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Related: Editorials & Other Articles, Issue Forums, Alliance Forums, Region ForumsAbandoning Algebra Is Not the Answer
Nothing to add except that I'm stunned to learn that there are people out there that want to remove algebra as a requirement for completing your secondary education.
Evelyn Lamb (Scientific American) fires back with a rebuttal...
About the Author: Evelyn is an AAAS mass media fellow with Scientific American for the summer of 2012. Follow on Twitter @evelynjlamb.
In an opinion piece for the New York Times on Sunday, political science professor Andrew Hacker asks, Is Algebra Necessary? and answers, No. Its not just algebra: geometry and calculus are on the chopping block, too. Its not that he doesnt think math is important; he wants the traditional sequence to be replaced by a general quantitative skills class, and perhaps some statistics.
Quite a few people have responded to Hackers column already. I highly recommend these posts by Rob Knop, Daniel Willingham, and RiShawn Biddle.
There are so many problems with Hackers essay that its hard to know where to start. Hackers first main point is that math is difficult, and the poor grades that result prevent too many people from graduating high school or college. His second is that the math we learn is not the math we need in our jobs.
Math certainly is incomprehensible to many students, but from where I sit, poor teaching is often the reason. Math education is failing many of our students. Few pre-college math teachers majored or even minored in math, and until more teachers do, improvements will be hard to come by. Ironically, it seems that people who have mastered useless algebra and other higher math topics tend to get jobs that pay more than middle school math teachers earn. I have the utmost respect for people with math degrees who choose to teach in spite of the poor pay and discipline problems, but few people make that choice. Math education needs help, but Hackers suggestions throw out the baby with the bathwater.
http://blogs.scientificamerican.com/observations/2012/07/30/abandoning-algebra-is-not-the-answer/
jberryhill
(62,444 posts)pokerfan
(27,677 posts)الجبر al-jabr
gollygee
(22,336 posts)We should get rid of all that and go back to Roman numerals.
Lizzie Poppet
(10,164 posts)Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.
― Robert A. Heinlein
cthulu2016
(10,960 posts)I'll admit my life path hasn't called for quadratic equations, but the basics of algebra shape how I think about everything.
Identifying the unknown quantity and looking for clues in what you do know to calculate what you don't know.
That's symbolic thinking, not just abstruse math.
pokerfan
(27,677 posts)coalition_unwilling
(14,180 posts)'Algebra' (properly speaking). Think it is more appropriate to classify it under Euclidean Geometry.
pokerfan
(27,677 posts)or more specifically, some of the proofs can be...
http://en.wikipedia.org/wiki/Pythagorean_theorem#Algebraic_proofs
coalition_unwilling
(14,180 posts)Last edited Wed Aug 1, 2012, 05:13 PM - Edit history (1)
be taking a look at the Wiki entry in more detail later today.
Very cool stuff.
HillWilliam
(3,310 posts)Dear Math: I'm tired of looking for your X. Dude, it's time to forget about her and move on.
aikoaiko
(34,183 posts)Algebra I and II were freshmen and sophomore year, trig in junior year, and pre-calc in senior year. The smarter kids had algebra nailed gown in 8th grade and were in Calculus I or II in senior year.
Even though I wasn't fond of trig, I did get very good advice from my trig teacher.
One day he warned the class that all the teachers who told that there were no dumb questions had been lying to us and that we had been asking dumb questions. He advised that we ask more intelligent questions when we got to college. It had a big impact on me.
pokerfan
(27,677 posts)as I went into electrical engineering...
But asking secondary students to just learn algebra seems to be setting the bar fairly low already.
redgreenandblue
(2,088 posts)Also using the 'R' symbol for "real part'.
Is such notation common in electrical engineering? I would have used 'i' and 'Re'.
What does this equation describe in the context of your field?
Dr. Strange
(25,923 posts)Yes, they use j for the imaginary unit. It's just not right.
pokerfan
(27,677 posts)because we use i to represent current. Don't ask.
