative and distributive laws to the new elements. If matrix multiplication, to be useful, must be noncommutative we abandon commutativity, though we could define a commutative multiplication of matrices. Hence, extending the associative, commutative and distributive axioms to new classes of numbers can lead to useless mathematics. Geometry too arose out of the study of real figures existing in physical space and the desire to know the properties of these real figures and space itself.

The historical origins of mathematical concepts and processes need not of course be the pedagogical approach. However, a valid objection to generating new concepts and operations through older ones is the meaninglessness of what is introduced. For example, to introduce negative numbers some modern texts ask, What number added to 2 gives 0? They then introduce -2 as the requisite number. As some texts put it, -2 is the unique additive inverse to 2. But this introduction of -2 gives no more understanding than the statement, “Antimatter is that substance which added to matter produces a vacuum”, gives any understanding of antimatter.

By generating mathematics through mathematical questions and by extending to new domains laws or axioms that hold in previously established ones, mathematics is isolated from all other bodies of knowledge. It exists for its own sake and is presumably self-sufficient. It then appears that by chance the deductive structures so erected fit some physical phenomena and mathematics can be applied to real problems. However, this seemingly fortuitous value is not utilized. Mathematics in the modern mathematics texts is not applied to real problems. Some authors make minor concessions to applications in the seventh and eighth-grade material. Having eased their consciences they ignore applications in the higher grades.

The isolation from the real world is evident from the artificial problems found in the texts. Beyond the purely technical exercises which serve as drill and which certainly have no connection with the real world, one finds exercises whose character is illustrated by the following.

Dividing a certain numbber by two yields the same result as subtracting fifteen from three times the number. Find the number.
Harry earns three times as much per week as Tom does, while Dick earns eighty dollars a week more than Tom. If Dick and Harry have the same salary, how much does each of the three men earn?

Bill is twice as old as Mary. lf he is exactly ten years older than Mary was last year, how old are Bill and Mary?
The Red Cross knitted fifty sweaters in ten days. The Junior Red Cross assisted, contributing two dozen fewer than the senior organization. How many did the Junior Red Cross knit?

How large is an angle whose supplement contains 21 less than four times its complement?

Here is a science problem: According to the Law of Reflection: i = r. Given that i = (2n + 30)° and that r = (4***n*** - 10)°, find n. Not a word is included about the meaning of the Law of Reflection. It could refer to mental reflection.

The artificiality of the problems is obvious. Their inanity and pointlessness should make any sensible student writhe with mental pain. Of course, these artificial problems have been used in the traditional curriculum also.

One would have thought from the pronouncements of several curriculum groups that real applications would have been incorporated and even stressed at least in some of the new programs. For example, the Commission on Mathematics in its 1959 report, Program for College Preparatory Mathematics, justified the need for a new curriculum by pointing out that there were many new uses of mathematics in fields such as the exploration of space, nuclear science, the social sciences, psychology, business, and industry. Other groups echoed this thought. But no such applications have been included, to say nothing about the older applications to the physical sciences.

The neglect of applications has been noted and deplored even by some advocates of the new mathematics. Thus Professor Paul Rosenbloom, one of the active workers on the new curriculum, said in an article on applied mathematics (see the reference to Carrier in the bibliography), “In the writing teams for grades 9 to 11, some of us were disappointed that the people we thought have been advocating applications came up with writing stuff about open sentences and the like.” But the applications have not been supplied.

One reason is that the professors and teachers who formulated the new curricula do not know science. The professors were pure mathematicians and the courses taken by teachers were offered largely by these professors, so that the teachers too are ignorant of what mathematics can accomplish. Both groups therefore even prefer a treatment which is purely mathematical because it avoids presenting and explaining a few physical concepts and how to formulate physical problems mathematically.

The modernists apparently also want to keep their subject pure. They don’t wish to sully it; they desire to remove the dross of earth from which mathematics has risen. But as they wash the ore they keep the iron and lose the gold. A perfect command of the English language is useless if a man has nothing to say, and pure mathematics has little to say to young students. As Bertrand Russell put it, “Mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true.” Though Russell had in mind the logical structure of mathematics his statement describes what is being taught. The contents and spirit of the modern mathematics curricula may suit the mathematical scholar but the relation to the real world has been ignored.

Of course mathematics is not an isolated self-sufficient body of knowledge. It exists primarily to help man understand and master the physical world and, to some extent, the economic and social worlds. Mathematics serves ends and purposes. If the subject did not have these values it would not get any place at all in the school program. It is because mathematics is extraordinarily helpful that it is in great demand and receives so much emphasis today. These values should be reflected in the curriculum.

During the last few years many of the curriculum leaders acknowledged that they had neglected to point out the applications of mathematics. But their approach to remedying this deficiency is ludicrous. They call upon applied mathematicians of some large research laboratories or industrial organizations to supply applications. These men abstract. from genuine applications snippets of mathematics that are indeed involved in applications But the snippets reveal nothing of what is accomplished. They are like salt in a cake. The students are asked to eat the salt in the expectation that they will thereby enjoy the cake.

The isolation of mathematics was attacked by Dr. Alvin M. Weinberg in his article “But Is the Teacher Also a Citizen?” Dr. Weinberg, director of the Oak Ridge National Laboratory, charged that professors are so much absorbed in their own disciplines that they are neglecting to teach students useful knowledge, knowledge that can be applied to other fields, as mathematics is applied to physics, and knowledge that would make them more useful members of society. The new mathematics he terms “a puristic monster.”

To present mathematics as self-generating is not only a denial of history but conceals its vital connections with other branches of knowledge. From a pedagogical standpoint this approach is most unfortunate because it foregoes the opportunity and great need to give motivation and meaning to mathematics. Since the ideas of elementary mathematics did axise from physical and practical problems, these very problems or more modem equivalent ones could be used to motivate the study of mathematics. We have already pointed out that the gravest defect of the traditional curriculum is the lack of motivation. Instead of remedying this most serious defect the modern curriculum has aggravated it. One cannot motivate young people to learn mathematics with more mathematics. Students who are not interested in solving x + 3 = 4 will certainly not be interested in solving x + 4 = 3.

To isolate mathematics is also to rob it of meaning.