My expertise is in communications and that equation describes QAM, quadrature amplitude modulation. More generally, we use trig and imaginary exponents to describe phase relationships in time-varying signals.
redqueen
(115,103 posts)susanna
(5,231 posts)Dr. Strange
(25,923 posts)Fifty Shades of Calculus.
redqueen
(115,103 posts)Oh yeah, baby... tie me up and teach me.
Ha no that'd never work. Learning is a pleasure. Ooh I know, read Ayn Rand. Now that's torture.
mathematic
(1,440 posts)Let's just say the title was highly misleading.
The first result in the chapter about polynomial equations:
Theorem 5.1.
A real closed field has a unique ordering endowing it with the structure of an ordered field. Any automorphism of such a field is an order isomorphism. If R is real closed, then its subfield of elements which are algebraic over Q is real closed.
Like all good math theorems, this one is disguised as english. It was so much simpler in high school.
Lucky Luciano
(11,258 posts)Clever kid he was.
mathematic
(1,440 posts)Dr. Strange
(25,923 posts)Although, really, if you're going to do algebra (basic or not), you should be using Hungerford.
Lucky Luciano
(11,258 posts)It is best to read a book like Dummit and Foote in advance for all the intuition that Lang does not give based on his expectation of some mathematical maturity.
Been a while since I did any real algebra. I am much more wrapped up in stochastic processes and real time curve/surface fitting.
Dr. Strange
(25,923 posts)Welcome to Ignore!
I've yet to read Dummit and Foote, but I've heard good things about it.
mathematic
(1,440 posts)It's great. Tons of examples and exercises. Perfect for self-learning or skipping ahead (or catching up!). That and Munkres' Topology were the most useful math textbooks I had.
Lucky Luciano
(11,258 posts)HopeHoops
(47,675 posts)I double-majored in Mathematics and Philosophy and almost got a third degree in Physics. I had all of the requirements except one - "Electricity and Magnetism". I took the course, but the professor was incompetent. He gave us a 500 level text (an expensive one at that) and all he did was write formulas on the board. Those formulas were in the book, but the book clearly expected about six semesters of backup knowledge to have a fucking clue how to apply the formulas. I could do the math, but he was incapable of explaining the context.
He had an open door policy and I went in several times for help. Not surprisingly, all he did was go back over the formulas with no context. The first segment was on field theory. Our first test started out with a very confusing question (again, no context) and ended with "not necessarily a field".
The only guy who ever topped me in math tests was in the class. He got a 66 on the exam. I got like a 42. There were a few in the 30's and the others were in the teens. It was a tough call, but I decided to drop it and forgo the third degree for the sake of my GPA (3.83 in math, 3.79 or so overall, Magna Cum Laude). I'm still fucking pissed about that. But hey, he's probably dead by now so I need to calm down.
HopeHoops
(47,675 posts)CrispyQ
(36,517 posts)My total was $7.76 & I gave the young checker a ten. She entered the amount I gave her, the change showed as $2.24. I gave her a penny. "I don't know what to do with that," she said. I said, "Give me a quarter instead of 24 cents." "My drawer will be off if I do that," she replied & handed me 24 cents & my penny back. I just shook my head.
For years I believed that I was not smart enough to do anything more than simple math. One of the best confidence boosts I got was acing a college algebra class . Math is good for your brain.
pokerfan
(27,677 posts)It confuses the cashier and annoys everyone waiting behind you. Now, I just walk around with about twenty dollars in loose change in my pockets.
XemaSab
(60,212 posts)More like this...
HopeHoops
(47,675 posts)I was stuck in bed at the time and she was sitting on the floor. In about 15 minutes she had a solid grasp of the concept - not the technique mind you, but what first year calculus is all about.
And here we are in a country where dumbfucks believe that cutting taxes on the rich helps reduce the deficit.
The GOP wants people to be ignorant, bigoted, and bad in math. They get votes from such people. You can't fix stupid, but you can fix ignorance.
On Edit: DISCLAIMER: I have a degree in mathematics so I might be a little biased on this subject.
exboyfil
(17,865 posts)My soon to be 11th grade daughter is starting Calculus I at a Community College in the Fall. She did very well in Advanced Algebra/Trig in 10th grade, and I decided to bypass Precalculus in 11th grade (significant amount of overlap). She probably missed covering 25% of the material in Precalculus, and most of that has to do with the later Trig identities.
She took General Chemistry I this summer at a regional university and basically set the curve so I think she is ready for Calculus.
I agree with you that math understanding is part of a broad liberal arts education, and I could not imagine cutting Algebra any more than cutting "Hamlet". Already the non-quant liberal arts majors take too little math and science (only six quant hours for a B.A. which can be filled with courses like Math for Decision Making and Molecules and Life).
HopeHoops
(47,675 posts)I also refused to read "1984" in 11th grade on the grounds that it hadn't arrived yet. The teacher, to his credit, agreed to give me an alternative assignment on the promise that I'd read it in 1985. I bought a copy on 2 Jan '85 and read it then and there. As disturbing a reality as it was then, things are way worse now than Orwell could have ever imagined. "Animal Farm" keeps coming to mind when I see rMoney - "All animals are equal. Some are just more equal."
coalition_unwilling
(14,180 posts)lastlib
(23,287 posts)...I gave the cashier two more pennies, and told her to give me a quarter back. She replied, "uh, Peyton Manning doesn't work here."
RebelOne
(30,947 posts)I do not now understand how I passed it. After that, I went to a vocational high school and did not have to take any math courses. I have never had to use algebra in the business world.
nadinbrzezinski
(154,021 posts)I swear, not writing dystopia, but future history.
HereSince1628
(36,063 posts)However in his autobiography he also wrote that he wished he had learned the basic principles of math, for men thus endowed seem to have an extra sense.
For ecologists, there is powerful insight hiding in the dominant latent root of a community transition matrix. Matrix algebra was part of my high school Algebra course. Little did I know in the late 1960's that the algebra I was learning would, 30 years later allow me to evaluate the stability of sea-bird communities along the Russian White Sea.
Who is it that can look at a classroom and say, no one here will need algebra? Who is it that can look a society and say you are all to be Wal-mart drones, don't bother learning algebra?
Culture is the cumulative whole that supports civilization. Culture is what is shared from generation to generation. How is anyone so empowered as to look out upon a generation and say--your life has no need for the gifts of mathematics handed down from the Arabs and the Greeks? Who would reduce entire generations to slaves?
redqueen
(115,103 posts)I loved math after reading an old boyfriend's textbooks on those subjects. Before that it was just boring math.
JVS
(61,935 posts)HereSince1628
(36,063 posts)statisiticians, etc?
Not every kid will have a job later in life in which they make decisions on whether the retail community in their town can support another big box store. But some kid will grow up to have that job for Wal-mart, or Target rather than the job of a greeter. And those kids will use Algebra.
Moreover, mathematics training is training in how to think your way through problem-solving. Even if people don't apply binomial theorem in their daily life, they need to solve what are essentially quantitative problems with multiple variables.
Captains on crab boats in the Bering sea need to update their decisions about optimizing effort (and expense) and reward, the pattern of thought used in those decisions is Algebra.
pokerfan
(27,677 posts)"Graduation from high school should require only 9th grade skills."
burnsei sensei
(1,820 posts)even for non-scientists.
I'm not good at math. I have no trouble admitting it. But even the little I have, including the algebra & geometry, has helped me IMMENSELY.
These subjects are like Latin, they seem like a lot of polish with no use, but wait, then you grow up.
Even a little knowledge of these is very, very helpful!
Yavin4
(35,446 posts)How can you learn Microeconomics without Calculus? How can you learn Accounting? How can you learn programming?
Mathematics builds upon itself.
Lucky Luciano
(11,258 posts)Initech
(100,103 posts)coalition_unwilling
(14,180 posts)McGovern walked that back to 999%
I love McGovern, but that was and is a cringe-worthy moment in American political history, imho.
4th law of robotics
(6,801 posts)So if you say something like "X is trending downward in the last few decades" you will get entirely earnest and sincere responses of "well how can X be on the downswing if my cousin knows someone and that happened to them last year. Huh!?!?".
MineralMan
(146,331 posts)Algebra forms the basis for all sorts of problem-solving methods using numbers. I cannot imagine how I would get along without it. I've used it in almost everything I've done, from woodworking and cooking to tax preparation and computer programming. Perhaps this political science professor never uses it, although I'm sure he does without realizing that he does. That he does not consider it essential is no argument against its inclusion in the secondary curriculum.
If this is his position, then I can do little but consider him a moron for having such a moronic prejudice against mathematics.
XemaSab
(60,212 posts)Say you have 10,000 people in a town, and half of them are men, half of them are women, 70% of them are white, and 30% of them are black. Also, 70% of the white people are over 18 and are eligible to vote while 80% of the black people are over 18 and eligible to vote.
Can you win an election with just black people and half of the white women?
If not, how many of the white men do you need to recruit for your candidate?
coalition_unwilling
(14,180 posts)Yavin4
(35,446 posts)Or .5%.
Assuming that the 50/50 ratio of men to women is constant among the voting age population.
Patiod
(11,816 posts)I write for a living, and require an understanding of basic statistics to get through my day to day business life every single day.
But I almost flunked out of college because I could not learn calculus. I've had tutors, I've had many different teachers (granted, English was not a first language for most of them) and smart friends try to help me. But I can't wrap my head around imaginary numbers. I got through Calc I with the help of a dopey boyfriend from the swim team - the less detail we go into on that one, the better. After failing Calc II twice, I ended up taking a class with the football team which feature all true-and-false tests. The last chapter was on matrices, and I scored a 100% on that test, which raised my average above 50%. The class was graded on a curve, and anything over 50% got you a "D", so I passed and was able to graduate (with a much lower GPA than I would have had without advancement mathematics, but I graduated).
To this day, if I hear the phrase "dee why, dee ex" I start to twitch (and not in a good way) .
I understand learning algebra and the way of thinking it teaches, but I don't understand why people who don't need to calculate the area under a curve should be punished for being unable to learn calculus. There should be a way to graduate from college in non-STEM fields (even a bachelors in business) even if you don't have the mind that allows you to grasp imaginary numbers.
HereSince1628
(36,063 posts)mostly in the upper midwest...none of the schools I taught at required more than algebra for a BA.
I can report to you that the majority of schools in the midwest provide the route you wish for.
My time in higher ed more of less spanned the transition period of higher ed from educating people who would be part of an educated minority in their communities to providing comprehensive training to a majority of HS grads seeking job skills.
Most kids no longer see life away from their future jobs as something for which education will be valuable. IMO, that's a terrible shame, and it's ruining the fabric of our communities, which are left in the hands of 'experienced business men'.
Patiod
(11,816 posts)Penn State required two levels of calculus for a BS in Business, hence the angst. And as I mentioned, I use math, math-thinking skills, and a deep understanding of the principals of statistics constantly in my market research work, but haven't encountered a situation where I thought "damn, I wish I understood calculus". But then again, I leave the quant studies to the Quants.
As to your comment about "life away from jobs" -- my mom used to work at a big department store in PA, which sponsored a scholarship competition. We found out about it when I was a junior, and the essay question was "what is the purpose of a college education?"
I wrote an angry diatribe about college NOT being tech school, and that the purpose of a college education SHOULD BE to teach people to think and communicate clearly and to understand the world around them. I wrote that I was getting an excellent business education at Penn State, but was saddened that I had passed over a solid liberal arts education for what amounted to a tech school
I was selected as a finalist, and had to defend the essay in person before 3 educators. It hit me on our drive up to Allentown that if any of these was a Penn Stater or engineering dean, I was probably screwed. Turned out the judges were an English professor, a dean of liberal arts, and the dean of a small, private liberal arts college. Needless to say, I won the scholarship.
Which is a long way of saying I'm with you 100% on educating vs training.
Taverner
(55,476 posts)You have to learn that, as well as calculus
It's a pain, and will drive you mad, but learning it is essential if you want to do anything other than serve fries
Turbineguy
(37,367 posts)Algebra and calculus make figuring things out so much faster. How else can we compete with other countries who want to re-enter the Dark Ages?
kaiden
(1,314 posts)Just couldn't get it. Numbers had no personal relationships or stories for me. Of course, the math teachers were always ancient farm marms ... on the other hand, I was a whiz at music which, if you think about it -- is all fractions and counting.
Now I knit. I use math more than I ever did in my life. I sometimes think I'd like to take a college algebra course again because I think I could do it now. I'm more focused.
HereSince1628
(36,063 posts)The ancient Greeks argued that a person's mind (i.e. a male person's mind) wasn't ready for mathematics until the age of 30 or there abouts.
I was terrible at most mathematics in elementary and secondary school, mostly because I was disciplined...what didn't come quick and effortlessly didn't come. In grad school my interests couldn't be addressed without mathematics. My interests drove me into places my jr high school and high school teachers would very likely never have thought possible for me.
Doc_Technical
(3,527 posts)n/t
backscatter712
(26,355 posts)C'mon, algebra isn't that hard. As a person that's done software development for a living, I have to think in pure algebra at times, when the math isn't even more advanced - you want to get into programming computer graphics, say hello to your friends trigonometry and calculus!
I understand that math isn't for everyone, but letting kids graduate without basic algebra is too much.
Lucky Luciano
(11,258 posts)a lot of linear algebra with 4x4 matrices over the quaternion algebra. Always looked interesting, but never had the time to twiddle around with that.
backscatter712
(26,355 posts)You look in any GPU in any PC these days, and the hardware is there explicitly to accelerate matrix math with lots of trig.
These days, you don't have to crunch matrices by yourself - you use an API, usually OpenGL or Direct3D to put together a scene, position your lights and your camera, and render your graphics. The computer does all the math for you, though in order to understand how to get the computer to do the math for you, you've got to have at least a little understanding of the math.
backscatter712
(26,355 posts)Formal logic, truth tables, sets, combinations & permutations (may I add that this math in particular is why it can be very dangerous to play poker with a math geek...), language theory...
hughee99
(16,113 posts)Perhaps Hacker might want to take a refresher course in critical thinking.
yellowcanine
(35,701 posts)redqueen
(115,103 posts)is the question, "How can we fall even further behind the rest of the world, academically speaking?"
:WTF:
4th law of robotics
(6,801 posts)are too good at math.
Tone it down guys, who are you trying to impress?
Also they're way to literate and aware of history.
Aerows
(39,961 posts)Do you learn Physics without knowing algebra, geometry and calculus? You need it in Biology and Chemistry for certain calculations, too.
Math and science are intertwined. The problem isn't that algebra is too hard, the problem is that it isn't taught effectively. People don't know WHY they are learning algebra until they get to classes that actually need it, then it makes sense. Algebra made no sense to me until I took calculus and physics. There isn't sufficient emphasis on practical application in most algebra classes.
RC
(25,592 posts)Each problem is self contained. We need to start in Kindergarten with applied math. Math applied to the real world. There is no real reason why we cannot.
I used to teach a high school electronics course that was articulated into the local collage electronics course.
One day as I was explaining a complex looking problem on the white board, I noticed the room was lighting up. (I had my back to the class, it was that obvious.)
It turned out most of the class had had the same problem in algebra that morning and none of them had understood it. The reason? They were just given a math problems in isolation and had no idea how it might apply in any way to the real world. What did all those letters stand for anyway?
When I presented the same problem in my class, it was tied to instantaneous charge/discharge voltages of a capacitor. I also presented it as something impressive to wow their friends, as was actually easy, despite the way it looked, if a little tedious to work through.
After class, I called and talked to the algebra teacher and she told me she had to teach algebra the way she did. They would not let her teach it as applied algebra. She could see the problem too, but her hands were tied.
For an idea what was involved
http://www.insula.com.au/physics/1221/L10.html
I don't remember the actual formula, but this is similar.
pokerfan
(27,677 posts)It put math in context. I realize that mathematicians can appreciate math for its own sake, its own beauty, but for me, applications was where it was at.
The Khan Academy is over 3000 videos now and they're all free.
Aerows
(39,961 posts)They made sense. Hell, I used to do calculations in my head on how soon I'd get a place with acceleration involved as I drove.
I was kind of awful at straight up theoreticals, but when it comes to conceptuals, such as volume or acceleration, I love them.
Aerows
(39,961 posts)And it angers me that teachers can't actually *teach* this version. It would help students, and help teachers reach out to students.
Applied math would help people understand why they are doing it and encourage them to take it even further.
Why can we not encourage this?
I think we need more practical application, and less rote learning. Science has never been about rote learning, but more about just plain learning.
Tikki
(14,559 posts)mightily with it but still made it through...the only victory is that those classes are over.
Tikki
OneTenthofOnePercent
(6,268 posts)I mean, I'm an engineer. I use math all the time. I know all sorts of calculus, multi-order differentials, geometry, etc...
But when I get to use simple equations to solve a problem at work... it really puts a smile on my face. I see the answer, the real-world relationship is immediately evident and there is the moment of epiphany "Oh, now I see it!" It's almost like the simplicity inspires confidence in the answer. There's just something about seeing two or three variables and saying to myself, "OK, Let's find two or three simple relationships here..." - it's like that first sip of a milkshake on a 90 degree day.
When I use calculus or other differential equations to arrive at a solution, it's almost like I see the answer - but the answer is foreign to me. It's usually correct, the math indicates that much, but there is no connection or solace in the answer. It's just a number. It's a shortcut to an answer that I could have used algebra to solve... like taking the Express Way instead of the scenic route. Bleh.
It just puzzles me that math so simple can instill such a sense of pride and accomplishment in myself. It'd be like Derek Jeter getting excited about hitting a single in a recreational slow-pitch softball game. Weird.
Cairycat
(1,706 posts)are lousy teachers. They know the subject matter, but don't relate well to students who don't pick up algebra, calc and so forth, easily. This was my experience in high school, and my three kids experience in high school as well. Now, my kids and I aren't dopes - B, B+ grade averages, even with the math in. But I know from conversations at conferences that the math teachers just don't seem to have empathy or the ability to put themselves in the shoes of a student who doesn't readily "get it". That's the art of teaching and that's what was lacking from my kids' and my math class experiences.
Not every math teacher is a poor teacher. But with fewer teachers who have mastered the subject matter, and with more lucrative opportunities available to them, math teachers don't have to prove their teaching ability as much as an English teacher, for example. So, what we need to do is not only have math teachers, but good ones.
Fumesucker
(45,851 posts)Then she took it one last time and made an A in the class..
The difference? The first three times she had coaches for algebra teachers and the last time the non-coach teacher actually cared about teaching the subject..
Aerows
(39,961 posts)I'm pretty good at math, and failed algebra once because the person teaching it had no interest whatsoever in teaching it. I excelled in the next class, calculus, and physics.
My family was so mad at me when I failed algebra, but when everyone that was pretty much bright students also failed, we had a different teacher.
patrice
(47,992 posts)I even dislike Algebra intensely, but I get that it's like weight-lifting for your brain. Certain meta-processes are going to be weak if they don't get appropriate challenge. It isn't the content itself, always, that matters, but the processing modalities that it develops that are important.
Quantess
(27,630 posts)I thought they graduate you even if you can't quite make it through regular algebra, as long as you appear to keep trying.
I seem to remember a couple of classmates who couldn't/wouldn't make it through algebra.